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https://journals.ametsoc.org/jamc/article/51/11/1980/13640/A-New-Approach-to-Modeling-Vehicle-Induced-Heat	[ "## Abstract\n\nThe distribution of vehicle-induced wind velocity in the transversal direction of roads is measured. A statistical analysis is also performed to find the vehicle stopping time and stopping position at traffic signals. These results are used to build a heat-balance model to predict the road surface temperature resulting from the thermal effects of vehicles. To validate the model, measured and calculated road surface temperatures for a free-running (single path) location and a traffic-signal location are compared. The contributions of meteorological and vehicle-induced heat fluxes to the road surface temperature are quantitatively analyzed. For the present traffic and meteorological conditions, the calculated and measured road surface temperatures were in agreement for both the free-running and traffic-signal locations. Furthermore, the thermal contribution of vehicles to the road surface temperature was found to be nonnegligible at both locations.\n\n## 1. Introduction\n\n### a. Background\n\nThese observations indicate that the thermal effects of vehicles on the road surface temperature are not negligible at traffic signals or when the volume of traffic is high.\n\n### b. Previous studies on thermal effects of vehicles and their modeling\n\nSubsequently, Fujimoto et al. (2008) developed a heat-transfer model by adding sensible heat due to the air movement by passing vehicles to the model built by Watanabe et al. These heat and air movements are hereafter referred to as the vehicle-induced sensible heat and vehicle-induced wind, respectively. We refer to this model as the vehicle road surface temperature (VRST) model. Fujimoto et al. (2008) also examined the thermal effects of vehicles on the road surface temperature by performing a numerical simulation using both an instantaneous and a time-averaged VRST model. The former calculates the time variation in vehicle-induced heat fluxes associated with the passage of vehicles (under pulselike conditions). The latter calculates the road surface temperature using time-averaged vehicle-induced heat fluxes. The following trends were observed: 1) the thermal effects of vehicles lowered the road surface temperature during the day and raised it at night and 2) the difference in the road surface temperatures of the two VRST models was small. Fujimoto et al. (2010) then conducted a simulation analysis of the road surface temperature at a traffic-signal location where vehicles repeatedly stop and start. The results showed that vehicles starting and stopping at traffic signals caused fluctuations in the road surface temperature, and that the temperature continuously fluctuated around 0°C (zero crossing).\n\nThus, the VRST model has made it possible to extract the properties of the road surface temperature overlooked in previous studies, by conducting experiments to identify heat transfer coefficients and variables relevant to traffic by field and indoor experiments using vehicles with tires. However, the VRST model has the following limitations:\n\n1. Spatial changes in the vehicle-induced wind velocity are not considered (currently, the wind velocity at the center of the vehicle is used as a representative value).\n\n2. At traffic-signal locations, it is assumed that vehicle stopping times and positions are fixed.\n\n3. The VRST model has not been satisfactorily validated. A quantitative comparison of the calculated and observed road surface temperatures has not yet been performed at a traffic signal.\n\n### c. Purpose of study\n\nThis study had the following major objectives:\n\n1. to derive a rational relationship between the vehicle speed and vehicle-induced wind velocity on the basis of the distribution of vehicle-induced wind velocity in the transversal direction of the road,\n\n2. to elucidate the properties of vehicle stopping time and position at traffic signals,\n\n3. to improve the vehicle-induced sensible heat and vehicle radiative heat using the results obtained from objectives 1 and 2, and\n\n4. to verify the reliability of the improved VRST model by comparing observed and calculated road surface temperatures at a free-running (single path) location and a traffic-signal location.\n\n## 2. VRST model\n\n### a. Assumptions\n\n• The VRST model is based on several assumptions. For vehicle operation, there are three assumptions:\n\n• 1) The target road surface is the center of the lane (i.e., at the vehicle’s centerline). At traffic-signal locations, the center of the vehicle that is stopped just before the stop line is the target road surface.\n\n• 2) All vehicles travel in the center of the lane and are the same size.\n\n• 3) The time interval between any two vehicles (the vehicle-passage time) is uniformly distributed on the basis of the hourly traffic volume.\n\n• For heat flux, there are two additional assumptions:\n\n• 4) Heat transfer in the transversal direction of the road is neglected.\n\n• 5) Additional wind velocity due to the interactions between natural wind and vehicle-induced wind is not considered. That is, there is no superposition of these two winds, and the sensible heat associated with a relatively high wind velocity is incorporated in the heat balance of the pavement surface layer [Eq. (1)].\n\n### b. Heat balance on pavement surface\n\nThe spikelike changes in heat flux in response to the passing of vehicles are expressed using unit step functions whose values are 0 or 1 [f(t) and g(t)], and the heat balance of the pavement surface layer is given by\n\nwhere ρp is the density of the pavement surface layer (kg m−3), cp is the specific heat of the pavement surface (kJ kg−1 K−1), Tp is the temperature of the pavement surface layer (°C), t is the time (s), Δzs is the thickness of the pavement surface layer (m), Cp is the pavement conductive heat flux (W m−2), Rlu is the road surface radiative heat flux (W m−2), S is the sensible heat flux (W m−2), L is the latent heat flux (W m−2), Rld is the sky radiative heat flux (W m−2), α is the albedo, Rs is the shortwave (insolation) heat flux (W m−2), Rυ is the vehicle radiative heat flux (W m−2), and Qnet is the net heat flux (W m−2). Here, S is given by the following formula based on assumption 5 in section 2a:\n\nwhere Vnw is the natural (background) wind velocity (m s−1), Sa is the natural wind sensible heat flux arising from Vnw (W m−2), Vw is the vehicle-induced wind velocity (m s−1), and Sυ is the vehicle-induced sensible heat flux arising from Vw (W m−2). The details of the heat flux in Eqs. (1) and (2) have been described by Fujimoto et al. (2008), and no further explanation is given here. In addition, in this analysis, the road surface is considered to be dry, and, therefore, L is eliminated. The unit step functions in Eq. (1) will be discussed in detail in the next section.\n\n### c. Modeling thermal effects of vehicles\n\nFigures 1a and 1b show the time variations in the heat fluxes due to the passing of vehicles at free-running and traffic-signal locations, respectively.\n\n#### 1) Free-running location\n\nIn Fig. 1a, t1 is the period during which the road surface is covered by a moving vehicle (the vehicle-passage time), and t2 is the subsequent period during which it is not covered (the non-vehicle-passage time). The quantities Cp, Rlu, and S act on the road surface at all times. During t1, Rυ acts on the road surface while Rld and Rs are zero. Conversely, during t2, Rld and (1 – α)Rs act on the road surface while Rυ is zero. The values of t1 and t2 are defined by the following equations:\n\nwhere Lυ is the vehicle length (m), Vυ is the vehicle speed (km h−1), and Fυ is the hourly traffic volume (vehicles per hour).\n\n#### 2) Traffic-signal location\n\nIn this section, we consider the time taken for a vehicle to stop at the designated point (just before the stop line) after the traffic signal turns red (i.e., the vehicle deceleration time), and the period for which the vehicle remains stationary until the next green signal (vehicle stop time). The stop time at the designated point, t4, is given by\n\nwhere tred is the red-signal period that includes the yellow-signal period, Pst (=t40/tred) is the stop-time ratio, and Psa (=Ns/Ns0) is the stopping-vehicle-number ratio. In addition, t40 is the stop time corresponding to the red-signal period (s), Ns0 is the frequency of the red signal per unit time, and Ns is the frequency of the red signal when a vehicle stops at the designated point in Ns0; t40 is the mean of the stop times measured at a traffic signal. As will be discussed in section 4b, Ns and t40 may be affected by the traffic volume.\n\nFinally, from Eq. (5), the vehicle deceleration time, t3 (h), is\n\nGiven the above thermal effects of vehicles, the unit step functions f(t) and g(t) in Eq. (1) are as listed in Table 1.\n\nTable 1.\n\nUnit step function for heat balance on road surface.", null, "## 3. Measurement and formulation of vehicle-induced wind velocity\n\n### a. Outline of experiment\n\nTo study the distribution of Vw in the transversal y direction of the road, we conducted an outdoor experiment using a typical passenger vehicle (4.97 m in length, 1.93 m in width, and 1.86 m in height). A thermal anemometer (manufactured by Kanomax) was set up at a height of 0.18 m above the road surface as shown in Fig. 2, and the y direction of Vw was measured by translating the driving of the vehicle in the y direction.\n\nThe vehicle’s centerline was considered to be y = 0. The vehicle’s speed was set to 30 km h−1.\n\n### b. Transversal distribution of vehicle-induced wind velocity\n\nFigure 3 shows the time variations in Vw for y* = 0, 0.4, 1.2, and 1.6, where y* is the normalized distance and y* = y/0.5Wυ (Wυ being the vehicle width). The value of Vw increases rapidly immediately after the vehicle passes (t = 0), reaching a peak at approximately 1 s and then decreasing gradually.\n\nThe maximum value of Vw, Vwmax (m s−1), occurred at the center of the vehicle (i.e., y* = 0) and decreased toward the roadside (as y* became larger). We have normalized Vwmax to express the y direction of Vw in a unified expression:\n\nwhere", null, "and", null, "= 0 indicates that Vwmax = Vnw.\n\nFigure 4 shows the relationship between", null, "and y. Here,", null, "decreases as y increases, and the relationship between", null, "and y* follows a Gaussian function. That is,\n\nFig. 4.\n\nRelationship between maximum normalized vehicle-induced wind velocity", null, "and normalized distance y.\n\nFig. 4.\n\nRelationship between maximum normalized vehicle-induced wind velocity", null, "and normalized distance y.\n\n### c. Representative velocity of vehicle-induced wind\n\nIn determining the representative value of Vw,", null, ", the following assumptions were made:\n\n1. Time variations in", null, "(=Vw0) depend on t but do not depend on y, as shown in Eq. (9), established by Fujimoto et al. (2008): where tmax is the time (s) for the wind velocity to reach Vwmax0 from the ambient velocity, t0 is the duration of the vehicle-induced wind, and a, b, and c are coefficients. For vehicle speeds Vυ (km h−1) ranging from 10 to 70 km h−1, these variables and coefficients are formulated in terms of Vυ as follows (see Fujimoto et al. 2008): In addition, t in Eq. (9) indicates the elapsed time (s) since the vehicle passage.\n2. The representative value of", null, ",", null, ", is the average of", null, "over half of the vehicle width (from y = 0 to 1.0, the shaded area in Fig. 4).\n\n3. Here,", null, "is the product of Vw0 and", null, ". On the basis of these assumptions and Eq. (8),", null, "is calculated as follows: where\n\n## 4. Micrometeorological observation, traffic-volume survey, and road surface temperature measurement on a national route\n\n### a. Outline of observation\n\nThis section describes the micrometeorological observations, the traffic-volume survey, and the road surface temperature measurements (hereinafter referred to as the observations). The observations were made at the free-running location and the traffic-signal location, and these are labeled case BS and case CS, respectively. Case BS was measured at National Route 8 (Echizen City, Fukui, Japan) from 0700 to 1700 LT 6 August 2008. Case CS was measured at an intersection on National Route 416 (Fukui City, Fukui) from 1700 to 0800 LT 29–30 December 2009. In both observations, the air temperature Ta and the relative humidity RHa (%) were measured using a thermohygrometer (HMP45, manufactured by Vaisala). The value of Vnw (m s−1) was measured using a vane anemometer (Weather Wizard III, manufactured by Davis). Both Rs and Rld were measured using a radiation balance meter (CNR1, manufactured by Kipp and Zonen). These values were recorded every minute by a datalogger. The road surface temperature Ts was measured using a radiation thermometer (ST 60, manufactured by Raytek) at points within and outside the vehicle’s passage. Furthermore, the spatial distribution of the road surface temperature was regularly recorded using a thermotracer (TH9100, manufactured by NEC). In case BS, Vυ was calculated by measuring the traveling time between two different positions. In case CS, the green-light period tgrn, tred, t4, and the vehicle-stopping positions near the traffic signal were recorded using a video camera.\n\n### b. Observation results\n\n#### 1) Free-running location\n\nThe weather on the day of observation was fine until 1200 LT, and then it became cloudy. The road surface was completely dry all day. The value of Ta increased from 23.1°C at 0700 LT to 34.8°C at 1230 LT, which was the maximum temperature during the observation period. Subsequently, Ta was around 30°C until 1700 LT. The value of RHa decreased from approximately 80% at 0700 LT to approximately 40% at 1000 LT. Subsequently, RHa varied within a range of 40%–60%, while Vnw was below 1 m s−1 until 1200 LT and reached a maximum of 2.4 m s−1 at 1300 LT. Subsequently, Vnw was in the range 0.5–2.0 m s−1, and Rs increased from the beginning of the observation to a maximum of 908 W m−2 at 1200 LT. It then oscillated because of the effect of the clouds. The value of Rld ranged from 420 to 475 W m−2, while Fυ ranged from 270 to 500 vehicles per hour with an average value of 376 vehicles per hour. In addition, Vυ varied between 37 and 42 km h−1 with an average value of 38 km h−1.\n\n#### 2) Traffic-signal location\n\nDuring the observation period, the weather was fine and the road surface was dry. The value of Ta decreased from 5.7°C at the beginning of the observation to 1.0°C at 0000 LT and then increased to around 2.0°C, while RHa was 60%–70% throughout the observation period. For most of the time, Vnw was less than 0.4 m s−1, and the maximum Vnw of 0.7 m s−1 was reached at 0100 LT. The value of Rld was approximately 300 W m−2, while Fυ decreased from approximately 360 vehicles per hour from 1700 to 1900 LT to a minimum of 51 vehicles per hour at 0400 LT. Throughout the observation period, tgrn was approximately 30 s, while tred was approximately 90 s from 1700 to 2000 LT and ranged from 60 to 75 s for the rest of the observation period. Furthermore, t4 was almost equal to tred at 1700 and 1800 LT but became shorter as Fυ decreased, reaching a minimum of 16 s at 0400 LT.\n\nFigures 7 and 8 show the relationship between Pst or Psa and Fυ. The value of Pst increased in proportion to the power function of Fυ and is given by\n\nThe relationship between Psa and Fυ is given by the same type of function as that for the relationship between Pst and Fυ:\n\n## 5. Comparison of measured and calculated results of road surface temperature\n\n### a. Boundary conditions and initial conditions\n\nA numerical analysis of the road surface temperature was performed for a pavement body of thickness 0.5 m and a subgrade of thickness 4.9 m. To obtain the initial temperatures in the pavement and subgrade, we entered weather data for August and December (from Fukui Local Meteorological Observatory) into the model and carried out a transient analysis until the vertical temperature profile varied with the thermal equilibrium state. The weather and traffic data obtained from the observations were used as the boundary conditions and were given by a linear interpolation of the data collected in time order. The temperature of the bottom boundary of the analysis area was fixed at 15°C in case BS and 10°C in case CS. In addition, on the basis of assumption 4 in section 2, it was considered that there was no heat transfer at the side boundary of the analysis area. Since Vυ could not be measured in case CS, it was fixed to 32 km h−1 with reference to the Fiscal 2005 Road Traffic Census. Table 2 lists the thermophysical property values given in a heat-transfer handbook (written by the Japan Society of Mechanical Engineers in 1993, pp. 238 and 375) for the pavement and ground used in the analysis.\n\nTable 2.\n\nThermophysical property values for pavement and ground.", null, "### b. Spatial distribution and time variation of road surface temperature\n\nThe model was validated by comparing the observed Ts with the calculated Ts. We also discuss the difference in Ts between the vehicle-passage and non-vehicle-passage areas.\n\n#### 1) Free-running location\n\nFigures 9a and 9b show the spatial distribution of Ts in case BS at 0635 and 1157 LT 6 August 2008. In Fig. 9a we see that Ts at all points (A–F) was almost uniform, in the range 27.2°–27.8°C, whether or not vehicles were passing. However, the values of Ts at points G, J, I, and L in the vehicle-passage area in Fig. 9b (50.6°–53.6°C) were approximately 1°–3°C lower than Ts at points H and K without vehicle passage (54.4°–54.8°C).\n\nFigure 10 shows the time variation in Ts in case BS. Hereinafter, the suffixes υ and n for Ts indicate the vehicle- and non-vehicle-passage areas, respectively, and the suffixes m and c indicate the measured and calculated values, respectively.\n\nThe initial Tsvm and Tsnm were both 30.6°C, and there was no difference between them: ΔTsm (=TsvmTsnm) = 0. Both Tsvm and Tsnm increased over time, but Tsnm became higher than Tsvm at around 0900 LT. Both values reached a maximum at 1200 LT (Tsnm = 55.5°C and Tsvm = 51.2°C) with ΔTsm = −4.3°C. Subsequently, both temperatures decreased gradually while maintaining ΔTsm ≈ −1.5°C. The average ΔTsm during the observation period", null, "was −2.0°C.\n\nThe calculated temperatures, Tsvc and Tsnc, reproduced the observed values in general, as shown in Fig. 10. However, when the vehicle-induced sensible heat Sυ is deleted from the heat balance in Eq. (1) [i.e., S = Sa in Eq. (1)], the calculated road surface temperature", null, "was slightly lower than Tsnc and became more inaccurate than Tsvc. As far as the present traffic and meteorological conditions are concerned, it is seen that Sυ cannot be disregarded from the calculation of the road surface temperature.\n\nDuring the observation period, the average difference between Tsvc and Tsnc, ΔTsc (=TsvcTsnc), was −2.0°C, which was in good agreement with", null, ".\n\n#### 2) Traffic-signal location\n\nFigures 11a and 11b indicate the spatial distribution of Ts in case CS at 2102 and 2103 LT 29 December 2009. It is evident from Fig. 11a that the vehicle-body temperature is higher than Ts except on the roof, side-view mirrors, and so on. The values of Ts at points M, N, and O in the non-vehicle-passage area were 7.2°, 8.6°, and 9.5°C, respectively. Here, Ts increased as the measurement point was closer to the vehicle-passage area. In Fig. 11a, the values of Ts at points P, S, R, and U in the vehicle-stopping area were 3°–4°C higher than Ts at points Q and T in the zone where vehicles did not stop or did not pass.\n\nAccording to Prusa et al. (2002), the width of the DM is 1.7–3.9 times that of a vehicle. Consequently, it is clear from Fig. 11 that the road surface temperature over the DM is not uniform. There is an obvious difference in the road surface temperature between the vehicle-passage area and the non-vehicle-passage area. The road surface temperature in the vehicle-passage area can be regarded as the representative surface temperature on the road that is subject to the vehicle-related heat.\n\nFigure 12 shows the time variations in Ts in case CS. At the beginning of the observation Tsvm and Tsnm were 10.9° and 8.2°C, respectively. Slight fluctuations in the temperature continued throughout the observation period. At the beginning of the observation, ΔTsm was 2.7°C, reaching 4.9°C at 2000 LT and then decreasing over time. After 0100 LT, ΔTsm was approximately 0.5°C and the value of", null, "was 1.9°C.\n\nWhile Tsnc varied gradually over time, Tsvc showed fluctuations with a small amplitude. The top-right graph in Fig. 12 shows an enlarged view of the time variation in Tsvc (solid line). It is evident that Tsvc decreased for tgrn (shown as A) and increased for tred (shown as B and C). The cause of the fluctuation will be discussed in detail in section 6a(2).\n\nThe amplitude for Tsvc, ΔTsvc, was approximately 0.3°C for Fυ = 360 vehicles per hour at 1700–1900 LT, approximately 0.2°C for Fυ = 225 vehicles per hour at 0000 LT, and lower than 0.1°C for Fυ = 51 vehicles per hour at 0400 LT. Increases in Fυ tended to increase ΔTsvc.\n\nThe values of Tsnc and Tsvc were in good agreement with the measured temperatures, Tsnm and Tsvm. In addition,", null, "was 1.6°C, which was 0.3°C lower than", null, ". This difference between", null, "and", null, "may depend on the temperature measurement position on the road surface and may be caused by an error in the initial temperature of the pavement body or subgrade.\n\n## 6. Discussion\n\n### a. Heat balance on road surface\n\n#### 1) Free-running location\n\nFigures 13a and 13b show the time variation in heat flux in the non-vehicle-passage area from 0700 to 1700 LT 6 August 2008 and in the vehicle-passage area for 20 s from 1105:30 to 1105:50 LT 8 August 2008 in case BS. The positive vertical (y) axis (top half) and the negative y axis (bottom half) indicate the heat gain and loss, respectively, of the road surface layer.\n\nWe first discuss the heat flux in the non-vehicle-passage area in Fig. 13a. The main causes of heat gain were (1 − α)Rs and Rld, while Rlu and Cp before 1300 LT and Rlu and S = Sa after 1300 LT were the main causes of heat loss. The values of Rlu and Cp were almost constant at approximately −573 and −339 W m−2.\n\nWe now consider the heat flux in the vehicle-passage area in Fig. 13b. For the t1 period (0.4 s), (1 − α)Rs and Rld were zero because of the vehicle’s shielding effect, but were 645 and 451 W m−2, respectively, for the t2 period (9.1 s). Instead, an Rυ of 547 W m−2 acted on the road surface for the t1 period. The maximum value of Sa was −136 W m−2 when Vnw > Vw, and the maximum value of Sυ reached −409 W m−2 (=3 times larger than Sa) when Vnw < Vw. It is seen that Sυ contributes to the decrease in the road surface temperature shown in Fig. 10 (i.e., Tsvc <", null, "), and that a running vehicle plays the role of a fan that cools the road surface.\n\n#### 2) Traffic-signal location\n\nFigures 14a and 14b show the time variations in the heat flux in the non-vehicle-passage area from 1700 to 0800 LT 29 December 2009 and in the vehicle-passage area for 3 min from 0000 LT 30 December 2009 in case CS.\n\nIn the non-vehicle-passage area in Fig. 14a, the heat loss by Rlu and heat gain by Rld were dominant, and S = Sa, Cp, and (1 – α)Rs were relatively small.\n\nWe now discuss the heat flux in the vehicle-passage area in Fig. 14b. The values for t1, t2, t3, and t4 during this period were 0.5, 4.1, 34.3, and 35.9 s, respectively. For the t2 and t3 periods, Rld was 319 W m−2 and reached zero for the t1 and t4 periods. For the t1 and t4 periods Rυ, was 369 W m−2. The maximum value of Sa was −16 W m−2 when Vnw > Vw, and Sυ reached a maximum value of −164 W m−2 when Vnw < Vw. Here, Cp increased as if to compensate for the negative Sυ for tgrn and reached a maximum value of 54 W m−2, but decreased for tred. The value of Rlu was −332 W m−2.\n\nThe average Qnet values for the t1, t2, t3, and t4 periods were 11, −72, 16, and 39 W m−2, respectively.\n\nThe minute fluctuations in Tsvc described in section 5b(2) are caused by abrupt changes in Qnet (from positive to negative and vice versa) associated with the thermal effects of the vehicle.\n\n### b. Evaluation of thermal effects of vehicles\n\nFigure 15 shows a schematic view of the heat balance in the vehicle-passage area (left) and that in the non-vehicle-passage area (right). The contribution of heat flux (Rld, Rlu, Rs, Cp, Rυ, and S) to ΔTsc was quantitatively evaluated as IP* by the following equation:\n\nwhere Pυ is the heat flux in the vehicle-passage area (Rld–υ, Rlu–υ, Rsυ, Cpυ, Rυυ, and Sυ) and Pn is the heat flux in the non-vehicle-passage area (Rld–n, Rlu–n, Rsn, Cpn, and Sn). Note that P* is the hourly heat flux calculated by the time integration of the subtraction of Pn from Pυ. Thus, IP* is the rate of each P* with regard to the sum of the absolute values of P. A positive IP increases ΔTsc and a negative IP* reduces ΔTsc.\n\nNext, let us consider IP* at the free-running and traffic-signal locations based on Figs. 16a and 16b, which show the time variations in IP* for cases BS and CS, respectively.\n\n#### 1) Free-running location\n\nAt the free-running location,", null, "and", null, "were always positive, but", null, "and", null, "were always negative because of the vehicle’s shielding effect. In addition, IS* was positive at 1300, 1400, and 1600 LT. This was because Tsvc < Tsnc and Vnw was large. Conversely,", null, "", null, "was positive until 1200 LT and negative at 1300, 1400, and 1600 LT. This was due to the increase in Cpn associated with a drop in Tsnc.\n\nThe values of", null, ",", null, ",", null, ",", null, ",", null, ", and", null, ", which are the means of IP* over the analysis period, were −0.15, 0.10, −0.14, 0.17, 0.18, and −0.16, respectively. At the free-running location, it was difficult to identify the dominant heat flux that affects ΔTsc.\n\n#### 2) Traffic-signal location\n\nAt the traffic-signal location,", null, "and", null, "played an important role in IP* and the contributions of", null, ", IS, and", null, "to Tsc were relatively small. However, the absolute values of", null, ", IS, and", null, "increased slightly toward 0400 LT, when Fυ reached its minimum. Because of this increase,", null, "and", null, "decreased, but they were approximately 3 times larger than the absolute values of", null, "or IS. At 0400 LT, the values of", null, ", IS, and", null, "were −0.07, 0.12, and −0.10, respectively.\n\nThe values of", null, ",", null, ",", null, ",", null, ",", null, ", and", null, "were −0.38, −0.04, 0.00, 0.04, −0.08, and 0.46, respectively. At the traffic-signal location, Rυ and Rld are the main heat fluxes that affect ΔTsc. However, the effects of Rlu, S, and Cp on ΔTsc are nonnegligible when Fυ becomes small.\n\n## 7. Conclusions\n\nWe measured the distribution of the vehicle-induced wind velocity in the transversal direction of roads, and used a video camera to statistically evaluate the characteristics of vehicle stopping time and position at traffic-signal locations. Using these results, we developed a heat-balance road surface temperature model that considers the thermal effects of vehicles. The measured road surface temperatures were compared with the temperatures calculated by the proposed model at a free-running (single path) location and a traffic-signal location. This clarified the thermal effects of vehicles on the road surface temperature.\n\nOur results are as follow:\n\n1. The maximum value of the vehicle-induced wind velocity appeared at the center of the vehicle and decreased toward the roadside, following a Gaussian distribution.\n\n2. The ratio of the vehicle-stopping period to the red-light period increased with an increase in traffic volume, following a power function. For example, this ratio was 0.25 for a traffic frequency of 50 vehicles per hour and 0.87 for 360 vehicles per hour.\n\n3. The ratio of the number of vehicles stopping at the designated point (just before the stop line) to the total number of stopping vehicles decreased from 0.90 to 0.50 following a power function, as the traffic volume decreased.\n\n4. For both the free-running and traffic-signal locations, the calculated road surface temperatures in the vehicle-passage area and the non-vehicle-passage area were in agreement with the observed values.\n\n5. The computation revealed the following two points: (i) the vehicle passage at the traffic-signal location causes fluctuations in road surface temperature with a small amplitude—the road surface temperature drops during the green-light period and increases during the red-light period, and (ii) the amplitude of the fluctuations in the road surface temperature tends to increase slightly as the traffic volume increases.\n\n6. At the free-running location, it was difficult to identify the dominant heat flux that influenced the difference in the road surface temperature between the vehicle-passage area and the non-vehicle-passage area. At the traffic-signal location, the vehicle relative heat flux and sky relative heat flux were the main contributors to this difference.\n\nAlthough traffic and weather conditions were limited, the proposed model enabled the calculation of the time variation in the road surface temperature in the vehicle-passage area and direct comparison with the observed one. Consequently, it was found that the thermal contribution of vehicles to road surface temperature cannot be neglected and is significantly different between the free-running location and the traffic-signal location. However, further studies will be needed to find the limitations of the parameterizations and formulation of the vehicle-related heat fluxes in this study through the change in vehicle size and vehicle speed.\n\n## Acknowledgments\n\nThis work was supported by KAKENHI (90456434).\n\n### APPENDIX\n\n#### List of Symbols\n\na, b, c Coefficients regarding Vw0\n\nCp Pavement conductive heat flux (W m−2)\n\ncp Specific heat of the pavement surface (kJ kg−1 K−1)\n\nFυ Hourly traffic volume (vehicles per hour)\n\nf(t), g(t) Unit step functions (0 or 1) to express the spikelike changes in heat flux in response to the passing of vehicles\n\nIP* Rate of each P* with regard to the sum of the absolute values of P", null, "Mean values of IP over the analysis period\n\nL Latent heat flux (W m−2)\n\nLυ Vehicle length (m)\n\nm, c Suffixes expressed as the measured and calculated values\n\nNs Frequency of the red signal when a vehicle stops at the designated point in Ns0\n\nNs0 Frequency of the red signal per unit time\n\nPsa Stopping-vehicle-number ratio (=Ns/Ns0)\n\nPst Stop-time ratio (=t40/tred)\n\nPn Heat flux in the non-vehicle-passage area (Rld–n, Rlu–n, Rsn, Cpn, and Sn)\n\nPυ Heat flux in the vehicle-passage area (Rld–υ, Rlu–υ, Rsυ, Cpυ, Rυυ, and Sυ)\n\nP* Hourly heat flux calculated by the time integration of the subtraction of Pn from Pυ\n\nQnet Net heat flux (W m−2)\n\nRld Sky radiative heat flux (W m−2)\n\nRs Shortwave (insolation) heat flux (W m−2)\n\nRυ Vehicle radiative heat flux (W m−2)\n\nRHa Relative humidity (%)\n\nS Sensible heat flux (W m−2)\n\nSa Natural wind sensible heat flux arising from Vnw (W m−2)\n\nSυ Vehicle-induced sensible heat flux arising from Vw (W m−2)\n\nTa Air temperature (°C)\n\nTp Temperature of the pavement surface layer (°C)", null, "Calculated road surface temperature without vehicle-induced sensible heat (°C)\n\nt Time (s)\n\nt0 Duration of the vehicle-induced wind (s)\n\nt1 Period during which the road surface is covered by a moving vehicle (the vehicle-passage time) (s)\n\nt2 Subsequent period during which it is not covered (the non-vehicle-passage time) (s)\n\nt3 Vehicle deceleration time (s)\n\nt4 Stop time at the designated point (s)\n\nt40 Stop time corresponding to the red-signal period (s)\n\ntgrn Green-light period (s)\n\ntmax Time for the wind velocity to reach Vwmax from the ambient velocity (s)\n\ntred Red-signal period (s)\n\nVnw Natural (background) wind velocity (m s−1)\n\nVυ Vehicle speed (km h−1)\n\nVw Vehicle-induced wind velocity (m s−1)", null, "Representative value of Vw (m s−1)\n\nVwmax Maximum value of Vw, (m s−1)\n\nVwmax0Vwmax at y* = 0 (m s−1)", null, "Normalized Vwmax", null, "Average of", null, "over half of the vehicle width\n\nVw0Vw at y* = 0 (m s−1)\n\nυ, n Suffixes expressed as the vehicle- and non-vehicle-passage areas\n\nWv Vehicle width (m)\n\ny Transversal direction of the road (m)\n\ny* Normalized distance\n\nα Albedo\n\nρp Density of the pavement surface layer (kg m−3)\n\nΔTsTsvTsn\n\nΔTsvc Amplitude for Tsvc\n\nΔzs Thickness of the pavement surface layer (m)", null, "The average ΔTs during the observation period\n\n## REFERENCES\n\nREFERENCES\nChapman\n,\nL.\n,\nJ. 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Road Weather Conf., Bingen, Germany, Standing International Road Weather Commission. [Available online at http://www.sirwec.org/Papers/bingen/6.pdf.]\nShao\n,\nJ.\n, and\nP. J.\nLister\n,\n1996\n:\nAn automated nowcasting model of road surface temperature and state for winter road maintenance\n.\nJ. Appl. Meteor.\n,\n35\n,\n1352\n1361\n.\nSurgue\n,\nJ. G.\n,\nJ. E.\nThornes\n, and\nR. D.\nOsborne\n,\n1983\n:\nThermal mapping of road surface temperatures\n.\nPhys. Technol.\n,\n13\n,\n212\n213\n.\nTakahashi\n,\nN.\n,\nR. A.\nTokunaga\n,\nM.\nAsano\n, and\nN.\nIshikawa\n,\n2006\n: Developing a method to predict road surface temperatures—Applying heat balance model considering traffic volume. Proc. 13th Standing Int. Road Weather Conf., Turin, Italy, Standing International Road Weather Commission, 58–66. [Available online at http://www.sirwec.org/Papers/torino/9.pdf.]\nWatanabe\n,\nH.\n,\nA.\nFujimoto\n, and\nT.\nFukuhara\n,\n2005\n: Modeling of heat supply to pavement from vehicle. 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https://physicsmax.com/resistors-parallel-7742	[ "# Resistors in parallel\n\nResistors in parallel\n\nResistors are said to be in parallel when they are placed side by side and their corresponding ends joined together (Fig. 35.6). The same potential difference will thus be applied to each, but they will share the main current in the circuit. We will suppose that the main current I divides into II, 12, and 13 through the resistors RI’ R2′ and R3 respectively and that the common potential difference across them is V. If R is the combined resistance we may write" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9600069,"math_prob":0.86746466,"size":485,"snap":"2020-10-2020-16","text_gpt3_token_len":109,"char_repetition_ratio":0.112266116,"word_repetition_ratio":0.0,"special_character_ratio":0.2185567,"punctuation_ratio":0.08421053,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9734824,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-29T09:14:38Z\",\"WARC-Record-ID\":\"<urn:uuid:124888a9-16c8-48ca-abcb-bdb99ba77af0>\",\"Content-Length\":\"47184\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:79b92d9a-5f7d-4e1e-a253-3bcc49f8de15>\",\"WARC-Concurrent-To\":\"<urn:uuid:4287f887-b180-4051-bb4d-52783ee3475d>\",\"WARC-IP-Address\":\"104.24.125.93\",\"WARC-Target-URI\":\"https://physicsmax.com/resistors-parallel-7742\",\"WARC-Payload-Digest\":\"sha1:IFO5FBEMWJMZNBMMF7F4OGSJTPHEXYGX\",\"WARC-Block-Digest\":\"sha1:MPRPCWIY4KRLJSGJM7NCR46CW33USEI3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875148850.96_warc_CC-MAIN-20200229083813-20200229113813-00558.warc.gz\"}"}
https://de2.slideshare.net/ZazzaNM/sxsw-2019-top-trends	[ "Successfully reported this slideshow.", null, "", null, "", null, "×\n1 of 219\n\nSXSW 2019 - Top Trends\n\n11\n\nShare\n\nA personal overview of the most interesting and relevant topics presented at SXSW 2019 in Austin\n\nFrom Artificial Intelligence to Healthcare through the power of algorithms and much more\n\nSee all\n\nSee all\n\nSXSW 2019 - Top Trends\n\n1. 1. S X S W 2 0 1 9 H I G H L I G H T S Matteo Sarzana digitalgonzo.it @zazzanm\n2. 2. Matteo Sarzana digitalgonzo.it @zazzanm W H A T I S S X S W ?\n3. 3. 2 . 1 4 7 S E S S I O N S - 4 . 9 6 7 S P E A K E R S Matteo Sarzana digitalgonzo.it @zazzanm\n4. 4. I M P A C T O F S X S W : 3 5 0 M I O \\$ Matteo Sarzana digitalgonzo.it @zazzanm\n5. 5. 7 5 . 0 9 8 A T T E N D E E S - 1 0 2 C O U N T R I E S Matteo Sarzana digitalgonzo.it @zazzanm\n6. 6. W H A T C A N W E L E A R N ? Matteo Sarzana digitalgonzo.it @zazzanm\n7. 7. N O O N E C A R E S A B O U T T E C H Matteo Sarzana digitalgonzo.it @zazzanm\n8. 8. T H E N E W R O L E O F T E C H Matteo Sarzana digitalgonzo.it @zazzanm\n9. 9. P E O P L E D O N ’ T G I V E A S H I T A B O U T T E C H Matteo Sarzana digitalgonzo.it @zazzanm\n10. 10. ( T H E Y C A R E A B O U T R E S U L T S ) Matteo Sarzana digitalgonzo.it @zazzanm\n11. 11. I T ’ S N O T T E C H U N T I L I T ’ S O N Y O U R P H O N E Matteo Sarzana digitalgonzo.it @zazzanm\n12. 12. C R E A T I O N O F A N E W E C O N O M Y Matteo Sarzana digitalgonzo.it @zazzanm\n13. 13. T E C H N O L O G Y D R I V E N Matteo Sarzana digitalgonzo.it @zazzanm\n14. 14. E Q U A L O P P O R T U N I T I E S Matteo Sarzana digitalgonzo.it @zazzanm\n15. 15. F R O M C O R P O R A T I O N T O C A R T V E N D O R S Matteo Sarzana digitalgonzo.it @zazzanm\n16. 16. C O S T = A C C E S S I B I L I T Y Matteo Sarzana digitalgonzo.it @zazzanm\n17. 17. A N Y O N E W H O O W N S A M O B I L E P H O N E Matteo Sarzana digitalgonzo.it @zazzanm\n18. 18. B U S I N E S S O R I E N T E D Matteo Sarzana digitalgonzo.it @zazzanm\n19. 19. W I T H S O C I A L R E S P O N S I B I L I T Y Matteo Sarzana digitalgonzo.it @zazzanm\n20. 20. U S E R C E N T R E D E X P E R I E N C E Matteo Sarzana digitalgonzo.it @zazzanm\n21. 21. N O T O N L Y O N L I N E Matteo Sarzana digitalgonzo.it @zazzanm\n22. 22. O N L I N E = O F F L I N E Matteo Sarzana digitalgonzo.it @zazzanm\n23. 23. F O R G E T Y O U R W A L L E T Matteo Sarzana digitalgonzo.it @zazzanm\n24. 24. A I F O R E V E R Y O N E Matteo Sarzana digitalgonzo.it @zazzanm\n25. 25. B E N E F I T P O O R > R I C H Matteo Sarzana digitalgonzo.it @zazzanm\n26. 26. P O W E R T O L O C A L B U S I N E S S E S Matteo Sarzana digitalgonzo.it @zazzanm\n27. 27. M A C H I N E E M P O W E R M E N T Matteo Sarzana digitalgonzo.it @zazzanm\n28. 28. A L G O R I T H M B A S E D D E S I G N Matteo Sarzana digitalgonzo.it @zazzanm\n29. 29. I N T E L L I G E N T C O L O R S C H E M E S Matteo Sarzana digitalgonzo.it @zazzanm\n30. 30. I N T E L L I G E N T C O P Y W R I T I N G Matteo Sarzana digitalgonzo.it @zazzanm\n31. 31. I N T E L L I G E N T D E S I G N C O M P O S I T I O N Matteo Sarzana digitalgonzo.it @zazzanm\n32. 32. 1 . 0 0 0 S C R E E N S - 1 I D E A Matteo Sarzana digitalgonzo.it @zazzanm\n33. 33. E N D L E S S P O S S I B I L I T I E S Matteo Sarzana digitalgonzo.it @zazzanm\n34. 34. B E S T O U T C O M E Matteo Sarzana digitalgonzo.it @zazzanm\n35. 35. W H Y M A T T E R S ? Matteo Sarzana digitalgonzo.it @zazzanm\n36. 36. A C C E S S T O P R O F E S S I O N A L T O O L S Matteo Sarzana digitalgonzo.it @zazzanm\n37. 37. P R E V I E W A N D T E S T Matteo Sarzana digitalgonzo.it @zazzanm\n38. 38. F R A C T I O N O F C O S T Matteo Sarzana digitalgonzo.it @zazzanm\n39. 39. E V E R Y T H I N G C A N B E A I T R A N S F O R M E D Matteo Sarzana digitalgonzo.it @zazzanm\n40. 40. L O G O Matteo Sarzana digitalgonzo.it @zazzanm\n41. 41. S T O R E D E S I G N Matteo Sarzana digitalgonzo.it @zazzanm\n42. 42. A D V E R T I S I N G Matteo Sarzana digitalgonzo.it @zazzanm\n43. 43. F R O M A R T I F I C I A L I N T E L L I G E N C E T O A R T I F I C I A L I N F L U E N C E Matteo Sarzana digitalgonzo.it @zazzanm\n44. 44. 1 5 % O F T W I T T E R A N D 6 0 M I O O F F A C E B O O K A R E F A K E Matteo Sarzana digitalgonzo.it @zazzanm\n45. 45. V I R T U A L P E R F O R M E R S Matteo Sarzana digitalgonzo.it @zazzanm\n46. 46. V I R T U A L I N F L U E N C E R S Matteo Sarzana digitalgonzo.it @zazzanm\n47. 47. I S I T R E A L L Y B A D ? Matteo Sarzana digitalgonzo.it @zazzanm\n48. 48. N O , B U T … Matteo Sarzana digitalgonzo.it @zazzanm\n49. 49. D O N ’ T H I D E A R T I F I C I A L I N G R E D I E N T S Matteo Sarzana digitalgonzo.it @zazzanm\n50. 50. W H O I S T H E A U T H O R ? Matteo Sarzana digitalgonzo.it @zazzanm\n51. 51. A W O R L D O F C O - C R E A T O R S Matteo Sarzana digitalgonzo.it @zazzanm\n52. 52. D A T A = C R E A T I O N T O O L S Matteo Sarzana digitalgonzo.it @zazzanm\n53. 53. M O R E D A T A = M O R E P O S S I B I L I T I E S Matteo Sarzana digitalgonzo.it @zazzanm\n54. 54. C O N T E X T I S K E Y Matteo Sarzana digitalgonzo.it @zazzanm\n55. 55. H O W H A S I T E V O L V E D Matteo Sarzana digitalgonzo.it @zazzanm\n56. 56. F R O M H U M A N S B E I N G C O M P U T E R S Matteo Sarzana digitalgonzo.it @zazzanm\n57. 57. T O H U M A N S B E I N G H U M A N S Matteo Sarzana digitalgonzo.it @zazzanm\n58. 58. H U M A N S A B I L I T I E S C A N B E M A T C H E D Matteo Sarzana digitalgonzo.it @zazzanm\n59. 59. D E F I N E T H E D E S I R E D O U T C O M E Matteo Sarzana digitalgonzo.it @zazzanm\n60. 60. C O - C R E A T E D C H A I R Matteo Sarzana digitalgonzo.it @zazzanm\n61. 61. A L P H A G O Matteo Sarzana digitalgonzo.it @zazzanm\n62. 62. R E T I N A S C A N F O R D I A B E T E S Matteo Sarzana digitalgonzo.it @zazzanm\n63. 63. D O T A + O P E N A I Matteo Sarzana digitalgonzo.it @zazzanm\n64. 64. L I P R E A D I N G Matteo Sarzana digitalgonzo.it @zazzanm\n65. 65. A N E W K I N D O F A R T I S A N S H I P Matteo Sarzana digitalgonzo.it @zazzanm\n66. 66. H U M A N + A I Matteo Sarzana digitalgonzo.it @zazzanm\n67. 67. C R E A T I V I T Y I S A L S O A A I T H I N G Matteo Sarzana digitalgonzo.it @zazzanm\n68. 68. W H A T W I L L “ N E V E R ” C H A N G E ? Matteo Sarzana digitalgonzo.it @zazzanm\n69. 69. J U D G E M E N T Matteo Sarzana digitalgonzo.it @zazzanm\n70. 70. T H E R O L E O F B R A N D S Matteo Sarzana digitalgonzo.it @zazzanm\n71. 71. I N N O V A T I O N E N V Y Matteo Sarzana digitalgonzo.it @zazzanm\n72. 72. B R A N D S A R E C O P Y I N G E A C H O T H E R Matteo Sarzana digitalgonzo.it @zazzanm\n73. 73. H A C K A T O N S ? Matteo Sarzana digitalgonzo.it @zazzanm\n74. 74. P R O B L E M S W H I C H C A N ’ T B E S O L V E D Matteo Sarzana digitalgonzo.it @zazzanm\n75. 75. P L A Y O F F E N C E Matteo Sarzana digitalgonzo.it @zazzanm\n76. 76. D O N O T C O P Y C A T Matteo Sarzana digitalgonzo.it @zazzanm\n77. 77. S O L V E T H E R I S K Matteo Sarzana digitalgonzo.it @zazzanm\n78. 78. C U R A T E Y O U R I D E A S Matteo Sarzana digitalgonzo.it @zazzanm\n79. 79. R E T R O T R U S T Matteo Sarzana digitalgonzo.it @zazzanm\n80. 80. L O O K B A C K A T T H I N G S W E T R U S T E D Matteo Sarzana digitalgonzo.it @zazzanm\n81. 81. D O W N G R A D I N G Matteo Sarzana digitalgonzo.it @zazzanm\n82. 82. C L A S S I C G A M E S A N D T O Y S Matteo Sarzana digitalgonzo.it @zazzanm\n83. 83. J O H N D E E R E X A M P L E Matteo Sarzana digitalgonzo.it @zazzanm\n84. 84. O L D A N D N E W C O L L A B O R A T I O N Matteo Sarzana digitalgonzo.it @zazzanm\n85. 85. B R A N D S A R E R E S P O N S I B L E F O R E X P E R I E N C E Matteo Sarzana digitalgonzo.it @zazzanm\n86. 86. G O B E Y O N D T E C H Matteo Sarzana digitalgonzo.it @zazzanm\n87. 87. F R O M S T O R Y T E L L I N G T O E X P E R I E N C E D E S I G N Matteo Sarzana digitalgonzo.it @zazzanm\n88. 88. D E A T H O F C O P Y A N D A R T Matteo Sarzana digitalgonzo.it @zazzanm\n89. 89. C R E A T E A N E W S T R U C T U R E Matteo Sarzana digitalgonzo.it @zazzanm\n90. 90. R E I N V E N T E V E R Y Q U A R T E R Matteo Sarzana digitalgonzo.it @zazzanm\n91. 91. D O N O T S E G M E N T B Y Z I P C O D E Matteo Sarzana digitalgonzo.it @zazzanm\n92. 92. D E S I G N F O R M I N O R I T I E S Matteo Sarzana digitalgonzo.it @zazzanm\n93. 93. D E S I G N F O R D I S A B I L I T I E S Matteo Sarzana digitalgonzo.it @zazzanm\n94. 94. D E S I G N F O R N E W G R O U P S Matteo Sarzana digitalgonzo.it @zazzanm\n95. 95. B A C K S T O R Y T E L L I N G Matteo Sarzana digitalgonzo.it @zazzanm\n96. 96. F A K E S T O R I E S Matteo Sarzana digitalgonzo.it @zazzanm\n97. 97. T H E N E W S T O R E E R A Matteo Sarzana digitalgonzo.it @zazzanm\n98. 98. S T O R E S A S F L A G S H I P S Matteo Sarzana digitalgonzo.it @zazzanm\n99. 99. B U Y I N G I S N O T T H E G O A L Matteo Sarzana digitalgonzo.it @zazzanm\n100. 100. E X P E R I E N C E I S Matteo Sarzana digitalgonzo.it @zazzanm\n101. 101. A N E W S T O R E E X P E R I E N C E Matteo Sarzana digitalgonzo.it @zazzanm\n102. 102. S T O R E S A S E X P E R I E N C E C E N T R E S Matteo Sarzana digitalgonzo.it @zazzanm\n103. 103. A R E S T O R E S D E A D ? Matteo Sarzana digitalgonzo.it @zazzanm\n104. 104. A M A Z O N A C C O U N T S F O R 1 , 9 8 % O F S A L E S G L O B A L L Y Matteo Sarzana digitalgonzo.it @zazzanm\n105. 105. A M A Z O N O F F L I N E Matteo Sarzana digitalgonzo.it @zazzanm\n106. 106. S T O R E S D E C R E A S E C O S T O F A C Q U I S I T I O N Matteo Sarzana digitalgonzo.it @zazzanm\n107. 107. C H A L L E N G E S Matteo Sarzana digitalgonzo.it @zazzanm\n108. 108. S T O C K M A R K E T V S S T O R E S Matteo Sarzana digitalgonzo.it @zazzanm\n109. 109. L O W M A R G I N S Matteo Sarzana digitalgonzo.it @zazzanm\n110. 110. D E M A N D I N G S T A F F Matteo Sarzana digitalgonzo.it @zazzanm\n111. 111. T E C H N O L O G Y S U C K S Matteo Sarzana digitalgonzo.it @zazzanm\n112. 112. T R I L L I O N S O F S K U S Matteo Sarzana digitalgonzo.it @zazzanm\n113. 113. C U S T O M E R S D O N ’ T C A R E A B O U T Y O U R P R O B L E M S Matteo Sarzana digitalgonzo.it @zazzanm\n114. 114. T H E Y C A R E A B O U T : Matteo Sarzana digitalgonzo.it @zazzanm\n115. 115. L O Y A L T Y Matteo Sarzana digitalgonzo.it @zazzanm\n116. 116. E V E R Y T H I N G P E R S O N A L I S E D Matteo Sarzana digitalgonzo.it @zazzanm\n117. 117. O F F L I N E = O N L I N E Matteo Sarzana digitalgonzo.it @zazzanm\n118. 118. O M N I C H A N N E L Matteo Sarzana digitalgonzo.it @zazzanm\n119. 119. B R A N D I S T H E U L T I M A T E R E S P O N S I B L E Matteo Sarzana digitalgonzo.it @zazzanm\n120. 120. P R O D U C T S Matteo Sarzana digitalgonzo.it @zazzanm\n121. 121. A V A I L A B I L I T Y I S K E Y Matteo Sarzana digitalgonzo.it @zazzanm\n122. 122. A I A N D S T O R E S ? Matteo Sarzana digitalgonzo.it @zazzanm\n123. 123. A I C A N ’ T P R E D I C T T R E N D S Matteo Sarzana digitalgonzo.it @zazzanm\n124. 124. I M P O S S I B L E B U R G E R Matteo Sarzana digitalgonzo.it @zazzanm\n125. 125. A I F O R P R O M O T I O N P L A N N I N G Matteo Sarzana digitalgonzo.it @zazzanm\n126. 126. A I F O R C U S T O M E R S E G M E N T A T I O N Matteo Sarzana digitalgonzo.it @zazzanm\n127. 127. A I F O R C R M Matteo Sarzana digitalgonzo.it @zazzanm\n128. 128. A I = E V E R Y T H I N G P E R S O N A L I S E D Matteo Sarzana digitalgonzo.it @zazzanm\n129. 129. G O A L ? Matteo Sarzana digitalgonzo.it @zazzanm\n130. 130. O F F L I N E = O N L I N E + E X P E R I E N C E Matteo Sarzana digitalgonzo.it @zazzanm\n131. 131. A G E O F R O B O T S ? Matteo Sarzana digitalgonzo.it @zazzanm\n132. 132. R O B O T S R E N A I S S A N C E Matteo Sarzana digitalgonzo.it @zazzanm\n133. 133. B U I L D E R S Matteo Sarzana digitalgonzo.it @zazzanm\n134. 134. E X P L O R E R S Matteo Sarzana digitalgonzo.it @zazzanm\n135. 135. O U R E Y E S A N D E A R S Matteo Sarzana digitalgonzo.it @zazzanm\n136. 136. B O E I N G E C H O V O Y A G E R Matteo Sarzana digitalgonzo.it @zazzanm\n137. 137. R O B O T H E S P I A N S Matteo Sarzana digitalgonzo.it @zazzanm\n138. 138. R O B O T H O T E L Matteo Sarzana digitalgonzo.it @zazzanm\n139. 139. B I N A 4 8 Matteo Sarzana digitalgonzo.it @zazzanm\n140. 140. E M B R A C E R O B O T S Matteo Sarzana digitalgonzo.it @zazzanm\n141. 141. R O B O T S W I L L N O T R E P L A C E H U M A N S Matteo Sarzana digitalgonzo.it @zazzanm\n142. 142. R O B O T S W I L L E M P O W E R H U M A N I T Y Matteo Sarzana digitalgonzo.it @zazzanm\n143. 143. H O W A R E M I L L E N N I A L S ? Matteo Sarzana digitalgonzo.it @zazzanm\n144. 144. H O W D O T H E Y L I V E ? Matteo Sarzana digitalgonzo.it @zazzanm\n145. 145. L O V E R E A L T I M E F E E D B A C K Matteo Sarzana digitalgonzo.it @zazzanm\n146. 146. S P E N D M O N E Y R E S P O N S I B L Y Matteo Sarzana digitalgonzo.it @zazzanm\n147. 147. D E B I T V S C R E D I T Matteo Sarzana digitalgonzo.it @zazzanm\n148. 148. V O C A L L Y L O Y A L Matteo Sarzana digitalgonzo.it @zazzanm\n149. 149. I F B R A N D S A R E S U P P O R T I N G T H E I R C H O I C E S Matteo Sarzana digitalgonzo.it @zazzanm\n150. 150. L I V E F O R A P U R P O S E Matteo Sarzana digitalgonzo.it @zazzanm\n151. 151. W A N T T O L E A V E A L E G A C Y Matteo Sarzana digitalgonzo.it @zazzanm\n152. 152. T R U S T I S E V E R Y T H I N G Matteo Sarzana digitalgonzo.it @zazzanm\n153. 153. M I L L E N N I A L S A S C H I L D S Matteo Sarzana digitalgonzo.it @zazzanm\n154. 154. “ D O N ’ T G E T I N A C A R W I T H A S T R A N G E R ” Matteo Sarzana digitalgonzo.it @zazzanm\n155. 155. “ D O N ’ T S L E E P I N A S T R A N G E R H O U S E ” Matteo Sarzana digitalgonzo.it @zazzanm\n156. 156. “ D O N ’ T B U Y F R O M S O M E O N E Y O U D O N ’ T K N O W ” Matteo Sarzana digitalgonzo.it @zazzanm\n157. 157. C A N Y O U I M A G E A W O R L D W I T H O U T U B E R , A I R B N B A N D A M A Z O N ? Matteo Sarzana digitalgonzo.it @zazzanm\n158. 158. M I L L E N N I A L S A N D S O C I A L M E D I A Matteo Sarzana digitalgonzo.it @zazzanm\n159. 159. L I F E B E C O M E S C U R A T E D Matteo Sarzana digitalgonzo.it @zazzanm\n160. 160. T H E B I G G E R T H E A U D I E N C E T H E M O R E C U R A T E D T H E L I F E Matteo Sarzana digitalgonzo.it @zazzanm\n161. 161. I G V S S T O R I E S V S P R I V A T E M E S S A G I N G Matteo Sarzana digitalgonzo.it @zazzanm\n162. 162. A N O P P O R T U N I T Y F O R B R A N D S Matteo Sarzana digitalgonzo.it @zazzanm\n163. 163. C R E A T E T R U S T W H E R E I T D I D N ’ T E X I S T B E F O R E Matteo Sarzana digitalgonzo.it @zazzanm\n164. 164. F R O M M I S B E H A V I O U R T O A W A R D S Matteo Sarzana digitalgonzo.it @zazzanm\n165. 165. S H A L L W E T A L K A B O U T G E N D E R ? Matteo Sarzana digitalgonzo.it @zazzanm\n166. 166. M U D D L E D M A S C U L I N I T Y Matteo Sarzana digitalgonzo.it @zazzanm\n167. 167. W H A T D O E S I T M E A N T O B E A M A N ? Matteo Sarzana digitalgonzo.it @zazzanm\n168. 168. N O T E V E R Y O N E I N T H E S A M E B O X Matteo Sarzana digitalgonzo.it @zazzanm\n169. 169. E N C O U R A G E T H E N O N C O N F O R M I N G Matteo Sarzana digitalgonzo.it @zazzanm\n170. 170. D I V E R S I T Y A N D I N C L U S I O N D O N O T S O L V E P R O B L E M S Matteo Sarzana digitalgonzo.it @zazzanm\n171. 171. C U L T U R E D O E S Matteo Sarzana digitalgonzo.it @zazzanm\n172. 172. L A W S E X I S T S B U T N E E D T O B E E N F O R C E D Matteo Sarzana digitalgonzo.it @zazzanm\n173. 173. Y O U D O N ’ T N E E D T O B E A N A C T I V I S T T O C H A N G E T H E W O R L D Matteo Sarzana digitalgonzo.it @zazzanm\n174. 174. C H A N G E H A P P E N S S L O W L Y Matteo Sarzana digitalgonzo.it @zazzanm\n175. 175. W O R D S C A N C H A N G E T H E W O R L D Matteo Sarzana digitalgonzo.it @zazzanm\n176. 176. U B E R E X A M P L E Matteo Sarzana digitalgonzo.it @zazzanm\n177. 177. W H A T N E X T ? Matteo Sarzana digitalgonzo.it @zazzanm\n178. 178. D E F I N E Y O U R P E R S O N A L B A T T L E Matteo Sarzana digitalgonzo.it @zazzanm\n179. 179. L I V E F O R I T Matteo Sarzana digitalgonzo.it @zazzanm\n180. 180. T A L K A B O U T I T Matteo Sarzana digitalgonzo.it @zazzanm\n181. 181. B E L I E V E I N I T Matteo Sarzana digitalgonzo.it @zazzanm\n182. 182. C O R P O R A T I O N S A S W E K N O W T H E M A R E D E A D Matteo Sarzana digitalgonzo.it @zazzanm\n183. 183. A C T U A L B U S I N E S S M O D E L S A R E W R O N G Matteo Sarzana digitalgonzo.it @zazzanm\n184. 184. P E R S O N A L D A T A + A I = I N F L U E N C E Matteo Sarzana digitalgonzo.it @zazzanm\n185. 185. H O S T I L E T O E V E R Y O N E Matteo Sarzana digitalgonzo.it @zazzanm\n186. 186. N O T O N L Y F A C E B O O K Matteo Sarzana digitalgonzo.it @zazzanm\n187. 187. E N C R Y P T I O N I S N O T T H E S O L U T I O N Matteo Sarzana digitalgonzo.it @zazzanm\n188. 188. M O N E Y I S K I L L I N G I D E A S Matteo Sarzana digitalgonzo.it @zazzanm\n189. 189. O C U L U S Matteo Sarzana digitalgonzo.it @zazzanm\n190. 190. C O M P E T I T I O N I S A L W A Y S G O O D Matteo Sarzana digitalgonzo.it @zazzanm\n191. 191. B I L L G A T E S Q U O T E Matteo Sarzana digitalgonzo.it @zazzanm\n192. 192. W H E R E I S T H E A N T I T R U S T ? Matteo Sarzana digitalgonzo.it @zazzanm\n193. 193. L E A R N F R O M T H E E U Matteo Sarzana digitalgonzo.it @zazzanm\n194. 194. C A L I F O R N I A L A W Matteo Sarzana digitalgonzo.it @zazzanm\n195. 195. R E C O V E R D A M A G E S F O R U N F A I R U S E O F P E R S O N A L D A T A Matteo Sarzana digitalgonzo.it @zazzanm\n196. 196. W H A T C A N W E D O ? Matteo Sarzana digitalgonzo.it @zazzanm\n197. 197. P R O M O T E S T A R T U P S N O T U S I N G D A T A A S B I Z M O D E L Matteo Sarzana digitalgonzo.it @zazzanm\n198. 198. N O T R A D E O F D A T A W I T H O U T E X P L I C I T C O N S E N T Matteo Sarzana digitalgonzo.it @zazzanm\n199. 199. F O C U S O N H U M A N T E C H Matteo Sarzana digitalgonzo.it @zazzanm\n200. 200. T E C H A S E M P O W E R M E N T Matteo Sarzana digitalgonzo.it @zazzanm\n201. 201. V A L U E O F P R I V A C Y Matteo Sarzana digitalgonzo.it @zazzanm\n202. 202. A P P L E Matteo Sarzana digitalgonzo.it @zazzanm\n203. 203. G O O D O R B A D Matteo Sarzana digitalgonzo.it @zazzanm\n204. 204. A I D R I V E R C A R S Matteo Sarzana digitalgonzo.it @zazzanm\n205. 205. H U M A N S A R E T R A I N E R S Matteo Sarzana digitalgonzo.it @zazzanm\n206. 206. M O U S E A N D P A R K I N S O N Matteo Sarzana digitalgonzo.it @zazzanm\n207. 207. N O R E G U L A T I O N = F E A R Matteo Sarzana digitalgonzo.it @zazzanm\n208. 208. T H E N E W C O R P . C O Matteo Sarzana digitalgonzo.it @zazzanm\n209. 209. E M P A T H Y A S B U S I N E S S T O O L Matteo Sarzana digitalgonzo.it @zazzanm\n210. 210. T E S C O S L O W L I N E S Matteo Sarzana digitalgonzo.it @zazzanm\n211. 211. H E R B A L E S S E N C E B O T T L E S Matteo Sarzana digitalgonzo.it @zazzanm\n212. 212. J O I N P A P A G R A N D K I D S O N D E M A N D Matteo Sarzana digitalgonzo.it @zazzanm\n213. 213. A N E W B U S I N E S S M O D E L Matteo Sarzana digitalgonzo.it @zazzanm\n214. 214. E M P A T H Y > M O N E Y Matteo Sarzana digitalgonzo.it @zazzanm\n215. 215. T E C H I S N O T T H E S O L U T I O N Matteo Sarzana digitalgonzo.it @zazzanm\n216. 216. H U M A N S A R E Matteo Sarzana digitalgonzo.it @zazzanm\n217. 217. “You can only understand people if you feel them in yourself.” John Steinbeck Matteo Sarzana digitalgonzo.it @zazzanm\n218. 218. T H A N K S ! Matteo Sarzana digitalgonzo.it @zazzanm\n219. 219. W A N T T O K N O W M O R E ? G E T I N T O U C H M A T T E O S A R Z A N A @ G M A I L . C O M - @ Z A Z Z A N M D I G I T A L G O N Z O . 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https://latex.org/forum/viewtopic.php?p=75481	[ "## LaTeX forum ⇒ General ⇒ musixtex \| Formatting for Notes Topic is solved\n\nLaTeX specific issues not fitting into one of the other forums of this category.\nLiben\nPosts: 5\nJoined: Tue Jan 01, 2013 6:10 pm\n\n###", null, "musixtex \| Formatting for Notes\n\nHello,\n\nI am doing some work in LaTeX and I am using package musixtex but I don't know how to write some commands. This is model of notes that I need to transfer into LaTeX.", null, "wanted.jpg (85.91 KiB) Viewed 10017 times\n\nbut there is five problems that I need to solve.\n\n1. For the \"align\" of notes I need same length.\n2. The number at the beginning of notes in red circle.\n3. The underscore behind the text in green circle.\n4. The symbol at the end of notes.\n5. In the yellow rectangle I don't know how can I put \"bar\" symbol between two notes.\n\nfor now I have this:", null, "have.jpg (110.7 KiB) Viewed 10017 times\n\nI found some solution but it doesn´t work so I hope that somebody could help me with this.\nbegin{music}\\generalsignature{2}\\def\\nbinstruments{1} \\debutextrait\\def\\writebarno{\\llap{\\tenbf\\the\\barno\\barnoadd}}%\\def\\raisebarno{2\\internote}%\\def\\shiftbarno{1.3\\Interligne}%\\NOtes\\zsong{Ra - }\\qu f\\enotes\\NOtes\\zsong{dosť}\\qu f\\enotes\\NOtes\\zsong{krás - }\\qu g\\enotes\\NOtes\\zsong{na }\\qu h\\enotes\\barre\\NOTes\\zsong{is - }\\qu h\\enotes\\NOTes\\zsong{kra }\\qu g\\enotes\\NOTes\\zsong{bo - }\\qu f\\enotes\\NOTes\\zsong{hov }\\qu e\\enotes\\barre\\NOtes\\zsong{E - }\\qu d\\enotes\\NOtes\\zsong{ly - }\\qu d\\enotes\\NOtes\\zsong{zej - }\\qu e\\enotes\\NOtes\\zsong{ská }\\qu f\\enotes\\barre\\NOTes\\zsong{dcé - }\\qu f\\enotes\\NOTes\\zsong{ra }\\cu e\\enotes\\NOTes\\zsong{ty, }\\hu e\\enotes\\barre\\NOtes\\zsong{o - }\\qu f\\enotes\\NOtes\\zsong{má - }\\qu f\\enotes\\NOtes\\zsong{me - }\\qu g\\enotes\\NOtes\\zsong{ní }\\qu h\\enotes\\finextrait.\\debutextrait...\n\nThank you.\nLast edited by cgnieder on Wed Jan 02, 2013 9:53 pm, edited 1 time in total.\n\nTags:\n\ncgnieder\nSite Moderator\nPosts: 1988\nJoined: Sat Apr 16, 2011 7:27 pm\nHi Liben,\n\nwelcome to the LaTeX-community!\n\n• bar numbers only at the beginning of a line can be achieved by calling \\systemnumbers\n• lyrics are best set up loading and using the musixlyr extension; my example below should give you an idea how to use it. You'll see that in the lyrics there are - and _ used to indicate where a word must be broken or be extended to the next note.\n• one should delete the aux files ending mx1 and mx2 before finally typesetting the whole piece and then run pdflatex, musixflx and pdflatex on the file again to get proper alignment.\n\n\\documentclass{article}\\usepackage[utf8]{inputenc}\\usepackage[T1]{fontenc}\\usepackage{musixtex}\\input{musixlyr} \\begin{document} \\begin{music}\\setlength\\parindent{0pt}%\\generalsignature{2}%\\renewcommand\\writebarno{\\textit{\\the\\barno}}%\\systemnumbers\\setlyrics{text}{% Ra-dosť krás-na isk-ra bo-hov E-ly-zej-ská dcé-ra ty, o-má-me-ní a_ sim-ple test to sho-ow}%\\assignlyrics1{text}%\\startpiece\\NOtes\\qu{ffgh}\\enotes\\barre\\NOTes\\qu{hgfe}\\enotes\\barre\\NOtes\\qu{ddef}\\enotes\\barre\\NOTes\\qup f\\cu e\\hu e\\enotes\\barre\\NOtes\\qu{ffgh}\\enotes\\barre\\NOtes\\qu{cdef}\\enotes\\barre\\NOtes\\qu{ghij}\\enotes\\endpiece\\end{music} \\end{document}", null, "musixtex.png (17.74 KiB) Viewed 10017 times\n\nRegards\nClemens\n------------------------------\nchemmacros · chemformula · leadsheets · xsim\n\nLiben\nPosts: 5\nJoined: Tue Jan 01, 2013 6:10 pm\nThank you for your help but I have another problem. I rewrote my old code into LaTeX by using MusiXTeX package but I don´t know how can I write some notes or text of song to separated note line. It means that these two lines", null, "15582906-note.jpg (25.24 KiB) Viewed 9971 times\n\nI need merge into one line.\n\nLast edited by localghost on Mon Jan 14, 2013 9:51 pm, edited 1 time in total.\nReason: Preferably no external links (see Board Rules). Attachments go onto the forum server where possible.\n\ncgnieder\nSite Moderator\nPosts: 1988\nJoined: Sat Apr 16, 2011 7:27 pm\nCan you please post a", null, "minimal working example, i.e., some code starting with \\documentclass and ending with \\end{document} that is compilable? Maybe you could simply post the code that you used to produce the image you posted?\n\nRegards\nClemens\n------------------------------\nchemmacros · chemformula · leadsheets · xsim\n\nLiben\nPosts: 5\nJoined: Tue Jan 01, 2013 6:10 pm\nsorry, I forgot\n\n\\documentclass{article}\\usepackage[utf8]{inputenc}\\usepackage[T1]{fontenc}\\usepackage{musixtex}\\input{musixlyr} \\begin{document} \\begin{music}\\setlength\\parindent{0pt}\\generalsignature{2}\\renewcommand\\writebarno{\\textit{\\the\\barno}}\\systemnumbers\\setlyrics{text}{ Ra-dosť krás-na isk-ra bo-hov E-ly-zej-ská dcé-ra ty, o-má-me-ní }\\assignlyrics1{text}\\startpiece\\NOtes\\qu{ffgh}\\enotes\\barre\\NOTes\\qu{hgfe}\\enotes\\barre\\NOtes\\qu{ddef}\\enotes\\barre\\NOTes\\qup f\\cu e\\hu e\\enotes\\barre\\NOtes\\qu{ffgh}\\enotes\\endpiece \\end{music} \\end{document}\n\ncgnieder\nSite Moderator\nPosts: 1988\nJoined: Sat Apr 16, 2011 7:27 pm\nYour image looks as if you haven't run »musixflx« on your document or have forgotten to delete the .mx1 and .mx2 files before doing so. Otherwise it would look like this:", null, "musix1.png (13.65 KiB) Viewed 9964 times\n\nYou may have observed that the texts starts with the second instead of with the first note. The reason for this is the endofline in\n\\setlyrics{text}{ Ra-dosť krás-na isk-ra bo-hov E-ly-zej-ská dcé-ra ty, o-má-me-ní }\n\nAdding % helpd here:\n\\setlyrics{text}{% Ra-dosť krás-na isk-ra bo-hov E-ly-zej-ská dcé-ra ty, o-má-me-ní }\n\nIf you want the whole piece in one line you can use \\startextract and \\endextract instead of \\startpiece and \\stoppiece. Beware that then the music line exceeds into the margin without warning. You might want to use the smallest music size and smaller margins then:\n\n\\documentclass{article}\\usepackage[utf8]{inputenc}\\usepackage[T1]{fontenc} % show page dimensions:\\usepackage{showframe} % reduce margins:\\usepackage[left=1in,right=1in]{geometry} \\usepackage{musixtex}\\input{musixlyr} \\begin{document} \\begin{music}\\setlength\\parindent{0pt}\\generalsignature{2}% use smallest available size:\\smallmusicsize\\renewcommand*\\writebarno{\\textit{\\the\\barno}}\\systemnumbers\\setlyrics{text}{% Ra-dosť krás-na isk-ra bo-hov E-ly-zej-ská dcé-ra ty, o-má-me-ní }\\assignlyrics1{text}\\startextract\\NOtes\\qu{ffgh}\\enotes\\barre\\NOTes\\qu{hgfe}\\enotes\\barre\\NOtes\\qu{ddef}\\enotes\\barre\\NOTes\\qup f\\cu e\\hu e\\enotes\\barre\\NOtes\\qu{ffgh}\\enotes\\endextract\\end{music} \\end{document}", null, "musix2.png (7.16 KiB) Viewed 9964 times\n\nRegards\nClemens\n------------------------------\nchemmacros · chemformula · leadsheets · xsim\n\nLiben\nPosts: 5\nJoined: Tue Jan 01, 2013 6:10 pm\nOK, I almost got it but there are some details I need to repair.", null, "15610005-notes.jpg (87.56 KiB) Viewed 9947 times\n\n1. Align doesn´t work.\n2. I don´t want number in first line (green circle).\n3. I need to put note symbol on the place where showing red circle. I found commands\n\\raisebox{0mm}{\\qu p}\nbut result is:", null, "15610101-notes-detail.jpg (8.75 KiB) Viewed 9947 times\n\none note is missing and note over note line have small line.\n4. Next problem is with \"\\Endpiece\" symbol. I don´t know why there are two black rectangle. In the picture yellow circle.\n\\documentclass{article}\\usepackage[utf8]{inputenc}\\usepackage[T1]{fontenc}\\usepackage{musixtex}\\usepackage[left=1in,right=1in]{geometry}\\input{musixlyr} \\begin{document} \\begin{music}\\setlength\\parindent{0pt}\\generalsignature{2}\\smallmusicsize\\def\\writebarno{\\llap{\\the\\barno\\barnoadd}}\\def\\raisebarno{2\\internote}\\def\\shiftbarno{1.3\\Interligne}\\systemnumbers\\setlyrics{text}{% Ra-dosť krás-na isk-ra bo-hov E-ly-zej-ská dcé-ra ty, o-má-me-ní žia-rou oh-ňov poď-me ktvo-jej svä-to-sti. Tvo-je ča-ro zno-vu_ zvia-že to čo_ mó-da de-lí dnes všet – kým ľu-ďom brat-mi ká-že stať sa tvo-jich krí-del let tvo-je ča-ro zno-vu_ zvia-že to čo_ mó-da de-lí dnes všet – kým ľu-ďom brat-mi ká-že stať sa tvo-jich krí-del let. }\\assignlyrics1{text}\\startbarno\\startextract\\NOTes\\raisebox{0mm}{\\qu p}\\enotes\\NOtes\\lcharnote{p}{100}\\qu{f}\\enotes\\NOTes\\qu{gh}\\enotes\\barre\\NOTes\\qu{hgfe}\\enotes\\barre\\NOtes\\qu{ddef}\\enotes\\barre\\NOTes\\qup f\\cu e\\hu e\\enotes\\barre\\NOtes\\qu{ffgh}\\enotes\\endextract\\vspace{5px} \\assignlyrics2{text}\\startbarno=6\\startextract\\NOtes\\qu{hgfe}\\enotes\\barre\\NOtes\\qu{ddef}\\enotes\\barre\\NOTes\\qup e\\cu d\\hu d\\enotes\\barre\\NOtes\\uptext{REF.:}\\qu{e}\\enotes\\NOtes\\qu{efd}\\enotes\\barre\\NOtes\\qu{e}\\enotes\\Notes\\Dqbu fg\\en\\NOtes\\qu{fd}\\enotes\\endextract\\vspace{5px} \\assignlyrics3{text}\\startbarno=11\\startextract\\NOtes\\qu{e}\\enotes\\Notes\\Dqbu fg\\en\\NOtes\\qu{fe}\\enotes\\barre\\NOTes\\qu{dea}\\enotes\\NOTes\\isslurd0e\\qu f\\enotes\\barre\\NOTes\\tsslur0e\\qu f\\enotes\\NOTes\\qu {fgh}\\enotes\\barre\\NOtes\\qu{hgfe}\\enotes\\barre\\NOtes\\qu{ddef}\\enotes\\endextract\\vspace{5px} \\assignlyrics4{text}\\startbarno=16\\startextract\\NOTes\\qup e\\cu d\\hu d\\enotes\\barre\\NOtes\\uptext{REF.:}\\qu{e}\\enotes\\NOtes\\qu{efd}\\enotes\\barre\\NOtes\\qu{e}\\enotes\\Notes\\Dqbu fg\\en\\NOtes\\qu{fd}\\enotes\\barre\\NOtes\\qu{e}\\enotes\\Notes\\Dqbu fg\\en\\NOtes\\qu{fe}\\enotes\\endextract\\vspace{5px} \\assignlyrics5{text}\\startbarno=20\\startextract\\NOTes\\qu{dea}\\enotes\\NOTes\\isslurd0e\\qu f\\enotes\\barre\\NOTes\\tsslur0e\\qu f\\enotes\\NOTes\\qu {fgh}\\enotes\\barre\\NOtes\\qu{hgfe}\\enotes\\barre\\NOtes\\qu{ddef}\\enotes\\barre\\NOTes\\qup e\\cu d\\hu d\\en\\Endpiece\\endextract \\end{music} \\end{document}\nLast edited by localghost on Tue Jan 15, 2013 6:59 pm, edited 1 time in total.\nReason: Preferably no external links (see Board Rules). Attachments go onto the forum server where possible.\n\ncgnieder\nSite Moderator\nPosts: 1988\nJoined: Sat Apr 16, 2011 7:27 pm\nOk, let's make this a little bit like a tutorial, just because I'm in the mood to.", null, "First of all: as I understand it you're trying to typeset a whole piece and not a series of extracts. For this case \\startextract and \\endextract are the wrong choice. The whole piece should be placed inside \\startpiece and \\endpiece (or \\stoppiece or the uppercase variants \\Endpiece or \\Stoppiece for the double bar that terminates a piece). (Using more that one of the ending commands will double the bar lines which is what causes your problem at the end of the piece.) The breaking into lines should be left to TeX or more precisely the program musixflx. Most of your problems will be solved following this rationale.\n\nCreating a piece normally has the following routine. Suppose your main file is called mycoolmusic.tex. Now, after typing the piece you run pdflatex mycoolmusic as you would normally do. Additional to the usual mycoolmusic.aux and mycoolmusic.log files a file named mycoolmusic.mx1 is created. This file serves as input for musixflx. So you now have to run musixflx mycoolmusic. This will create an additional file named mycoolmusic.mx2. This serves as help file for the next latex run to get the right alignment and spacing. So you need to run pdflatex mycoolmusic another time.\n\nIf you now see that you have to change details of the piece you have go through this whole routine again. In order to get it right you should delete both mycoolmusic.mx1 and mycoolmusic.mx2 before doing so or you might observe strange displacements and the like.\n\nNow, just like with LaTeX and normal text one sometimes has to help musixflx to get the line breaking right. Every \\bar (\\barre is an alias) is considered as potential break point. If you want to prohibit this for a certain \\bar you can use \\xbar instead. You can also insert a potential break point without creating a bar line with \\zbar. If you want to force a line break you can use \\alaligne (as equivalent to \\bar) or \\zalaligne (as equivalent to \\zbar).\n\nThe next problem: I guess you want to insert some tempo information above the first bar. As you have noticed \\qu{<pitch>} won't help here. Raising it with a box will at best lead to strange effects. Specifically \\qu{p} creates a quarter note with a stem pointing up at pitch p. Pitch p corresponds to b'' which is exactly what you're getting. I'll present a better solution later using a combination of \\metron, \\Uptext and \\qu. A little more on \\qu{<pitch>} first. There are to siblings, \\ql{<pitch>} which creates a quarter note with a lower stem and \\qa{<pitch>} which creates a quarter note with automatic stem placement.\n\nThe \\qu in \\metron below unfortunately is not hidden from musixlyr. In order to get it ignored we have to remove the % I suggested in my last posting. So at the beginning we'll place something like\n\\notes\\Uptext{\\metron{\\qu}{100}}\\en\n\nHiding the system bar number at the beginning can be done via a conditional. In the following code I test if the number is 1. It will only be printed if otherwise:\n\\def\\thebarno{\\ifnum\\barno=1\\relax\\else\\the\\barno\\fi}\\def\\writebarno{\\llap{\\thebarno\\barnoadd}}\n\nNow, - at last - let's put everything together (to be compiled twice with one run of musixflx in between):\n\n\\documentclass{article}\\usepackage[utf8]{inputenc}\\usepackage[T1]{fontenc}\\usepackage{musixtex}\\usepackage[left=1in,right=1in]{geometry}\\input{musixlyr} \\begin{document} \\begin{music}% general settings:\\setlength\\parindent{0pt}\\generalsignature{2}% more vertical space above of staffs, default is 3\\Interligne:\\stafftopmarg=5\\Interligne\\smallmusicsize% hide bar number if bar number is 1, use systemnumbers:\\def\\thebarno{\\ifnum\\barno=1\\relax\\else\\the\\barno\\fi}\\def\\writebarno{\\llap{\\thebarno\\barnoadd}}\\def\\raisebarno{2\\internote}\\def\\shiftbarno{1.3\\Interligne}\\systemnumbers% lyrics:\\setlyrics{text}{ Ra-dosť krás-na isk-ra bo-hov E-ly-zej-ská dcé-ra ty, o-má-me-ní žia-rou oh-ňov poď-me ktvo-jej svä-to-sti. Tvo-je ča-ro zno-vu_ zvia-že to čo_ mó-da de-lí dnes všet – kým ľu-ďom brat-mi ká-že stať sa tvo-jich krí-del let tvo-je ča-ro zno-vu_ zvia-že to čo_ mó-da de-lí dnes všet – kým ľu-ďom brat-mi ká-že stať sa tvo-jich krí-del let. }\\assignlyrics1{text}% the actual piece:\\startpiece\\notes\\Uptext{\\metron{\\qu}{100}}\\en\\NOTes\\qu{ffgh}\\enotes\\bar\\NOTes\\qu{hgfe}\\enotes\\bar\\NOtes\\qu{ddef}\\enotes\\bar\\NOTes\\qup f\\cu e\\hu e\\enotes\\bar\\NOtes\\qu{ffgh}\\enotes\\bar\\NOtes\\qu{hgfe}\\enotes\\bar\\NOtes\\qu{ddef}\\enotes\\bar\\NOTes\\qup e\\cu d\\hu d\\enotes% get a double bar line to indicate that a new part starts% and force line break:\\setdoublebar\\alaligne\\NOtes\\uptext{REF.:}\\qu{e}\\enotes\\NOtes\\qu{efd}\\enotes\\bar\\NOtes\\qu{e}\\enotes\\Notes\\Dqbu fg\\en\\NOtes\\qu{fd}\\enotes\\bar\\NOtes\\qu{e}\\enotes\\Notes\\Dqbu fg\\en\\NOtes\\qu{fe}\\enotes\\bar\\NOTes\\qu{dea}\\enotes\\NOTes\\isslurd0e\\qu f\\enotes\\bar\\NOTes\\tsslur0e\\qu f\\enotes\\NOTes\\qu {fgh}\\enotes\\bar\\NOtes\\qu{hgfe}\\enotes\\bar\\NOtes\\qu{ddef}\\enotes\\bar\\NOTes\\qup e\\cu d\\hu d\\enotes\\setdoublebar\\alaligne\\NOtes\\uptext{REF.:}\\qu{e}\\enotes\\NOtes\\qu{efd}\\enotes\\bar\\NOtes\\qu{e}\\enotes\\Notes\\Dqbu fg\\en\\NOtes\\qu{fd}\\enotes\\bar\\NOtes\\qu{e}\\enotes\\Notes\\Dqbu fg\\en\\NOtes\\qu{fe}\\enotes\\bar\\NOTes\\qu{dea}\\enotes\\NOTes\\isslurd0e\\qu f\\enotes\\bar\\NOTes\\tsslur0e\\qu f\\enotes\\NOTes\\qu {fgh}\\enotes\\bar\\NOtes\\qu{hgfe}\\enotes\\bar\\NOtes\\qu{ddef}\\enotes\\bar\\NOTes\\qup e\\cu d\\hu d\\en\\Endpiece\\end{music} \\end{document}", null, "musixtexpiece.png (32.87 KiB) Viewed 9928 times\n\nLast but not least: it really is worth reading through the whole documentation of musixtex. Admittedly: it is rather long. Also, it is in English which is not perfect for us non-native speakers. And third, since musixtex is a generic package the syntax often is more plainTeX- than LaTeX-like. Nevertheless it pays off!\n\nRegards\nClemens\n------------------------------\nchemmacros · chemformula · leadsheets · xsim\n\nLiben\nPosts: 5\nJoined: Tue Jan 01, 2013 6:10 pm\nFinally, I have it. Big thanks cgnieder. I don´t understood how to create .mx2 file but I download \"musixflx\" and run .mx1 file with this musixflx and .mx2 file was created. Then when I start .tex file all was align like I need", null, "I have to make some details like title,autor but it wouldn´t be a problem. I read many pdf and another literature about musixtex and I found some useful commands which could helped me but I didn´t know how to used them so they didn´t worked and very often literature was very extensive for me as a beginner of Latex", null, "Thank you for your time and help.\n\ncgnieder\nSite Moderator\nPosts: 1988\nJoined: Sat Apr 16, 2011 7:27 pm\nLiben wrote:Finally, I have it. Big thanks cgnieder.\n\nYou're welcome!\n\nLiben wrote:I don´t understood how to create .mx2 file but I download \"musixflx\" and run .mx1 file with this musixflx and .mx2 file was created.\n\nI don't know which TeX distribution you're using but musixflx is part of TeX Live and of MiKTeX so I assumed you must have it installed already...\n\nLiben wrote:I read many pdf and another literature about musixtex and I found some useful commands which could helped me but I didn´t know how to used them so they didn´t worked and very often literature was very extensive for me as a beginner of Latex", null, "Thank you for your time and help.\n\nWell, at the beginning TeX and LaTeX and all the details can be quite confusing and it takes quite some time to learn good practices and the like. Just ask again if you have another question.\n\nRegards\nClemens\n------------------------------\nchemmacros · chemformula · leadsheets · xsim" ]	[ null, "https://latex.org/forum/images/icons/misc/orangeflag.gif", null, "https://latex.org/forum/download/file.php", null, "https://latex.org/forum/download/file.php", null, "https://latex.org/forum/download/file.php", null, "https://latex.org/forum/download/file.php", null, "http://latex-community.org/forum/images/icons/smile/info.gif", null, "https://latex.org/forum/download/file.php", null, "https://latex.org/forum/download/file.php", null, "https://latex.org/forum/download/file.php", null, "https://latex.org/forum/download/file.php", null, "https://latex.org/forum/images/smilies/icon_e_smile.gif", null, "https://latex.org/forum/download/file.php", null, "https://latex.org/forum/images/smilies/icon_e_smile.gif", null, "https://latex.org/forum/images/smilies/icon_e_wink.gif", null, "https://latex.org/forum/images/smilies/icon_e_wink.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6088656,"math_prob":0.60669345,"size":1588,"snap":"2019-51-2020-05","text_gpt3_token_len":613,"char_repetition_ratio":0.27462122,"word_repetition_ratio":0.0,"special_character_ratio":0.31234258,"punctuation_ratio":0.0652921,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9561211,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-06T08:20:32Z\",\"WARC-Record-ID\":\"<urn:uuid:bf993604-6e68-49c8-a736-2d2ddb957859>\",\"Content-Length\":\"211886\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dd3ab011-6d64-489a-b677-1d876c11ce3e>\",\"WARC-Concurrent-To\":\"<urn:uuid:e2e4c964-fa89-4fa1-9b58-ecb5c4f5fe4a>\",\"WARC-IP-Address\":\"78.46.26.59\",\"WARC-Target-URI\":\"https://latex.org/forum/viewtopic.php?p=75481\",\"WARC-Payload-Digest\":\"sha1:GKKKE736VMHBY5RGK3C7EHUPTXABX3FC\",\"WARC-Block-Digest\":\"sha1:AP44D63CWH7GDUUVY2ALIM44AZQJAXWP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540486979.4_warc_CC-MAIN-20191206073120-20191206101120-00514.warc.gz\"}"}
https://math.stackexchange.com/questions/2170576/v-finite-dimensional-vector-space-and-isomorphic-to-mathbbrn/2170600#2170600	[ "# $V$ finite-dimensional vector space and isomorphic to $\\mathbb{R}^n$?\n\nIf $V$ is a finite-dimensional vector space, does it mean that $V$ is also isomorphic to $\\mathbb{R}^n$ for some $n$? I am having a hard time trying to picture this. I was wondering if someone could explain this to me.\n\n• Just map the finite basis set to any basis set of $\\mathbb{R}^n$ for some $n$ and extend linearly to whole space. This map then should be an isomorphism. we can do this becase we know the space is finite dimensional. Mar 3 '17 at 18:46\n• If it's a finite-dimensional real vector space, then yes. Mar 3 '17 at 18:46\n• The answer is no. A simple counter example is the vector space $\\mathbb{F}_2^n$ where $\\mathbb{F}_2 = \\mathbb{Z}/2\\mathbb{Z}$. Mar 3 '17 at 19:14\n\nLet $V$ have dimension $n$ over $\\Bbb R$, say with basis $\\{v_1,\\dots,v_n\\}$. Define a map $f:V\\to\\Bbb R^n$ by\n$$f(a_1v_1+\\dots+a_nv_n)=(a_1,\\dots,a_n).$$" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83365005,"math_prob":0.9999182,"size":1040,"snap":"2021-43-2021-49","text_gpt3_token_len":340,"char_repetition_ratio":0.112934366,"word_repetition_ratio":0.0124223605,"special_character_ratio":0.32307693,"punctuation_ratio":0.110091746,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000004,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-28T15:13:37Z\",\"WARC-Record-ID\":\"<urn:uuid:a5540224-e135-4b26-81a7-a21de9227064>\",\"Content-Length\":\"169729\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cad5d649-9443-4313-a3bd-17b0c66364d4>\",\"WARC-Concurrent-To\":\"<urn:uuid:01554a26-6a27-4dcf-ad58-83012424d334>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/2170576/v-finite-dimensional-vector-space-and-isomorphic-to-mathbbrn/2170600#2170600\",\"WARC-Payload-Digest\":\"sha1:2J52D7P4VYUS6OUYHZTWKRNNC2UR5PHB\",\"WARC-Block-Digest\":\"sha1:XNK5SQLT4EJBITUZUGD7QXXWBUZ6UV4I\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323588341.58_warc_CC-MAIN-20211028131628-20211028161628-00032.warc.gz\"}"}
https://www.raymaps.com/index.php/how-to-find-point-of-intersection-of-two-lines/	[ "# How to Find Point of Intersection of Two Lines\n\nFinding the point of intersection of two lines has many important application such as in Ray-Tracing Simulation. Two lines always intersect at some point unless they are absolutely parallel, like the rails of a railway track. We start with writing the equations of the two lines in slope-intercept form.\n\ny1=b1+m1x1\n\ny2=b2+m2x2", null, "Here m1 and m2 are the slopes of the two lines and b1 and b2 are their y-intercepts. At the point of intesection y1=y2, so we have.\n\nb1+m1x1=b2+m2x2\n\nBut at the point of intersection x1=x2 as well, so replacing x1 and x2 with x we have.\n\nb1+m1x=b2+m2x\n\nor\n\nb1-b2=-x(m1-m2)\n\nor\n\nx=-(b1-b2)/(m1-m2)\n\nOnce the x-component of the point of intersection is found we can easily find the y-component by substituting x in any of the two line equations above.\n\ny=b1+m1x\n\nIn future posts we would like to discuss the cases of intersection of two surfaces and the intersection of two volumes.", null, "#### Author: Yasir Ahmed (aka John)\n\nMore than 20 years of experience in various organizations in Pakistan, USA and Europe. Worked as Research Assistant within Mobile and Portable Radio Group (MPRG) of Virginia Tech and was one of the first researchers to propose Space Time Block Codes for eight transmit antennas. The collaboration with MPRG continued even after graduating with an MSEE degree and has resulted in 12 research publications and a book on Wireless Communications. Worked for Qualcomm USA as an Engineer with the key role of performance and conformance testing of UMTS modems. Qualcomm is the inventor of CDMA technology and owns patents critical to the 5G and 4G standards.\n\n2.67 avg. rating (60% score) - 3 votes" ]	[ null, "http://www.raymaps.com/wp-content/uploads/2016/09/straight-lines.jpg", null, "https://secure.gravatar.com/avatar/8f5c607215ecef1fc06a2dfa3d0c4dbf", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9463769,"math_prob":0.939875,"size":1588,"snap":"2023-14-2023-23","text_gpt3_token_len":394,"char_repetition_ratio":0.13699494,"word_repetition_ratio":0.0,"special_character_ratio":0.23236775,"punctuation_ratio":0.05732484,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9677195,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,7,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-24T02:43:13Z\",\"WARC-Record-ID\":\"<urn:uuid:302fd0c0-853b-484b-895e-0da5e51b3cb8>\",\"Content-Length\":\"62579\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7764d0ec-c51e-4fdb-a94f-f8535ec2dfe6>\",\"WARC-Concurrent-To\":\"<urn:uuid:118b43f2-473f-4267-a9f1-3166df255858>\",\"WARC-IP-Address\":\"203.124.44.74\",\"WARC-Target-URI\":\"https://www.raymaps.com/index.php/how-to-find-point-of-intersection-of-two-lines/\",\"WARC-Payload-Digest\":\"sha1:2TXJTFNNZMUMBVUFBKV7DSEG2Y33CLHY\",\"WARC-Block-Digest\":\"sha1:W5P4FBFYVGACONBH5DZERQAX4ZOWOAKL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296945242.64_warc_CC-MAIN-20230324020038-20230324050038-00520.warc.gz\"}"}
https://ficheterrain.com/prices4q441255zhmme.html	[ "Home\n\n# 4/12 pitch roof calculator\n\n95% Accuracy. Simple, Easy To Read Two-Page Report. Access Your Report Now Search For Localized Results. Find It Here! Search For Information And Products With Us\n\n### Roofing Measurements Online - Fast Reports in 1 Business Da\n\n• A 4/12 is a roof slope that rises by 4 inches for every 12 inches across. This forms an angle of 18.5° between the horizontal section and the roof, and creates a gentle incline that is seen as a midpoint between a low-pitch and medium-pitch roof\n• Learn more about finding the angle of a line using our slope calculator. Standard Roof Pitches. Most roofs have a pitch in the 4:12 to 9:12 range. A pitch over 9:12 is considered a steep-slope roof, between 2:12 and 4:12 is a low-slope roof, and less than 2:12 is a flat roof\n• These roofs have a pitch less than 4:12. Conventional roofs are the easiest to construct and you can walk on them safely. They have a pitch ranging from 4:12 to 9:12. • High-pitched roofs often need extra fasteners and their pitch can be as high as 21:12. You can also calculate roof pitch even without using a roof slope calculator\n• Roof Pitch. Roof pitch is the measurement of a roof's vertical rise divided by its horizontal run. It is often compared to slope, but is not exactly the same. In the United States, a run of 12 inches (1 foot) is used, and pitch is measured as the rise of the roof over 12 inches. For instance, a 7/12 roof pitch means that the roof rises 7 inches.\n• Use our roof pitch calculator to find the pitch of your roof. Next, multiply the footprint of the roof by the multiplier below for your roof pitch to find the overall roof area. For example, a 4/12 pitch roof that is 100 square feet: 100 × 1.054 = 105.4ft 2. Roof Pitch Area Multipliers\n• Pitch Measurement Method 1. 1. On a ladder beside the roof, place the level a foot or so up the roof, hold it level, and measure from the 12-inch mark on the level's bottom, straight down to the roof. If this distance measures 4 inches, you have a 4 in 12 pitch; 8 inches and you have an 8 in 12 pitch\n• 10-12. 39.81°. 11-12. 42.51°. 12-12. 45°. This is our pitch calculator which will convert pitch to angle or angle to pitch for half degree roof slope calculations. Enter any pitch or fraction of pitch to find angle. Enter any angle or fraction of angle to find pitch\n\nRoof Pitch Calculator Results Explained. Slope - The slope of a roof is represented as X/12, where X is the number of inches in rise for every 12 inches of run.This is very useful information for many purposes, especially for roof framing - the slope, sometimes called pitch, is calibrated on speed squares.. Angle - The angle of a roof is the same as the roof's slope, except instead of being. Estimate the cost to install a new roof in a click of a button! Just plug in your house dimensions, select your roof pitch, relative roof difficulty, choice of materials, and let our Calculator do the rest. To get a 100% free roof quote, enter your zip code above and fill out a simple estimate request form on the next page Calculate Sheathing Needed. Once you have the area you can divide by the area of a sheet of plywood to find the number of sheets needed. A 4×8 sheet of plywood is 32 ft 2. So, dividing the area of the roof by 32 will give you the number of sheets needed. For example, if your roof is 1,500 ft 2 then it will take 47 sheets of plywood to sheath it Enter the diameter of the roof ridge vent gap (1-3) Finally, enter the coverage area (width) of the panels you plan to buy. For instance a 38 panel will have an effective coverage width of 36. The metal roof length calculator calculates the distance from peak to trim so add the length you want the roof metal to extend beyond the eave trim.", null, "### Delivering one-click aerial roof measurement reports to contractors\n\nIn roof pitch calculator, pitch value can be obtained by dividing N by 12 and divide S by the answer. To find slope divide rise by run and multiply it by 100 and for angle take tan -1 of S/N. Calculator. Formula. The rise is the distance from the top of the roof to the bottom. The run is the distance from the outside of the wall to the inside. The rise is the distance from the top of a stud wall to the peak of the roof. A roof's pitch is determined by how much it rises for every foot it runs. Thus, a moderate 6 in 12 roof pitch means the roof rises 6 inches for every 12 horizontal inches it runs. A 12 in 12 pitch is a steep, 45-degree angle roof Our roof rafter calculator tools are handy for calculating the number of rafters needed, rafter length calculator, lineal feet of rafter, board feed in ridge and sub-facia,and the total board feet in the roof. Rise and Run means that a 6/12 pitch roof has 6 of rise (vertical) for each foot of run (horizontal). Roof Pitch Calculator", null, "Use our roof pitch calculator to find the pitch of your roof. Next, find the square footage of the metal roofing panels you want to use. Measure the length and width in feet, then multiply together to find the square footage. Panels are often measured in inches, use our inches to feet conversion calculator to convert to feet Once you know your roof slope expressed as X-in-12 (rise-in-run), the roof pitch multiplier is determined by finding the square root of ( (rise/run)² + 1). Remember that the slope of the roof provides the rise and the run to be plugged into the equation. A roof pitch of 4-in-12 (4:12) has a rise of 4 and a run of 12 Roof Pitch Calculator. The roof pitch measures the steepness of your shed roof and typically takes values from 1 to 12. If your roof pitch is greater than 3 your roof is considered pitched.Read more about roof pitch at Wikipedia.. This free roof pitch calculator will take your roof width (see the picture) and rise (the height of the roof) and will calculate the roof pitch both as numeric value.\n\nWhat is the roof pitch? The roof pitch is the slope of the rafter. The pitch is commonly defined as the ratio of rise over run in the form of x/12.. The rise is the height of the roof, and the run is the horizontal span (as pictured above).. For example, if a roof has a pitch of 4/12, then for every 12 inches the building extends horizontally, it rises 4 inches Share this Calculation. Hip roof framing calculator plan diagram with full dimensions. Rafter Join Detail. Hip roof framing - hip to common to ridge join diagram. Walls (building) 40' x 20'. Eave Overhang (level) 2'. Roof 44' x 24'. Roof Angle 22 ° (Pitch 4.85:12) Overall rise above outer wall 4'- 8~5/16\n\nRafter Length using Pitch = V + (R/2)sqrt (1+P 2 ) Where, V = Overhang R = Roof Span P = Pitch. Use our online Rafter Length Calculator to quickly compute the length of the shed roof rafter by entering the measurements of overhead, length of roof span, pitch or angle. This calculator helps you make the rafters of the suitable sizes required for. Rise 1'- 4. Pitch 4:12. Angle 18.4 °. Slope 33.3 %. Slope Length 4'- 2~19/32. Area 2.67 ft². Enter Run (the flat, level length) then click Pitch, Angle or Rise and enter other known dimension, angle or pitch. The triangle diagram will be re-drawn to scale, with all dimensions marked. Pitch Run Scale Calculate the length of a rafter from the roof slope ratio of inches per foot and a building width measurement. The calculation includes results for hip/valley factor, slope factor and the roof slope in degrees. If you add an eaves overhang dimension, then the calculator will add the amount the rafter sticks passed the wall to the rafter length This roof shingle calculator requires four basic inputs: Roof length (measured in feet) Roof width (measured in feet) Roof pitch. Roof type (either gable or hip) Using these four inputs, you will get several basic outputs: Roof area (measured in sq ft) Number of squares. Number of bundles Does that mean 4:12 pitch? (2 foot rise - 4inches every foot). I'm confused with few things. 1. The deck span is 10 foot. But the rafters will be 12foot 2. I'll like the rafters to end about 1 foot past the headers of deck which will be at 7'6″. I feel like I'm looking at wrong information to calculate the roof pitch\n\n### Roll Data Into Estimates · 95% Accuracy Guarantee\n\nThe combination of two numbers are used to display or show the roof pitch. Two most common methods (4/12 or 4:12) are used for marking the pitch of a roof. On blue prints architects & engineers usually display the pitch of a roof in the format shown on the image where number (4) represents a rise and number (12) represents a length. This means. As a reminder, please, don't forget to add height of rafter, thickness of roofing material and ridge vent to the number that you'll get using our calculator. If your goal is to only calculate the roof height, do not enter any numbers in Wall Height field and only use Building Width and Roof Pitch fields 500 Sycamore Street P.O. Box 177 La Crescent, MN 55947 (507) 895-840 Rafter Stock Size Calculator. Building Supplies. Input the rafter span (on the flat), eave overhang and pitch of the roof. Click the button to calculate the stock size needed for this job. This calculator is to be used as an estimating tool ONLY. Shop Dimensional Lumber Measuring the Pitch. To calculate the area of your roof, first you'll need to calculate the pitch of it: First, use your measuring tape to measure 12 inches on your large level and make a mark at the 12-inch line. Next, place your ladder against your house at the gable end. Climb to the top of your roof\n\nFast Roof Measurements. Reports Delivered in 1 Business Day. Order Yours Now Answer: 4/12 roof pitch equivalents roof rises 4″ in a length of 12″. 4/12 roof pitch angle = 18.43 degrees. 4/12 roof pitch to angle 18.43 degrees. Also referred to as 4/12 roof slope, 4 on 12, 4 to 12 and 4/12 roof angle. 4/12 roof pitch to angle = 18.43 degrees equivalents. Tags. 4 on 12 roof pitch 4/12 roof pitch 4/12 roof slope Measure. It's the measure of the steepness of a roof, or its slope. Roof pitch is expressed as a ratio of the roof's vertical rise to its horizontal span, or run. The most commonly used roof pitches fall in a range between 4/12 and 9/12. Pitches lower than 4/12 have a slight angle, and they are defined as low-slope roofs\n\n### RoofScope® Aerial Roof Reports - Get Roof Pitch Measurement\n\nRoof Pitch = / 12¨. Roofing calculator is a tool which is obtainable on the web for the precise calculation of the materials needed to develop a new roof or to renovate the old roof. This Roofing Calculator tool is extremely useful as it saves time and cash. You do not have to search for the specialists in roofing and employ their solutions to. The best part of a roofing calculator is that it offers a free insight into the total cost of the replacement roof project on a sq ft basis. As you begin to calculate various costs, you will see that the cost is a result of the interplay of many different variables, including roof area (in terms of footage), measurement of any roof extras (like.\n\nThis online truss calculator will determine the all-in cost of your truss based on key inputs related to the pitch, width and overhang of your roof. It will use the current cost of wooden rafters based on the average price found at home improvement stores. The important point to keep in mind when you use your truss calculator is that every. Gable Roof Sheathing Calculator (Imperial) Estimate the amount of plywood or OSB needed for sheathing a roof. The calculation is based on that the Plywood or OSB (Oriented Strand Board) sheets are of a 4' x 8' size. One sheet = 32 ft². This basically calculates the number of sheets needed for a Gable roof. The square footage of a Hip roof area. 4/12 roof pitch angle = 18.43 degrees. 24 Related Question Answers Found What is the length of a common rafter? Calculate the tangent of the roof angle by dividing the roof height by the roof width. For example, if the height is 7.5 feet and the width is 15 feet,. Common Rafter Calculator - Rafter Dimensions - Plumb Cuts - Birds-mouth Dimensions + Cutting Templates - Inch. Allow for Ridge Thickness when determining Rafter Run to Outer Wall. eg: Half building width minus 1/2 ridge thickness. See Rafter Run to Outer Wall Calculator below The slope/pitch of the roof is the incline of the roof expressed as a ratio of the vertical rise to the horizontal run. This ratio is expressed as inches per foot. So a a roof that rises 4 inches in 1 foot or in 12 inches is called a 4/12 pitch or slope\n\nIf your roof is pitched, enter the length and width of the flat area covered by the roof. Roof pitch. You can enter this value either as a ratio x:12 or as an angle, whichever suits you better. Snow cover thickness. Intuitively, this is the number of inches of snow on your roof in the place where the cover is the thickest. Snow type truss count = ( (roof length * 12)/24) + 1, Rounded up to the closest whole number (for example if the result is 14.5, you need to get 15 trusses). To calculate the costs, we use the following two formulas: Including installation costs: total costs = truss count * single truss price + cost per time unit of work * duration of work The pitch usually ranges from 4:12 to 9:12. High-pitched - This type typically requires additional fasteners. The pitch can be as high as 21:12. Roof Pitch Degrees. If you'd like to know how to convert roof pitch to degrees, check out the chart below: 1-12 4.76° 2-12 9.46° 3-12 14.04° 4-12 18.43° 5-12 22.62° 6-12 26.57° 7-12 30.26° 8. Generally, such roofs are characterized by Roof pitch angles that correspond to the pitch slope of between 1/2:12 and 2:12. Low pitched ones are characterized by a pitch of less than 4:12. These are usually not easy in terms of maintenance since they have need of special materials for avoiding leaks", null, "### Find More Results - Search for Informatio\n\n1. 4/12 35 41 52* 36 45* 54* 39 50* 58* 42* 49* 62* ‡ Other pitch combinations available with these spans For Example, a 5/12 - 2/12 combination has approx. the same allowable span as a 6/12 - 3/12 Top Chord 2x4 2x6 2x6 2x4 2x6 2x6 2x4 2x6 2x6 2x4 2x6 2x6 Bottom Chord 2x4 2x4 2x6 2x4 2x4 2x6 2x4 2x4 2x6 2x4 2x4 2x\n2. Rise 437. Pitch 4.37:12. Angle 20°. Slope 36.4%. Slope Length 1277. Area 0.262 m². Enter Run (the flat, level length) then click Pitch, Angle or Rise and enter other known dimension, angle or pitch. The triangle diagram will be re-drawn to scale, with all dimensions marked. Angle Run Scale\n3. us ridge thickness, into the 'Wall Width' entries. (\n4. Watch this short video titled Area of a roof instead. Measuring the Roof's Pitch. The incline or pitch of a roof can be easily measured with a level, tape measure, and a pencil. The roof's pitch is the number of inches the roof rises in 12 inches. Therefore, mark off 12 inches on the level and place it down horizontally against the roof rafter\n\n### Video: Roof Pitch Calculato", null, "### Roof Pitch Calculator - Inch Calculato\n\nFor 20 degrees to roof pitch:- 1) tan of 20 degrees as tan 20° = 0.3639, this will give you the pitch of the roof, 2) multiply the pitch by 12 to find the X in the ratio X/12 such as 0.3639 ×12 = 4.36, thus, a 20 degrees angle of roof pitch is same as 4/12 or 4 in 12 slope, or pitch ratio 4:12 Example calculations: Roof is 8/12 pitch and measures at 1900 square feet 1900 x 1.2= 2280 2280 - 1900= 380 feet added for pitch If the home measures 20 X 40 and has a 7:12 roof, then to calculate the slope of the roof follow these steps: Step 1: Multiply 20 and 40 which equals 800. Step 2: Find the value of 7:12 from the roof slope multiplier table which is 1.16 Hip roof calculator. One of our users asked us to create a calculator that would help him estimate hip roof parameters, such as rafter lengths, roof rise and roof area. So, here it is. To get results you need to provide the roof base dimensions (length and width) and the roof pitch (we assume it is identical for all sides) Our roof truss calculator can be used to aid you in the purchase of your trusses by determining the quantity of trusses and lineal feet required. Connector plates are generally 16 gauge to 20 gauge depending on truss design requirements. The information provided here is not intended to replace truss drawings. Engineered truss drawings should be. Determining the Ridge Beam Height. If you know the slope (X in 12) you want to use for your roof framing design, you can use it, along with the run (R), to determine the height of the ridge beam.For example, if the slope is 4 in 12, and the run is 12 feet, the ridge beam height (M) will be 4 feet. The finished ridge beam height (Z) above the top of the wall will be (M) plus the Y Height\n\nOnline calculator produces an accurate calculation of the rafters online (calculates the sizes of rafters for the roof: the length of rafters, length overhang, the angle of the saw cut, the distance to drinking). The drawings and the size of the rafters are generated in real-time. The calculator provides online calculate the length of rafters a gable roof Hip Roof Area Calculator. Hip roof is a roof with a sharp edge or edges from the ridge to the eaves where the two sides meet. Here is the online hip roof area calculator which helps you calculate the hip roof parameters such as roof rise, common and hip rafters length and roof area based on width, height of roof base and the roof pitch (identical for all sides)\n\nSo you must roof calculate the pitch very carefully and correctly to know about the cost that you need to pay. If your house roof is built with multiple pitches, then square per roof must be calculated differently. 4/12 18.43° 1.0541 5/12 22.62° 1.0833 6/12 26.57° 1.1180 7/12 30.26° 1.1577. For most home styles, roof pitches fall in a range 4/12 (a moderate) slope up to 8/12 (fairly steep). Examples of extreme slopes range from 1/4 /12 (almost flat) to 12/12 (sloping down at a perfect 45-degree angle)\n\n### 2021 Roofing Calculator & Estimator Roof Area, Pitch\n\nOver time the ratio over 12″ (1 foot) was more commonly used as it was easy to reference on the framing square. The term Pitch when used over 12 became to be understood as the standard , and is commonly called the Pitch of the Roof. Just look at the Calculator entry the button is labeled pitch' not slope or incline The way pitch, also known as roof slope, is measured is rise over run. So, if your roof rises 4 inches for every 12 inches of horizontal length, then the pitch of your roof is expressed as 4:12. A ratio is the most common way of expressing roof pitch or roof slope, but degrees are also possible. A 4:12 pitch is around 18.5 degrees, but not exactly A description of what pitch is and how to manipulate the numbers when framing and planning a project. Carpentry is mostly breaking down the elements of a bui.. When building a roof, how do you calculate the length of the rafters? All you need to know are the span of the building and the slope of the roof\n\n### Roof Pitch Calculator Pitches To Angle Char\n\nThe pitch fraction represents a certain amount of vertical rise over the entire span. For example, given a roof with a rise of 4 feet and a span of 24 feet, the pitch is 1 to 6 pitch, which can be expressed as the fraction of 1/6. A 12 to 24 pitch is expressed as 1/2. The term pitch and slope are often used. Our goal is to have a huge inventory of the common trusses like 20, 24, 30, 36 &40' 4:12 pitch trusses and 10,12,14 foot 2:12 lean to trusses in stock and ready to be picked up or delivered. But for right now, we do not guarantee what is in stock. Please call for availability before arranging a delivery or pick-up Tristate Areas Best Roofing Company Delaware Chester Montgomery Buck\n\nA 4/12 roof pitch is referred to as the roof rises 4 inches in height for every 12 inches, as it measured horizontally from the edge of the roof to the centerline. The gentle slope of a 4/12 roof pitch falls on the cusp between moderate-pitch and low-pitch Your roof area is 3500 sq feet Your Roof Pitch is 6/12 pitch. Your Output. Multiplier 0.12. Feet added for pitch = Multiplier x 3500 = 420 sq feet. Total = 3500 + 20 = 3920. Total Squares = 3920 / 100 = 339.20 squares. Roof Pitch to Angle Calculator (enter pitch in the first box - calculation is automatic) Roof Span: ft. in.Roof Rise: ft. in A 4/12 roof pitch can also be expressed as 4 over 12 and when you're talking to a roofer, this is the most common way you'll hear it explained because it's easy to say in conversation. Another way to express a 4/12 pitch is 4 and 12. In this pitch, the four is your roof's rise and the twelve is the roof's run. The roof's incline increases four feet for every 12 feet of horizontal measurement Valley Roof The Valley roof option is used to calculate valleys for 90 degree intersecting roofs with equal slopes and wall plates at the same height. The heel height, overhang, and ridge and fascia boards for both roofs will be the same. The Blind Valley roof can be used to calculate valleys for roofs with unequal slopes 3) Enter roof pitch / slope: Roof pitch is the value of roof rise over roof run, using 12 as the base for roof run. Example: If your roof rises 5 for every 12 of run, enter 5 as roof pitch. If your roof pitch is in degrees, use our roof pitch calc to convert degrees to pitch value. 4) Select rafter spacing and width\n\n• Corkcicle Tumbler.\n• Caswell Beach real estate.\n• Annabel Lee analysis.\n• Norwegian Christmas cookies for sale.\n• Can you adopt if you have a criminal record UK.\n• Glass verandas prices.\n• Grey Peel and Stick Backsplash.\n• Connor McDavid Instagram.\n• What allows you to forward a received email to someone else.\n• When do cinemas open in Scotland.\n• Carpentry PowerPoint templates.\n• Oudtshoorn Farm accommodation.\n• Royal Isabela rentals.\n• Spoof website will stay online.\n• Redskins roster 2014.\n• 🦥sloth.\n• Exotic purple strains.\n• Trio Wedding Ring Sets Walmart.\n• Share chat tamil comedy.\n• National Geographic Elementary.\n• Corgis in CA.\n• Dce089d1g xe.\n• Double endorsement test.\n• Xbox 360 OLX Lahore.\n• Theme name for farewell party.\n• Wind Waker Treasure Charts.\n• How to delete birthdays from iPhone calendar.\n• Kansas State Women's Soccer recruits.\n• Removable Glue Dots for Balloons.\n• KOA Zion National Park.\n• Wudu sequence.\n• Endometrial cancer ultrasound findings.\n• Would you have a relationship with the first person meaning in tamil.\n• Mora whittling knife set.\n• Hazy PPDT pictures.\n• Lilim UKULELE Chords.\n• FOTS stands for.\n• Trolley for moving Furniture." ]	[ null, "https://ficheterrain.com/jfexc/L6JKLQt1q7j7UqmHx49qUgHaGT.jpg", null, "https://ficheterrain.com/jfexc/pWEDmn2Hleay89vJb0vmpQHaEc.jpg", null, "https://ficheterrain.com/jfexc/hVEwmZ-Y8eSRQ0ziZWrlWgHaDj.jpg", null, "https://ficheterrain.com/jfexc/MvK0CpnNUl0q4etfrD7HQAHaEc.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92517173,"math_prob":0.9775247,"size":21107,"snap":"2021-43-2021-49","text_gpt3_token_len":5278,"char_repetition_ratio":0.17945316,"word_repetition_ratio":0.017100561,"special_character_ratio":0.25981903,"punctuation_ratio":0.10383847,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9609931,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-20T19:42:09Z\",\"WARC-Record-ID\":\"<urn:uuid:1a654ee9-41b3-492e-b9a0-3cb865117347>\",\"Content-Length\":\"34781\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cc263732-fbea-4dec-8c27-794561e28c92>\",\"WARC-Concurrent-To\":\"<urn:uuid:51bb7c0f-2374-408d-96d0-266655247d5b>\",\"WARC-IP-Address\":\"37.1.204.220\",\"WARC-Target-URI\":\"https://ficheterrain.com/prices4q441255zhmme.html\",\"WARC-Payload-Digest\":\"sha1:CUW3HWRERYQ3KB3J7BDLXGW4PHSGLBNB\",\"WARC-Block-Digest\":\"sha1:XSBCEFSSNLTJ6X5ADECPUE4NPETYXWN7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585348.66_warc_CC-MAIN-20211020183354-20211020213354-00222.warc.gz\"}"}
https://jp.mathworks.com/help/msblks/ref/singlemodulusprescaler.html	[ "# Single Modulus Prescaler\n\nInteger clock divider that divides frequency of input signal\n\n• Library:\n• Mixed-Signal Blockset / PLL / Building Blocks\n\n•", null, "## Description\n\nThe Single Modulus Prescaler subsystem block divides the frequency of the input signal by a tunable integer value, N, passed to the div-by port. In frequency synthesizer circuits, such as a phase-locked loop (PLL) system, these prescalers divide the VCO output frequency by an integer value. The resulting lower frequency at the prescaler output port is comparable to the reference input at the PFD block. The Single Modulus Prescaler is also termed as integer clock divider.\n\n## Ports\n\n### Input\n\nexpand all\n\nInput clock frequency, specified as a scalar. In a PLL system, the clk in port is connected to the output port of a VCO block.\n\nData Types: `double`\n\nRatio of output to input clock frequency, expressed as a scalar integer.\n\nData Types: `double`\n\n### Output\n\nexpand all\n\nOutput clock frequency, expressed as a scalar. In a PLL system, the clk out port is connected to the feedback input port of a PFD block. The output at the clk out port is a square pulse train of 1 V amplitude.\n\nData Types: `double`\n\n## Parameters\n\nexpand all\n\nSelect to enable increased buffer size during simulation. This increases the buffer size of the Logic Decision inside the Single Modulus Prescaler block. By default, this option is deselected.\n\nNumber of samples of the input buffering available during simulation, specified as a positive integer scalar. This sets the buffer size of the Logic Decision inside the Single Modulus Prescaler block.\n\nSelecting different simulation solver or sampling strategies can change the number of input samples needed to produce an accurate output sample. Set the Buffer size to a large enough value so that the input buffer contains all the input samples required.\n\n#### Dependencies\n\nThis parameter is only available when Enable increased buffer size option is selected in the Block Parameters dialog box.\n\n#### Programmatic Use\n\n• Use `get_param(gcb,'NBuffer')` to view the current value of Buffer size.\n\n• Use `set_param(gcb,'NBuffer',value)` to set Buffer size to a specific value.", null, "" ]	[ null, "https://jp.mathworks.com/help/msblks/ref/block_single_modulus_prescaler.png", null, "https://jp.mathworks.com/images/responsive/supporting/apps/doc_center/bg-trial-arrow.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.81154215,"math_prob":0.82364607,"size":787,"snap":"2020-24-2020-29","text_gpt3_token_len":178,"char_repetition_ratio":0.14048532,"word_repetition_ratio":0.016666668,"special_character_ratio":0.19822109,"punctuation_ratio":0.11029412,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9595798,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,3,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-02T21:29:46Z\",\"WARC-Record-ID\":\"<urn:uuid:aa3a40d3-1432-4c97-9749-c9715b28e8a8>\",\"Content-Length\":\"79466\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2dc6b250-c2d8-4d38-bb2f-750b46b5e909>\",\"WARC-Concurrent-To\":\"<urn:uuid:6f45de37-575a-42a0-9a5e-d77af335e944>\",\"WARC-IP-Address\":\"96.7.70.236\",\"WARC-Target-URI\":\"https://jp.mathworks.com/help/msblks/ref/singlemodulusprescaler.html\",\"WARC-Payload-Digest\":\"sha1:7OPOJY3JBOFMEW3FRA4MQOBZSVS4O7JX\",\"WARC-Block-Digest\":\"sha1:AGKXANW73SSQ6D7QVPI2IGVIATILEPE6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655880243.25_warc_CC-MAIN-20200702205206-20200702235206-00598.warc.gz\"}"}
https://cs.stackexchange.com/questions/3239/reducing-tsp-to-ham-cycle-to-vertex-cover-to-clique-to-3-cnf-sat-to-sat	[ "# Reducing TSP to HAM-CYCLE to VERTEX-COVER to CLIQUE to 3 CNF-SAT to SAT\n\nIn Cormen's Algorithms book on NP-completeness they prove various problems are NP-complete by reducing a previously proved NP-complete problem (call $K$) to current problem (call $L$). Each proof involves some clever construction which reduces all instances of $K$ to few instances of $L$. Here is the proof order they follow. CIRCUIT-SAT, SAT, 3 CNF-SAT, CLIQUE, VERTEX-COVER, HAM-CYCLE, TSP. e.g. in reducing VERTEX-COVER to HAM-CYCLE they use a widget which does the trick.\n\nAfter this previous question of mine, I think one can reduce back. i.e. one can reduce HAM-CYCLE to VERTEX-COVER problem. I tried searching web for such reductions, but most of the link return the normal reduction order. I'm interested to see if one can reduce in reverse order. i.e. TSP to HAM-CYCLE to VERTEX-COVER to CLIQUE to 3 CNF-SAT to SAT\n\nI'm looking for reverse constructive proofs. I know all of these problems belong to NP-complete hence equivalent.\n\nYou don't have to give complete proof as an answer. Proof sketches are fine too. If you can point me where these proofs are available online, that's completely fine too. I'm just trying to lean how constructions are leveraged among problems that look so different on surface. Thanks!\n\n• Well I found most reductions interesting because they are construction proofs. It's hard to think out-of-the-box constructions. So I wanted to see if reverse construction is possible. – Ankush Aug 17 '12 at 14:34\n• What have you tried? All stated problems are $\\mathsf{NP}$-Complete. Thus every problem in $\\mathsf{NP}$ can be reduced to your problems (by definition of $\\mathsf{NPC}$). Hint: Start reducing TSP to HAM-CYCLE. – Christopher Aug 17 '12 at 14:40\n• @Chris As of now nothing. I mean till yesterday I was under impression that above isn't possible. Let me start with TSP to HAM-CYCLE :) – Ankush Aug 17 '12 at 15:13\n• Note that not all NPC problems are equally hard, see e.g. weakly vs strongly NP-completeness. Therefore, not all reductions are equally simple; those from strong to weak problems have to be complex enough to prevent e.g. efficient approximations to carry over (unless P=NP). – Raphael Aug 18 '12 at 6:16\n• I'd offer you to read Garey & Johnson book, they provide iff proof for some of problems, proof techniques are not easy and you can't expect to solve them yourself in few days. – user742 Aug 18 '12 at 18:32\n\nAs mentioned in one of the comments on the question, $3SAT$ to $SAT$ is trivial, an instance of $3SAT$ is already and instance of $SAT$, so there's no work needed at all.\nTo get from $VERTEX$ $COVER$ $(VC)$ to $CLIQUE$ we can do a couple of short jumps, that'll also put another problem in the loop. $VC$ is the dual of $INDEPENDENT$ $SET$ $(IS)$, that is, we can find a vertex cover of size $k$ in a graph $G$ iff we can find an independent set of size $n-k$ in $G$. Play around with this a little and you'll see why this is true. If we then take the edge-complement graph $\\bar{G}$ of $G$, an independent set of size $t$ in $G$ is the same as a clique of size $t$ in $\\bar{G}$, so that gets us to $CLIQUE$." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.94059616,"math_prob":0.9709133,"size":1221,"snap":"2019-51-2020-05","text_gpt3_token_len":299,"char_repetition_ratio":0.121610515,"word_repetition_ratio":0.0,"special_character_ratio":0.21539721,"punctuation_ratio":0.12550607,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99662083,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-19T03:13:20Z\",\"WARC-Record-ID\":\"<urn:uuid:b0db466b-d05e-41d9-bf12-c9c3913a4842>\",\"Content-Length\":\"146140\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:877e24df-9de3-4897-9ce6-6a491cd41262>\",\"WARC-Concurrent-To\":\"<urn:uuid:1fa45850-d93b-4f3a-b16e-02194cfab9cf>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://cs.stackexchange.com/questions/3239/reducing-tsp-to-ham-cycle-to-vertex-cover-to-clique-to-3-cnf-sat-to-sat\",\"WARC-Payload-Digest\":\"sha1:F7TBVLSIXKC3PVEW5XUBXX5AEYPXVPE4\",\"WARC-Block-Digest\":\"sha1:6GIV22YGG2J76S56ZU3QKFRDOOEHJ5H6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250594101.10_warc_CC-MAIN-20200119010920-20200119034920-00045.warc.gz\"}"}
https://answers.everydaycalculation.com/add-fractions/75-50-plus-18-40	[ "Solutions by everydaycalculation.com\n\n1st number: 1 25/50, 2nd number: 18/40\n\n75/50 + 18/40 is 39/20.\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 50 and 40 is 200\n2. For the 1st fraction, since 50 × 4 = 200,\n75/50 = 75 × 4/50 × 4 = 300/200\n3. Likewise, for the 2nd fraction, since 40 × 5 = 200,\n18/40 = 18 × 5/40 × 5 = 90/200\n300/200 + 90/200 = 300 + 90/200 = 390/200\n5. 390/200 simplified gives 39/20\n6. So, 75/50 + 18/40 = 39/20\nIn mixed form: 119/20\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]	[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83571714,"math_prob":0.997826,"size":720,"snap":"2020-34-2020-40","text_gpt3_token_len":290,"char_repetition_ratio":0.1452514,"word_repetition_ratio":0.0,"special_character_ratio":0.53333336,"punctuation_ratio":0.09756097,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99686176,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-23T20:00:31Z\",\"WARC-Record-ID\":\"<urn:uuid:3365ed72-6810-4b2f-8b52-7ac432f42964>\",\"Content-Length\":\"7462\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3bcb9942-4d93-469a-ab0e-014458765909>\",\"WARC-Concurrent-To\":\"<urn:uuid:bf7550e7-0918-4d80-a898-60915783cab2>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/add-fractions/75-50-plus-18-40\",\"WARC-Payload-Digest\":\"sha1:GJLAQ34YGXSCA42IQRRFJJKLGKXPYZKC\",\"WARC-Block-Digest\":\"sha1:BBQ53DVRRSCTFPPTR3OQRORCUNOTFIN4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400212039.16_warc_CC-MAIN-20200923175652-20200923205652-00345.warc.gz\"}"}
https://eduzip.com/ask/question/in-classical-physics-the-force-f-acting-on-a-body-is-assumed-to-b-274052	[ "Physics\n\n# In classical physics the force F acting on a body is assumed to be the product of mass m and acceleration a.If m=2.31 kg and acceleration is $3.123 m/s^2$,then taking into account significant figures the force F should be reported as\n\n7.21 N\n\n##### SOLUTION\n$F=m \\times a$\n$=2.31 \\times 3.123=7.21413 N$\nRounding off two decimal places since one of the products has two decimal places only.\n$F=7.21 N$\n\nYou're just one step away\n\nSingle Correct Medium Published on 18th 08, 2020\nQuestions 244531\nSubjects 8\nChapters 125\nEnrolled Students 204\n\n#### Realted Questions\n\nQ1 Subjective Medium\nIn the United States, a doll house has the scale of $1:12$ of a real house (that is,each length of the doll house is $\\dfrac{1}{12}$ that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of $1:44$ of a real house. Suppose a real house has a front length of $20\\ m$, a depth of $12\\ m$, a height of $6.0\\ m$, and a standard sloped roof (vertical triangular faces on the ends) of height $3.0\\ m$ In cubic meters, what are the volumes of the corresponding\nminiature house?\n\nAsked in: Physics - Units and Measurement\n\n1 Verified Answer \| Published on 18th 08, 2020\n\nQ2 Subjective Medium\n$1$ kgf= _____ (nearly)\n\nAsked in: Physics - Units and Measurement\n\n1 Verified Answer \| Published on 18th 08, 2020\n\nQ3 Single Correct Medium\nA quantity $X$ is given by $X$ $={ \\epsilon }_{ 0 }L\\dfrac { \\Delta V }{ \\Delta t }$, where ${ \\epsilon}_{0 }$ is the permittivity of free space, $L$ is a length, $V$ is a potential difference and $t$ is time interval. The dimensional formula for $X$ is the same as that of :\n• A. resistance\n• B. charge\n• C. voltage\n• D. current\n\nAsked in: Physics - Units and Measurement\n\n1 Verified Answer \| Published on 18th 08, 2020\n\nQ4 Single Correct Medium\nThe dimensions of $\\varepsilon _0\\mu_0$ are\n• A. $[LT^{-1}]$\n• B. $[LT^{-2}]$\n• C. $[L^2T^{-2}]$\n• D. $[L^{-2}T^2]$\n\nAsked in: Physics - Units and Measurement\n\n1 Verified Answer \| Published on 18th 08, 2020\n\nQ5 Single Correct Medium\n1 $\\mathring{A}$ is equal to :\n• A. $0.1$ nm\n• B. $10^{-10}$ cm\n• C. $10^{-8} m$\n• D. $10^{-4} \\mu$.\n\nAsked in: Physics - Units and Measurement\n\n1 Verified Answer \| Published on 18th 08, 2020" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.74137914,"math_prob":0.99064136,"size":1973,"snap":"2021-43-2021-49","text_gpt3_token_len":609,"char_repetition_ratio":0.117826305,"word_repetition_ratio":0.05263158,"special_character_ratio":0.3482007,"punctuation_ratio":0.11838791,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999749,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-09T08:23:57Z\",\"WARC-Record-ID\":\"<urn:uuid:536d2c3b-3d5a-425e-bce9-9607b30a1f65>\",\"Content-Length\":\"43139\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c2d57982-0bbb-4d30-80a2-428cc90b7327>\",\"WARC-Concurrent-To\":\"<urn:uuid:741c7631-fef5-4852-8f47-ef20cb0c3cff>\",\"WARC-IP-Address\":\"178.63.16.225\",\"WARC-Target-URI\":\"https://eduzip.com/ask/question/in-classical-physics-the-force-f-acting-on-a-body-is-assumed-to-b-274052\",\"WARC-Payload-Digest\":\"sha1:KZGVMFFSPB5BBZCONZGEJ5TQWKIXJFI3\",\"WARC-Block-Digest\":\"sha1:DDUPBL4TKEUQRFGBSG3L2LXKWKGEGBBD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363689.56_warc_CC-MAIN-20211209061259-20211209091259-00416.warc.gz\"}"}
https://chemistry.stackexchange.com/questions/56982/is-lif-a-weak-electrolyte-in-acetic-acid/56984	[ "# Is LiF a weak electrolyte in acetic acid?\n\nThe vapor pressure of acetic acid is 0.033 atm at 25°C. If 5.00g of $$\\ce{LiF}$$ is added to 100g of acetic acid, what would be the vapor pressure of the solution at 25°C?\n\nThe lowering in vapor pressure (VP) can be calculated with this equation:\n\n$${∆P = X_{solute} * P°_{solvent} * i}$$\n\n$${∆P}$$ is the change (lowering) in VP.\n\n$${X_{solute}}$$ is the mole fraction of the solute.\n\n$${P°_{solvent}}$$ is the VP of the pure solvent.\n\n$${i}$$ is the van't Hoff factor of the solute.\n\nWhat is the \"correct\" van't Hoff for this problem, from the perspective of a general chemistry student? I know that $$\\ce{LiF}$$ is not very soluble in water, and I know there are papers on lithium fluoride and acetic acid, but that's all beyond the scope of a general chemistry class.\n\nTherefore, I think it's 2, because $$\\ce{LiF}$$ is expected to be a strong electrolyte. It's ionic, and the solvent is similarly polar (acetic acid has hydrogen bonds). The solvent even resembles water in that both have hydrogen-bonding. So I would expect $$\\ce{LiF}$$ to dissolve fully in acetic acid.\n\nRemember, this is a general chemistry class, and the students aren't expected to know much beyond \"like dissolves like.\" $$\\ce{LiF}$$is polar, and so is acetic acid. So to them, $$\\ce{LiF}$$ should dissolve in acetic acid.\n\nProblem is that I'm in trouble with my supervisor since I told someone that i = 2. My supervisor is telling me that the van't Hoff factor should be 1. I looked over his work to see if he accounted for the dissolving of $$\\ce{LiF}$$when calculating the mole fraction of the solute but he didn't - he just found the mole fraction of $$\\ce{LiF}$$, not the combined mole fractions of $$\\ce{Li+}$$ and $$\\ce{F-}$$.\n\nSo, what's the deal with this problem? Is there some weird exception I'm not aware of regarding $$\\ce{LiF}$$ and acetic acid? The van't Hoff factor should be 2, correct?\n\nAccording to Acid-Base Equilibria in Glacial Acetic Acid. III. Acidity Scale. Potentiometric Determination of Dissociation Constants of Acids, Bases and Salts J. Am. Chem. Soc., 1956, 78 (13), pp 2974–2979:\n\nIt is generally agreed [references 3 and 4] that acids, bases and salts are only slightly dissociated in glacial acetic acid.\n\nWhile the article does not specifically address lithium fluoride, it has quantitative data for lithium chloride.\n\nLithium Chloride dissociates with a pK of 7.08 +/- 0.02 in acetic acid.\n\nSo considering the high concentration of LiF in the problem (5 in 100 grams), if LiF is similar to LiCl and the other salts studied, 1 rather than 2 is correct.\n\nThis knowledge is not part of a standard general chemistry curriculum, so unless a specific book or lecture provided relevant information, I wouldn't expect students to know this.\n\nFurthermore, the solubility of LiF in acetic acid is only 0.84 grams per kilogram according to Glacial Acetic Acid as a Non-aqueous Solvent for Metal Fluorides, so the problem is not realistic. (Only 0.084g of the 5.00 g would dissolve). Also, HF is a strong acid in acetic acid according to that paper, so LiF might even be an exception to the general observation that salts do not dissociate in acetic acid.\n\nAlso, keep in mind that in the liquid phase, acetic acid exists as mostly cyclic dimers, which gives the solvent some non-polar characteristics." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9460661,"math_prob":0.9748161,"size":1838,"snap":"2020-45-2020-50","text_gpt3_token_len":501,"char_repetition_ratio":0.14449291,"word_repetition_ratio":0.012698413,"special_character_ratio":0.2704026,"punctuation_ratio":0.10106383,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9923373,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-20T03:42:10Z\",\"WARC-Record-ID\":\"<urn:uuid:fcdb9af6-a651-4b28-a1ba-d409250849de>\",\"Content-Length\":\"147823\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9c31f0e8-6edd-471e-a6dc-35ea65671db5>\",\"WARC-Concurrent-To\":\"<urn:uuid:7bc56f7f-1499-4653-8769-950ae7a21640>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://chemistry.stackexchange.com/questions/56982/is-lif-a-weak-electrolyte-in-acetic-acid/56984\",\"WARC-Payload-Digest\":\"sha1:IIMDITCIWFCBETS3NM3GMKJL7UW7BMVL\",\"WARC-Block-Digest\":\"sha1:WQ76YD6JFC27NFUBFHR7Q3NYR4WODWEJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107869785.9_warc_CC-MAIN-20201020021700-20201020051700-00235.warc.gz\"}"}
http://blog.imxh.com/archives/3245	[ "## 花了一个晚上弄了个模版，把老域名用起来，弄个站\n\nUPDATE `dede_archives` SET `flag` = ‘c’ WHERE `flag` IS NULL ORDER BY rand() LIMIT 50;\n\n``` //替换随机图片 function add_randimg(\\$me){ \\$id=mt_rand(1,105); \\$me = str_replace(\"/images/defaultpic.gif\",\"/uploads/rand/a (\".\\$id.\").jpg\",\\$me); return \\$me; } ```\n\n`[field:litpic function='add_randimg(@me)'/]`\n\n``` echo \\$idlist; ```\n\n`{dede:field name='typeid' function=\"GetTopTypename(@me)\" /}`\n\n``` //获取顶级栏目名 function GetTopTypename(\\$id) { global \\$dsql; \\$row = \\$dsql->GetOne(\"SELECT typename,topid FROM #@__arctype WHERE id= \\$id\"); if (\\$row['topid'] == '0') { return \\$row['typename']; } else { \\$row1 = \\$dsql->GetOne(\"SELECT typename FROM #@__arctype WHERE id= \\$row[topid]\"); return \\$row1['typename']; } } ```" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.56317955,"math_prob":0.8301257,"size":1097,"snap":"2020-34-2020-40","text_gpt3_token_len":631,"char_repetition_ratio":0.08874657,"word_repetition_ratio":0.0,"special_character_ratio":0.2698268,"punctuation_ratio":0.15189873,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9714518,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-25T11:22:59Z\",\"WARC-Record-ID\":\"<urn:uuid:adbdf7c1-7b7c-4011-95c1-8113e8fb212e>\",\"Content-Length\":\"44587\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c191555c-b11b-4612-a303-7d6cf8db0d6b>\",\"WARC-Concurrent-To\":\"<urn:uuid:b6467dc3-5b16-4f57-b205-e33b2d8a8849>\",\"WARC-IP-Address\":\"45.124.112.98\",\"WARC-Target-URI\":\"http://blog.imxh.com/archives/3245\",\"WARC-Payload-Digest\":\"sha1:BZO2TTVGPM3L55RCJFLKKUNWKG7N4MSQ\",\"WARC-Block-Digest\":\"sha1:FGMRPYCHOGYHV3FKID7P566IV2GMV3LH\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400223922.43_warc_CC-MAIN-20200925084428-20200925114428-00753.warc.gz\"}"}
https://pxiaoer.blog/category/rust/cs110l/	[ "# CS110L-Week 2 Exercises: Ownership and structs\n\n## 第一部分：所有权\n\n``````\nfn main()\n{\n\nlet mut s = String::from(\"hello\");\nlet ref1 = &s;\nlet ref2 = &ref1;\nlet ref3 = &ref2;\n\n//s = String::from(\"goodboy\"); //错误 s\n\nprintln!(\"{}\", ref3.to_uppercase());\n}``````\n``````fn drip_drop() -> String {\n\nlet s = String::from(\"hello,world\");\n\n//return &s; //错误\n\nreturn s;\n}\n``````\n``````\nlet s1 = String::from(\"hello\");\nlet mut v = Vec::new();\nv.push(s1);\n\n//let s2: String = v; //错误\n\nlet ref s2: String = v;\nprintln!(\"{}\",s2);``````\n\n# CS110L-Week 1 Exercises: Hello world\n\n## 第一部分 helloworld\n\nhelloworld\n\ncargo 提供了命令行来创建rust项目\n\ncargo new helloworld\n\n``````➜ helloworld git:(main) ✗ tree\n.\n├── Cargo.lock\n├── Cargo.toml\n├── src\n│ └── main.rs\n└── target\n├── CACHEDIR.TAG\n└── debug\n├── build\n├── deps\n├── examples\n├── helloworld\n├── helloworld.d\n└── incremental\n└── helloworld-3gmsxxterlir4\n├── s-fw1pxstg53-1leo6ld-2439fudoc3hif\n│ ├── 15ne1gcrt9rvpglq.o\n│ ├── 18abmkatn3n4l0hu.o\n│ ├── 27s29o1kcsspusdg.o\n│ ├── 2xwm4i2jxgoiz5co.o\n│ ├── 3050lnwbirtj1yb5.o\n│ ├── dep-graph.bin\n│ ├── gp126zvew3eug9.o\n│ ├── q4wkdgq1k2s2v4m.o\n│ ├── query-cache.bin\n│ └── work-products.bin\n└── s-fw1pxstg53-1leo6ld.lock``````\n\nmain.rs 自带hello,world\n\n``````fn main() {\nprintln!(\"Hello, world!\");\n}\n``````\n\nCargo.toml是包依赖\n\n``````[package]\nname = \"helloworld\"\nversion = \"0.1.0\"\nauthors = [\"Jimmy Xiang <xxg1413@gmail.com>\"]\nedition = \"2018\"\n\n# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html\n\n[dependencies]\n``````\n\n## 第二部分 Rust语法热身\n\n`````` let n:i32 = 1;\nlet n = 1;\n\n//可变类型\nlet mut n = 0;\nn = n + 1;\n\n//Rust有两种字符串： &str和String\nlet s: &str = \"hello,world\"; //只读数据段\n\nlet mut s: String = String::from(\"hello,\");\ns.push_str(\"world\");\nprintln!(\"{}\", s);\n\n//动态数组\nlet mut v: Vec<i32> = Vec::new();\nv.push(2);\nv.push(3);\n\n//固定大小数组\nlet mut arr: [i32; 4] = [0,2,4,8];\narr = -2;\nprintln!(\"{}\", arr+arr);\n\n//迭代器\nfor i in arr.iter()\n{\nprintln!(\"{}\",i);\n}\n\n//while\nlet mut sum = 0;\nlet mut i = 0;\nwhile i < 20\n{\ni += 1;\nsum += i;\n\n}\n\nprintln!(\"sum={}\",sum);\n\n//loop 它有助于编译器对变量初始化进行一些假设。\nlet mut i = 0;\nloop {\n\ni += 1;\n\nif i == 10 {\nbreak;\n}\n}\n\nprintln!(\"i={}\",i);\n\n//函数\n\nfn mysum(a: i32, b:i32) -> i32\n{\na + b //Rust是一种基于表达式的语言，不需要分号\n\n//a + b ; 会出错\n}\n\nprintln!(\"sum={}\", mysum(1,2));``````\n\n``````use std::collections::HashSet;\n//练习\n\nfn add_n(v: Vec<i32>, n: i32) -> Vec<i32> {\n\nlet mut result: Vec<i32> = Vec::new();\n\nfor i in v.iter() {\nresult.push(i+n)\n}\n\nresult\n}\n\nfn add_n_inplace(v: &mut Vec<i32>, n: i32) {\n\nlet mut i = 0;\n\nwhile i < v.len() {\n\nv[i] = v[i] + n;\ni = i + 1;\n}\n}\n\nfn dedup(v: &mut Vec<i32>) {\n\nlet mut hs = HashSet::new();\nlet mut i = 0;\n\nwhile i < v.len() {\n\nif !hs.contains(&v[i]) {\n\nhs.insert(v[i]);\ni += 1;\n\n} else {\n\nv.remove(i);\n}\n\n}\n}\n\n#[cfg(test)]\nmod test {\nuse super::;\n\n#[test]\n}\n\n#[test]\nlet mut v = vec!;\nassert_eq!(v, vec!);\n}\n\n#[test]\nfn test_dedup() {\nlet mut v = vec![3, 1, 0, 1, 4, 4];\ndedup(&mut v);\nassert_eq!(v, vec![3, 1, 0, 4]);\n}\n}\n``````\n\n# 笔记\n\n#### 0.上节课的练习的答案\n\n```#include <stdio.h>\n#include <stdlib.h>\n#include <assert.h>\n\n// There are at least 7 bugs relating to memory on this snippet.\n// Find them all!\n\n// Vec is short for \"vector\", a common term for a resizable array.\n// For simplicity, our vector type can only hold ints.\ntypedef struct {\nint data; // Pointer to our array on the heap\nint length; // How many elements are in our array\nint capacity; // How many elements our array can hold\n} Vec;\n\nVec* vec_new() {\nVec vec; //本地变量\nvec.data = NULL;\nvec.length = 0;\nvec.capacity = 0;\nreturn &vec; //悬浮指针\n}\n\nvoid vec_push(Vec* vec, int n) {\nif (vec->length == vec->capacity) {\nint new_capacity = vec->capacity * 2;\nint* new_data = (int) malloc(new_capacity);\nassert(new_data != NULL);\n\nfor (int i = 0; i < vec->length; ++i) {\nnew_data[i] = vec->data[i];\n}\n\nvec->data = new_data; //忘记释放内存内存泄露\nvec->capacity = new_capacity;\n}\n\nvec->data[vec->length] = n; //指针的值改变了 n就改变了\n++vec->length;\n}\n\nvoid vec_free(Vec vec) {\nfree(vec);\nfree(vec->data);\n}\n\nvoid main() {\nVec* vec = vec_new();\nvec_push(vec, 107);\n\nint* n = &vec->data;\nvec_push(vec, 110);\nprintf(\"%d\\n\", n);//n 迭代失效\n\nfree(vec->data);\nvec_free(vec);// 双重释放\n}\n```\n\n## 1.Rust编写bug的一些问题\n\nRust只是比其他语言犯错更难一些，并不代表不可以犯错。而且很多逻辑错误是无关语言的。\n\n## 资源：\n\nhttps://stanford-cs242.github.io/f19/lectures/06-2-memory-safety\n\n# CS110L-#01: Welcome to CS 110L\n\n## 笔记\n\n1.为什么使用Rust\n\n2.为什么不是用C/C++？\n\n``````➜ 01 git:(main) ✗ ./a.out\n\nEnter a string:ashdasihdddddddddddddddddddddddddddddddddddddddddddddddddddddddd\n\nString in Upper Case = ASHDASIHDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD%\n➜ 01 git:(main) ✗ ./a.out\n\nEnter a string:GgaudiasSSSSSSSSSASUGDAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\n\n* stack smashing detected : terminated\n 18336 abort ./a.out``````\n\n``````char buffer;\nint bytesToCopy = packet.length;\nif (bytesToCopy < 128) {\nstrncpy(buffer, packet.data, bytesToCopy);\n}``````\n\nC/C++的内存安全问题，也有很多人搞了一些工具来检查。主要是动态分析和静态分析，动态分析需要预测输入，静态分析主要是错误非常多。\n\n``````➜ 01 git:(main) ✗ valgrind --tool=memcheck --leak-check=full ./conver\n==2022== Memcheck, a memory error detector\n==2022== Copyright (C) 2002-2017, and GNU GPL'd, by Julian Seward et al.\n==2022== Using Valgrind-3.16.1 and LibVEX; rerun with -h for copyright info\n==2022== Command: ./conver\n==2022==\n\nEnter a string:aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n\n stack smashing detected : terminated\n==2022==\n==2022== Process terminating with default action of signal 6 (SIGABRT)\n==2022== at 0x489C18B: raise (raise.c:51)\n==2022== by 0x487B858: abort (abort.c:79)\n==2022== by 0x48E63ED: __libc_message (libc_fatal.c:155)\n==2022== by 0x4988B49: __fortify_fail (fortify_fail.c:26)\n==2022== by 0x4988B15: __stack_chk_fail (stack_chk_fail.c:24)\n==2022== by 0x109245: main (convert.c:22)\nString in Upper Case = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA==2022==\n==2022== HEAP SUMMARY:\n==2022== in use at exit: 0 bytes in 0 blocks\n==2022== total heap usage: 2 allocs, 2 frees, 2,048 bytes allocated\n==2022==\n==2022== All heap blocks were freed -- no leaks are possible\n==2022==\n==2022== For lists of detected and suppressed errors, rerun with: -s\n==2022== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0)\n 2022 abort valgrind --tool=memcheck --leak-check=full ./conver``````\n\n3.为什么不是用其他有GC的语言？\n\nGC 有性能问题，垃圾一般都是丢在你家里，收集垃圾的需要敲你的门来收集垃圾。\n\n• 代价昂贵\n• 具有破坏性\n• 存在非确定性\n• 排除了手动优化的可能\n\n• 用户界面程序\n• 游戏\n• 自动驾驶\n• 支付处理\n• 高频交易\n\n4.预习\n\n``````#include <stdio.h>\n#include <stdlib.h>\n#include <assert.h>\n\n// There are at least 7 bugs relating to memory on this snippet.\n// Find them all!\n\n// Vec is short for \"vector\", a common term for a resizable array.\n// For simplicity, our vector type can only hold ints.\ntypedef struct {\nint data; // Pointer to our array on the heap\nint length; // How many elements are in our array\nint capacity; // How many elements our array can hold\n} Vec;\n\nVec* vec_new() {\nVec vec;\nvec.data = NULL;\nvec.length = 0;\nvec.capacity = 0;\nreturn &vec;\n}\n\nvoid vec_push(Vec* vec, int n) {\nif (vec->length == vec->capacity) {\nint new_capacity = vec->capacity * 2;\nint* new_data = (int) malloc(new_capacity);\nassert(new_data != NULL);\n\nfor (int i = 0; i < vec->length; ++i) {\nnew_data[i] = vec->data[i];\n}\n\nvec->data = new_data;\nvec->capacity = new_capacity;\n}\n\nvec->data[vec->length] = n;\n++vec->length;\n}\n\nvoid vec_free(Vec vec) {\nfree(vec);\nfree(vec->data);\n}\n\nvoid main() {\nVec* vec = vec_new();\nvec_push(vec, 107);\n\nint* n = &vec->data;\nvec_push(vec, 110);\nprintf(\"%d\\n\", *n);\n\nfree(vec->data);\nvec_free(vec);\n}``````\n\n 4278 segmentation fault ./pre\n\n7处错误：\n\n1. 在vec_new中，创建了一个局部变量vec，并返回了&vec\n2. vec.data 应该是vec->data = NULL\n3. vec_push中不要使用assert\n4. vec_push中vec->length没有检查，而且可以设置为unsigned\n5. free(vec->data)错误\n6. vec_free中应该先free(vec->data)\n7. vec_push 中 ++vec->length错误" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5838112,"math_prob":0.90953857,"size":5652,"snap":"2023-14-2023-23","text_gpt3_token_len":1916,"char_repetition_ratio":0.19086403,"word_repetition_ratio":0.39342266,"special_character_ratio":0.38411182,"punctuation_ratio":0.23813787,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9918178,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-09T03:39:06Z\",\"WARC-Record-ID\":\"<urn:uuid:cc9502fb-83c4-40c5-bdda-13469973d861>\",\"Content-Length\":\"119459\",\"Content-Type\":\"application/http; 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https://www.clutchprep.com/analytical-chemistry/practice-problems/148150/find-the-number-of-millimoles-of-solute-in-3-50-l-of-a-solution-that-contains-3-	[ "# Problem: Find the number of millimoles of solute in 3.50 L of a solution that contains 3.33 ppm of CuSO4.\n\n###### Problem Details\n\nFind the number of millimoles of solute in 3.50 L of a solution that contains 3.33 ppm of CuSO4.\n\nFrequently Asked Questions\n\nWhat scientific concept do you need to know in order to solve this problem?\n\nOur tutors have indicated that to solve this problem you will need to apply the Volumetric Analysis concept. You can view video lessons to learn Volumetric Analysis. Or if you need more Volumetric Analysis practice, you can also practice Volumetric Analysis practice problems.\n\nWhat is the difficulty of this problem?\n\nOur tutors rated the difficulty ofFind the number of millimoles of solute in 3.50 L of a solut...as low difficulty.\n\nHow long does this problem take to solve?\n\nOur expert Analytical Chemistry tutor, Jules took 1 minute and 36 seconds to solve this problem. You can follow their steps in the video explanation above.\n\nWhat professor is this problem relevant for?\n\nBased on our data, we think this problem is relevant for Professor Torres' class at UCF." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9224729,"math_prob":0.78565586,"size":964,"snap":"2021-04-2021-17","text_gpt3_token_len":215,"char_repetition_ratio":0.14270833,"word_repetition_ratio":0.08805031,"special_character_ratio":0.20435685,"punctuation_ratio":0.11170213,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97031516,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-20T06:12:48Z\",\"WARC-Record-ID\":\"<urn:uuid:9709b300-fc26-4b77-9780-9fa79274cb9a>\",\"Content-Length\":\"106645\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7ad73d81-3e0f-4675-b447-2a945742f02f>\",\"WARC-Concurrent-To\":\"<urn:uuid:f410ab9d-bf07-4f8b-b396-16fa6498ef0d>\",\"WARC-IP-Address\":\"18.205.129.29\",\"WARC-Target-URI\":\"https://www.clutchprep.com/analytical-chemistry/practice-problems/148150/find-the-number-of-millimoles-of-solute-in-3-50-l-of-a-solution-that-contains-3-\",\"WARC-Payload-Digest\":\"sha1:RCQEHROQNL2QDV6GZ5VL5AU662WW3BJ6\",\"WARC-Block-Digest\":\"sha1:N66OPF2NO6ZOA2SM7S3DPDMLYYFVYAGP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039379601.74_warc_CC-MAIN-20210420060507-20210420090507-00592.warc.gz\"}"}
https://www.sqlservercentral.com/articles/monitoring-job-history-using-reporting-services	[ "", null, "# Monitoring job history using Reporting Services\n\n,\n\nSQL Server Management Studio has a built-in Job Activity monitor available under the SQL Server Agent folder in SSMS. This provides a neat dialog window for easy access to all-you-need-to know about your jobs. One can also run the T-SQL command `EXEC msdb.dbo.sp_help_jobactivity`; to get job status. These cover statistics, statuses, categories, scheduled times and in-depth results of job executions.\n\nFrom time to time, handling couple of jobs is not a problem. However, it might become a problem when the number of jobs exceeds a manageable number in terms of job execution times, scheduled runs and job outcomes. The job history monitor report is a quick solution for getting general overview of your job history in graphical outcome using all the advantages of Reporting Services (SSRS). The report was prepared for monitoring the concurrent job execution and getting full overview of current situation on job activities. It can be used by DBAs, resource monitoring people, system analysts and even middle management as part of Microsoft Sharepoint implementation.\n\nThe query underneath the report is mainly constructed from three major parts worth taking a closer look for better understanding of the report.\n\n### Part A\n\nPart A is a general query for retrieving job history from system tables msdb.dbo.sysjobhistory and msdb.dbo.sysjobs. Query returns results for current day (day of execution) and does some general string conversions and calculations.\n\n```SELECT\nh.job_id\n,j.name\n,CAST( SUBSTRING(CONVERT(VARCHAR(10),h.run_date) , 5,2) +'-'\n+ SUBSTRING(CONVERT(VARCHAR(10),h.run_date) , 7,2) +'-'\n+ SUBSTRING(CONVERT(VARCHAR(10),h.run_date),1,4) + ' ' +\n+ SUBSTRING(CONVERT(VARCHAR(10),replicate('0',6-len(h.run_time)) + CAST(h.run_time AS VARCHAR)), 1, 2) + ':'\n+ SUBSTRING(CONVERT(VARCHAR(10),replicate('0',6-len(h.run_time)) + CAST(h.run_time AS VARCHAR)), 3, 2) + ':'\n+ SUBSTRING(CONVERT(VARCHAR(10),replicate('0',6-len(h.run_time)) + CAST(h.run_time AS VARCHAR)), 5, 2) AS SMALLDATETIME)\nAS JobStart\n,DATEADD(SECOND, CASE WHEN h.run_duration > 0 THEN (h.run_duration / 1000000) * (3600 * 24)\n+ (h.run_duration / 10000 % 100) * 3600\n+ (h.run_duration / 100 % 100) * 60\n+ (h.run_duration % 100) ELSE 0 END,CAST( SUBSTRING(CONVERT(VARCHAR(10),h.run_date) , 5,2) +'-'\n+ SUBSTRING(CONVERT(VARCHAR(10),h.run_date) , 7,2) +'-'\n+ SUBSTRING(CONVERT(VARCHAR(10),h.run_date),1,4) + ' ' +\n+ SUBSTRING(CONVERT(VARCHAR(10),replicate('0',6-len(h.run_time)) + CAST(h.run_time AS VARCHAR)), 1, 2) + ':'\n+ SUBSTRING(CONVERT(VARCHAR(10),replicate('0',6-len(h.run_time)) + CAST(h.run_time AS VARCHAR)), 3, 2) + ':'\n+ SUBSTRING(CONVERT(VARCHAR(10),replicate('0',6-len(h.run_time)) + CAST(h.run_time AS VARCHAR)), 5, 2) AS SMALLDATETIME))\nAS JobEND\n,outcome = CASE\nWHEN h.run_status = 0 THEN 'Fail'\nWHEN h.run_status = 1 THEN 'Success'\nWHEN h.run_status = 2 THEN 'Retry'\nWHEN h.run_status = 3 THEN 'Cancel'\nWHEN h.run_status = 4 THEN 'In progress'\nEND\nFROM sysjobhistory AS h\nJOIN sysjobs AS j\non j.job_id = h.job_id\nWHERE\nh.step_id = 0\nAND j.enabled = 1\nAND CAST(SUBSTRING(CONVERT(VARCHAR(10),h.run_date) , 5,2) +'-'\n+ SUBSTRING(CONVERT(VARCHAR(10),h.run_date) , 7,2) +'-'\n+ SUBSTRING(CONVERT(VARCHAR(10),h.run_date),1,4) AS SMALLDATETIME) = CONVERT(VARCHAR(10), GETDATE(), 121)```\n\n### Part B\n\nPart B generated and prepares the time frame. For purpose of Job history monitor report, 5 minutes time (300 seconds) interval was used. And system table master.dbo.spt_values was used as pre-prepared tally table.\n\n```SELECT\nv.number\nFROM\nmaster.dbo.spt_values AS v\nWHERE\nv.type = 'P'\nAND v.number <= 288\n```\n\n### Part C\n\nPart C generates empty rows for continuous presentation of time table used later in SSRS. It refers to previously generated part B and adds all missing 5 minutes intervals (or any other desired time interval), and creating actual time flow of a job executions on real time scale. In this part 5 minutes intervals are used again so we keep consistency throughout the query.\n\n```-- Data \"imputation\" of empty rows for all jobs.\n-- To appear in SSRS as a continous block, when job is running for more than 5 minutes\nSELECT\n,a.JobName\n,a.outcome\nFROM\n(\nSELECT\na.JobName\n,a.outcome\n,a.jobStart\n,MIN(a.TimeInterval) AS minTI\n,MAX(a.TimeInterval) AS maxTI\nFROM timeset AS a\nGROUP BY\na.JobName\n,a.outcome\n,a.jobStart\n) AS a\nINNER JOIN master.dbo.spt_values AS s\nON DATEADD(SECOND,300s.number,DATEDIFF(dd,0,GETDATE())) BETWEEN a.minTI AND a.maxTI\nWHERE\ns.type = 'P'\nAND s.number <= 288\nORDER BY TimeInterval;\nGO```\n\n### Creating report\n\nThe query is copied to SSRS and we create a general matrix in the Report designer. We show the time interval in the first column with the jobs in rows.", null, "For better readability of the matrix, some additional conditional formatting is introduced on field [outcome]. The colours of job outcome correspond to definition of job outcome introduced in Part A in select list as field {outcome}.\n\n### Executing report\n\nOnce the look of the report is finished, it is built and deployed to your reporting manager TargetServerURL. The report will come out like this:", null, "A 25% Zoom is used intentionally to stress the graphical overview of the report. The sample picture holds a minimum of 25 different job outcomes. One can immediately see concurrent jobs running and their approximate length (remember we used 5 minutes interval; each cell represents 5 minutes). The far left is the timeline continuing with all jobs (in this sample, jobs are sorted alphabetically). The colours denote the job results as prepared in report builder with the SWITCH command.\n\n### Customizing query and report\n\nA quick guide on how to customize the query. If 1 minute (or any other desired time frame will be used; e.g.: 30 minutes) is what you need, two changes are needed.\n\nIn code Part B, under point (1) 300 seconds should be changed to 60 seconds (when 1 minute interval will be used) and under point (2) 288 should be changed to 1440. Point (2) is literally number of minutes per hour. 1 day = 1minute 1440 intervals (1 day = 1440 minutes); creating 1 minute timeframe. 1 day= 5 minutes288 intervals (1 day = 5288 minutes). 10 minute interval would mean 144 intervals. Respectively.\n\n```SELECT\nv.number\n/* POINT (1) / ,DATEADD(SECOND,60v.number,DATEDIFF(dd,0,GETDATE())) AS timeInterval_FROM\nFROM\nmaster.dbo.spt_values AS v\nWHERE\nv.type = 'P'\n/* POINT (2) /AND v.number <= 1440\n```\n\nThe same time alterations are applied to the code in Part C.\n\n```SELECT\n/ POINT (1) / DATEADD(SECOND,60s.number,DATEDIFF(dd,0,GETDATE())) AS TimeInterval\n,a.JobName\n,a.outcome\nFROM\n(\nSELECT\na.JobName\n,a.outcome\n,a.jobStart\n,MIN(a.TimeInterval) AS minTI\n,MAX(a.TimeInterval) AS maxTI\nFROM timeset AS a\nGROUP BY\na.JobName\n,a.outcome\n,a.jobStart\n) AS a\nINNER JOIN master.dbo.spt_values AS s\n/* POINT (2) / ON DATEADD(SECOND,60s.number,DATEDIFF(dd,0,GETDATE())) BETWEEN a.minTI AND a.maxTI\nWHERE\ns.type = 'P'\n/* POINT (3) */AND s.number <= 1440```\n\n### Conclusion\n\nThe Job History monitor report is a simple but very robust and adaptable quick T-SQL solution, using all the advantages of system job tables and SSRS. It is used for a general overview and quick pin pointing the causes and fixing problems resulting in automated job executions. The T-SQL query is quickly adaptable to any SQL Server system, one can even omit this report to only very critical daily jobs, weekly/monthly jobs, alter time intervals. Report results can be part of any scorecard or dashboard for your DBA or even management. At the same time, report can take advantages of report manager features such as zooming in/out, exporting to excel, PDF, sending as attachment in report subscription.\n\nAuthor: Tomaz Kastrun (tomaz.kastrun@gmail.com)\n\n4.42 (19)\n\n4.42 (19)" ]	[ null, "https://www.sqlservercentral.com/wp-content/mu-plugins/ssc/ssc-post-thumbnails/images/technical-article.png", null, "data:image/gif;base64,R0lGODlhAQABAPAAAPLy8v///yH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAPAAAPLy8v///yH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6742864,"math_prob":0.9212049,"size":7955,"snap":"2022-27-2022-33","text_gpt3_token_len":2072,"char_repetition_ratio":0.13168155,"word_repetition_ratio":0.14775726,"special_character_ratio":0.27064738,"punctuation_ratio":0.17672151,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95191276,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-05T14:56:35Z\",\"WARC-Record-ID\":\"<urn:uuid:bbb2af33-2005-46d5-9fb0-16506e1ebef0>\",\"Content-Length\":\"274781\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:54046183-fecd-496d-b74b-1364c76dfa3d>\",\"WARC-Concurrent-To\":\"<urn:uuid:e22b1bc2-0d28-4f8f-b3d1-1d7eebf7b987>\",\"WARC-IP-Address\":\"34.242.253.12\",\"WARC-Target-URI\":\"https://www.sqlservercentral.com/articles/monitoring-job-history-using-reporting-services\",\"WARC-Payload-Digest\":\"sha1:BMJRPMIFADGWITUQ2UQLPYWB2QSIEBXU\",\"WARC-Block-Digest\":\"sha1:IZ2ZFTCJKHL7C2MUQTBIRSA62WG6FBND\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104585887.84_warc_CC-MAIN-20220705144321-20220705174321-00723.warc.gz\"}"}
https://www.sheetzoom.com/Tips/how-to-use-ifs-function-in-excel	[ "How To Use IFS Function In Excel", null, "IFS function is a new function added to Excel and only available in the latest version of Office (EXCEL 2016, Excel Online and latest mobile excel versions). Therefore when opening an IFS function containing excel workbook in an earlier version of excel, IFS function containing cells will be shown as #NAME? error notification and become unusable.\n\nThe basic function of this is to check pre-defined conditions and then return a corresponding value which are specified by the user.\n\nThe syntax used is explained below:\n\nIFS(logical_test1, value_if_true1, [logical_test2, value_if_true2], [logical_test3, value_if_true3],…)\n\nlogical_test1: The conditional argument 1, which would be evaluated as TRUE or FALSE. (Required)\n\nvalue_if_true1: The value to be returned if the condition 1 (i.e. logical_test1) is true. This can be left empty.\n\nlogical_test2: The conditional argument 2, which would be evaluated as TRUE or FALSE. (Optional)\n\nvalue_if_true2: The value to be returned if the condition 2 (i.e. logical_test2) is true. This can be left empty.\n\nNote: Up to 127 conditions can be added to this function, following the same argument style.\n\nExample #1:\n\nConsider the following data set, the IFS function has been used to assign grades for exam marks.", null, "The used syntax is explained below.\n\n=IFS(B2>74,\"A\",B2>64,\"B\",B2>49,\"C\",B2>34,\"D\",TRUE,\"F\")\n\nB2>74,\"A\" – if B2 is greater than 74, then it will return “A”\n\nB2>64,\"B\" – if B2 is greater than 64, then it will return “B”\n\nB2>49,\"C\" – if B2 is greater than 49, then it will return “C”\n\nB2>34,\"D\" – if B2 is greater than 35, then it will return “D”\n\nTRUE,\"F\") – the values below 35 will not meet any of the above conditions, so it would be considered as ‘TRUE’ and then it will return “F”", null, "Note: The same result can be obtained using the Nested IF function. But the IFS function allows to perform it in a much easier and compact way.\n\nTips:\n\n• If a logical_test is entered without specifying a return value (i.e. value_if_true), the function will return an error message “You've entered too few arguments for this function”.\n\n• If the function is unable find a ‘TRUE’ condition, then #N/A error would be returned." ]	[ null, "https://sheetzoom.blob.core.windows.net/snackbarimages/How To Use IFS Function In Excel.png", null, "https://sheetzoom.blob.core.windows.net/snackbarimages/ifsfunction1.png", null, "https://sheetzoom.blob.core.windows.net/snackbarimages/ifsfunction2.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83915335,"math_prob":0.93176836,"size":517,"snap":"2019-43-2019-47","text_gpt3_token_len":100,"char_repetition_ratio":0.14619882,"word_repetition_ratio":0.0,"special_character_ratio":0.18955512,"punctuation_ratio":0.07608695,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98931,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-19T12:10:38Z\",\"WARC-Record-ID\":\"<urn:uuid:332fe9c3-cd19-4a17-a685-da6a00cb97ae>\",\"Content-Length\":\"39881\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f3b70627-5d68-437b-86dc-c51721f03ea1>\",\"WARC-Concurrent-To\":\"<urn:uuid:cad6c4e1-7491-49c6-a77d-1e3ebb7d65b9>\",\"WARC-IP-Address\":\"93.94.253.16\",\"WARC-Target-URI\":\"https://www.sheetzoom.com/Tips/how-to-use-ifs-function-in-excel\",\"WARC-Payload-Digest\":\"sha1:5GEHVT6FKNI3EZL7WSUVGN3J6NT6VMEW\",\"WARC-Block-Digest\":\"sha1:6A5D5NSBE45CNJUWKNH2TT6RCL43577V\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986693979.65_warc_CC-MAIN-20191019114429-20191019141929-00328.warc.gz\"}"}
https://weightle.com/bmw-z4	[ "", null, "", null, "", null, "# BMW Z4 Curb Weight in Easy-to-Read Graphs\n\n#### Choose Generation", null, "", null, "## Average weight of BMW Z4", null, "## Quick notes on BMW Z4 weight\n\n• Average weight for generation: 1452 kg (3202 lbs)\n• Difference from world average: 31 kg or 68 lbs lighter\n• Difference from world's heaviest: 2965 kg or 6538 lbs lighter\n• Load to one wheel: 363 kg (801 lbs)\n• Maximum allowable weight: 1602 kg (3532 lbs)\n• Weight to torque ratio: 4 kg per 1 Nm\n• Weight to length ratio: 3 mm per 1 kg\n• Engine capacity to weight: 1.6 cc per 1 kg\n• Pounds per 1 kW: 16 lbs/kW\n• Weightly rating: 8 / 10\n\n## 2019 BMW Z4 curb weight\n\n• 30i —1415 kg (3120 lbs)\n• 20i —1405 kg (3098 lbs)\n• M40i —1535 kg (3385 lbs)\n\n## 2019 BMW Z4 weight to consumption ratio\n\n• 30i —36 kg/mpg (79 lbs/mpg)\n• 20i —40 kg/mpg (88 lbs/mpg)\n• M40i —47 kg/mpg (104 lbs/mpg)\n\n## 2019 BMW Z4 weight to consumption ratio\n\n• 30i is 4.6% lighter than average\n• 20i is 5.3% lighter than average\n• M40i is 3.5% heavier tran average\n• Vehicle Curb weight Difference from world's smallest Weight to power ratio 0—60 mph acceleration ratio Consumption ratio\n30i 1415 kg /\n3120 lbs\n990 kg (2183 lbs) heavier 5 kg to 1 hp 277 kg/s (611 lbs/s) 236 kg/L\n(520 lbs/L)\n20i 1405 kg /\n3098 lbs\n980 kg (2161 lbs) heavier 7 kg to 1 hp 216 kg/s (476 lbs/s) 207 kg/L\n(456 lbs/L)\nM40i 1535 kg /\n3385 lbs\n1110 kg (2448 lbs) heavier 5 kg to 1 hp 357 kg/s (787 lbs/s) 216 kg/L\n(476 lbs/L)\nVehicle 30i\nCurb weight 1415 kg /\n3120 lbs\nDifference from world's smallest 990 kg (990 lbs) heavier\nWeight to power ratio 5 kg to 1 hp\n0—60 mph acceleration ratio 277 kg/s (611 lbs/s)\nConsumption ratio 236 kg/L\n(520 lbs/L)\nVehicle 20i\nCurb weight 1405 kg /\n3098 lbs\nDifference from world's smallest 980 kg (980 lbs) heavier\nWeight to power ratio 7 kg to 1 hp\n0—60 mph acceleration ratio 216 kg/s (476 lbs/s)\nConsumption ratio 207 kg/L\n(456 lbs/L)\nVehicle M40i\nCurb weight 1535 kg /\n3385 lbs\nDifference from world's smallest 1110 kg (1110 lbs) heavier\nWeight to power ratio 5 kg to 1 hp\n0—60 mph acceleration ratio 357 kg/s (787 lbs/s)\nConsumption ratio 216 kg/L\n(476 lbs/L)", null, "## Quick notes on BMW Z4 weight\n\n• Average weight for generation: 1458 kg (3215 lbs)\n• Difference from world average: 25 kg or 55 lbs lighter\n• Difference from world's heaviest: 2975 kg or 6560 lbs lighter\n• Load to one wheel: 365 kg (804 lbs)\n• Maximum allowable weight: 1608 kg (3546 lbs)\n• Weight to torque ratio: 4 kg per 1 Nm\n• Weight to length ratio: 2.9 mm per 1 kg\n• Engine capacity to weight: 1.6 cc per 1 kg\n• Pounds per 1 kW: 18 lbs/kW\n• Weightly rating: 8 / 10\n\n## 2013 BMW Z4 curb weight\n\n• 35i —1525 kg (3363 lbs)\n• 20i —1420 kg (3131 lbs)\n• 28i —1400 kg (3087 lbs)\n• 18i —1420 kg (3131 lbs)\n• 35is —1525 kg (3363 lbs)\n\n## 2013 BMW Z4 weight to consumption ratio\n\n• 35i —59 kg/mpg (130 lbs/mpg)\n• 20i —41 kg/mpg (90 lbs/mpg)\n• 28i —40 kg/mpg (88 lbs/mpg)\n• 18i —41 kg/mpg (90 lbs/mpg)\n• 35is —59 kg/mpg (130 lbs/mpg)\n\n## 2013 BMW Z4 weight to consumption ratio\n\n• 35i is 2.8% heavier tran average\n• 20i is 4.2% lighter than average\n• 28i is 5.6% lighter than average\n• 18i is 4.2% lighter than average\n• 35is is 2.8% heavier tran average\n• Vehicle Curb weight Difference from world's smallest Weight to power ratio 0—60 mph acceleration ratio Consumption ratio\n35i 1525 kg /\n3363 lbs\n1100 kg (2426 lbs) heavier 5 kg to 1 hp 318 kg/s (701 lbs/s) 169 kg/L\n(373 lbs/L)\n20i 1420 kg /\n3131 lbs\n995 kg (2194 lbs) heavier 8 kg to 1 hp 215 kg/s (474 lbs/s) 209 kg/L\n(461 lbs/L)\n28i 1400 kg /\n3087 lbs\n975 kg (2150 lbs) heavier 6 kg to 1 hp 259 kg/s (571 lbs/s) 206 kg/L\n(454 lbs/L)\n18i 1420 kg /\n3131 lbs\n995 kg (2194 lbs) heavier 9 kg to 1 hp 184 kg/s (406 lbs/s) 209 kg/L\n(461 lbs/L)\n35is 1525 kg /\n3363 lbs\n1100 kg (2426 lbs) heavier 4 kg to 1 hp 332 kg/s (732 lbs/s) 169 kg/L\n(373 lbs/L)\nVehicle 35i\nCurb weight 1525 kg /\n3363 lbs\nDifference from world's smallest 1100 kg (1100 lbs) heavier\nWeight to power ratio 5 kg to 1 hp\n0—60 mph acceleration ratio 318 kg/s (701 lbs/s)\nConsumption ratio 169 kg/L\n(373 lbs/L)\nVehicle 20i\nCurb weight 1420 kg /\n3131 lbs\nDifference from world's smallest 995 kg (995 lbs) heavier\nWeight to power ratio 8 kg to 1 hp\n0—60 mph acceleration ratio 215 kg/s (474 lbs/s)\nConsumption ratio 209 kg/L\n(461 lbs/L)\nVehicle 28i\nCurb weight 1400 kg /\n3087 lbs\nDifference from world's smallest 975 kg (975 lbs) heavier\nWeight to power ratio 6 kg to 1 hp\n0—60 mph acceleration ratio 259 kg/s (571 lbs/s)\nConsumption ratio 206 kg/L\n(454 lbs/L)\nVehicle 18i\nCurb weight 1420 kg /\n3131 lbs\nDifference from world's smallest 995 kg (995 lbs) heavier\nWeight to power ratio 9 kg to 1 hp\n0—60 mph acceleration ratio 184 kg/s (406 lbs/s)\nConsumption ratio 209 kg/L\n(461 lbs/L)\nVehicle 35is\nCurb weight 1525 kg /\n3363 lbs\nDifference from world's smallest 1100 kg (1100 lbs) heavier\nWeight to power ratio 4 kg to 1 hp\n0—60 mph acceleration ratio 332 kg/s (732 lbs/s)\nConsumption ratio 169 kg/L\n(373 lbs/L)", null, "## Quick notes on BMW Z4 weight\n\n• Average weight for generation: 1523 kg (3358 lbs)\n• Difference from world average: 40 kg or 88 lbs heavier\n• Difference from world's heaviest: 2900 kg or 6395 lbs lighter\n• Load to one wheel: 381 kg (840 lbs)\n• Maximum allowable weight: 1673 kg (3689 lbs)\n• Weight to torque ratio: 5 kg per 1 Nm\n• Weight to length ratio: 2.8 mm per 1 kg\n• Engine capacity to weight: 1.7 cc per 1 kg\n• Pounds per 1 kW: 18 lbs/kW\n• Weightly rating: 8 / 10\n\n## 2010 BMW Z4 curb weight\n\n• 28i —1475 kg (3252 lbs)\n• 35i —1580 kg (3484 lbs)\n• 20i —1470 kg (3241 lbs)\n• 30i —1505 kg (3319 lbs)\n• 23i —1505 kg (3319 lbs)\n• 35 is —1600 kg (3528 lbs)\n\n## 2010 BMW Z4 weight to consumption ratio\n\n• 28i —42 kg/mpg (93 lbs/mpg)\n• 35i —63 kg/mpg (139 lbs/mpg)\n• 20i —42 kg/mpg (93 lbs/mpg)\n• 30i —54 kg/mpg (119 lbs/mpg)\n• 23i —52 kg/mpg (115 lbs/mpg)\n• 35 is —62 kg/mpg (137 lbs/mpg)\n\n## 2010 BMW Z4 weight to consumption ratio\n\n• 28i is 0.5% lighter than average\n• 35i is 6.5% heavier tran average\n• 20i is 0.9% lighter than average\n• 30i is 1.5% heavier tran average\n• 23i is 1.5% heavier tran average\n• 35 is is 7.9% heavier tran average\n• Vehicle Curb weight Difference from world's smallest Weight to power ratio 0—60 mph acceleration ratio Consumption ratio\n28i 1475 kg /\n3252 lbs\n1050 kg (2315 lbs) heavier 6 kg to 1 hp 273 kg/s (602 lbs/s) 217 kg/L\n(478 lbs/L)\n35i 1580 kg /\n3484 lbs\n1155 kg (2547 lbs) heavier 5 kg to 1 hp 322 kg/s (710 lbs/s) 168 kg/L\n(370 lbs/L)\n20i 1470 kg /\n3241 lbs\n1045 kg (2304 lbs) heavier 8 kg to 1 hp 223 kg/s (492 lbs/s) 216 kg/L\n(476 lbs/L)\n30i 1505 kg /\n3319 lbs\n1080 kg (2382 lbs) heavier 6 kg to 1 hp 259 kg/s (571 lbs/s) 181 kg/L\n(399 lbs/L)\n23i 1505 kg /\n3319 lbs\n1080 kg (2382 lbs) heavier 7 kg to 1 hp 218 kg/s (481 lbs/s) 184 kg/L\n(406 lbs/L)\n35 is 1600 kg /\n3528 lbs\n1175 kg (2591 lbs) heavier 5 kg to 1 hp 348 kg/s (767 lbs/s) 178 kg/L\n(392 lbs/L)\nVehicle 28i\nCurb weight 1475 kg /\n3252 lbs\nDifference from world's smallest 1050 kg (1050 lbs) heavier\nWeight to power ratio 6 kg to 1 hp\n0—60 mph acceleration ratio 273 kg/s (602 lbs/s)\nConsumption ratio 217 kg/L\n(478 lbs/L)\nVehicle 35i\nCurb weight 1580 kg /\n3484 lbs\nDifference from world's smallest 1155 kg (1155 lbs) heavier\nWeight to power ratio 5 kg to 1 hp\n0—60 mph acceleration ratio 322 kg/s (710 lbs/s)\nConsumption ratio 168 kg/L\n(370 lbs/L)\nVehicle 20i\nCurb weight 1470 kg /\n3241 lbs\nDifference from world's smallest 1045 kg (1045 lbs) heavier\nWeight to power ratio 8 kg to 1 hp\n0—60 mph acceleration ratio 223 kg/s (492 lbs/s)\nConsumption ratio 216 kg/L\n(476 lbs/L)\nVehicle 30i\nCurb weight 1505 kg /\n3319 lbs\nDifference from world's smallest 1080 kg (1080 lbs) heavier\nWeight to power ratio 6 kg to 1 hp\n0—60 mph acceleration ratio 259 kg/s (571 lbs/s)\nConsumption ratio 181 kg/L\n(399 lbs/L)\nVehicle 23i\nCurb weight 1505 kg /\n3319 lbs\nDifference from world's smallest 1080 kg (1080 lbs) heavier\nWeight to power ratio 7 kg to 1 hp\n0—60 mph acceleration ratio 218 kg/s (481 lbs/s)\nConsumption ratio 184 kg/L\n(406 lbs/L)\nVehicle 35 is\nCurb weight 1600 kg /\n3528 lbs\nDifference from world's smallest 1175 kg (1175 lbs) heavier\nWeight to power ratio 5 kg to 1 hp\n0—60 mph acceleration ratio 348 kg/s (767 lbs/s)\nConsumption ratio 178 kg/L\n(392 lbs/L)", null, "## Quick notes on BMW Z4 weight\n\n• Average weight for generation: 1296 kg (2858 lbs)\n• Difference from world average: 187 kg or 412 lbs lighter\n• Difference from world's heaviest: 3105 kg or 6847 lbs lighter\n• Load to one wheel: 324 kg (715 lbs)\n• Maximum allowable weight: 1446 kg (3188 lbs)\n• Weight to torque ratio: 5 kg per 1 Nm\n• Weight to length ratio: 3.2 mm per 1 kg\n• Engine capacity to weight: 1.9 cc per 1 kg\n• Pounds per 1 kW: 19 lbs/kW\n• Weightly rating: 8 / 10\n\n## 2006 BMW Z4 curb weight\n\n• 2.5 si —1290 kg (2844 lbs)\n• 3.0 si —1395 kg (3076 lbs)\n• 2.5i —1275 kg (2811 lbs)\n• 2.0i 16V —1225 kg (2701 lbs)\n\n## 2006 BMW Z4 weight to consumption ratio\n\n• 3.0 si —54 kg/mpg (119 lbs/mpg)\n\n## 2006 BMW Z4 weight to consumption ratio\n\n• 2.5 si is 13% lighter than average\n• 3.0 si is 5.9% lighter than average\n• 2.5i is 14% lighter than average\n• 2.0i 16V is 17.4% lighter than average\n• Vehicle Curb weight Difference from world's smallest Weight to power ratio 0—60 mph acceleration ratio Consumption ratio\n2.5 si 1290 kg /\n2844 lbs\n865 kg (1907 lbs) heavier 6 kg to 1 hp 208 kg/s (459 lbs/s) -\n3.0 si 1395 kg /\n3076 lbs\n970 kg (2139 lbs) heavier 5 kg to 1 hp 258 kg/s (569 lbs/s) 157 kg/L\n(346 lbs/L)\n2.5i 1275 kg /\n2811 lbs\n850 kg (1874 lbs) heavier 7 kg to 1 hp 190 kg/s (419 lbs/s) -\n2.0i 16V 1225 kg /\n2701 lbs\n800 kg (1764 lbs) heavier 8 kg to 1 hp 157 kg/s (346 lbs/s) -\nVehicle 2.5 si\nCurb weight 1290 kg /\n2844 lbs\nDifference from world's smallest 865 kg (865 lbs) heavier\nWeight to power ratio 6 kg to 1 hp\n0—60 mph acceleration ratio 208 kg/s (459 lbs/s)\nConsumption ratio -\nVehicle 3.0 si\nCurb weight 1395 kg /\n3076 lbs\nDifference from world's smallest 970 kg (970 lbs) heavier\nWeight to power ratio 5 kg to 1 hp\n0—60 mph acceleration ratio 258 kg/s (569 lbs/s)\nConsumption ratio 157 kg/L\n(346 lbs/L)\nVehicle 2.5i\nCurb weight 1275 kg /\n2811 lbs\nDifference from world's smallest 850 kg (850 lbs) heavier\nWeight to power ratio 7 kg to 1 hp\n0—60 mph acceleration ratio 190 kg/s (419 lbs/s)\nConsumption ratio -\nVehicle 2.0i 16V\nCurb weight 1225 kg /\n2701 lbs\nDifference from world's smallest 800 kg (800 lbs) heavier\nWeight to power ratio 8 kg to 1 hp\n0—60 mph acceleration ratio 157 kg/s (346 lbs/s)\nConsumption ratio -", null, "## Quick notes on BMW Z4 weight\n\n• Average weight for generation: 1325 kg (2922 lbs)\n• Difference from world average: 158 kg or 348 lbs lighter\n• Difference from world's heaviest: 3175 kg or 7001 lbs lighter\n• Load to one wheel: 331 kg (731 lbs)\n• Maximum allowable weight: 1475 kg (3252 lbs)\n• Weight to torque ratio: 4 kg per 1 Nm\n• Weight to length ratio: 3.1 mm per 1 kg\n• Engine capacity to weight: 2.3 cc per 1 kg\n• Pounds per 1 kW: 15 lbs/kW\n• Weightly rating: 6 / 10\n\n## 2006 BMW Z4 curb weight\n\n• 3.0 si —1325 kg (2922 lbs)\n\n## 2006 BMW Z4 weight to consumption ratio\n\n• 3.0 si is 10.7% lighter than average\n• Vehicle Curb weight Difference from world's smallest Weight to power ratio 0—60 mph acceleration ratio Consumption ratio\n3.0 si 1325 kg /\n2922 lbs\n900 kg (1985 lbs) heavier 5 kg to 1 hp 245 kg/s (540 lbs/s) -\nVehicle 3.0 si\nCurb weight 1325 kg /\n2922 lbs\nDifference from world's smallest 900 kg (900 lbs) heavier\nWeight to power ratio 5 kg to 1 hp\n0—60 mph acceleration ratio 245 kg/s (540 lbs/s)\nConsumption ratio -", null, "## Quick notes on BMW Z4 weight\n\n• Average weight for generation: 1415 kg (3120 lbs)\n• Difference from world average: 68 kg or 150 lbs lighter\n• Difference from world's heaviest: 3085 kg or 6803 lbs lighter\n• Load to one wheel: 354 kg (780 lbs)\n• Maximum allowable weight: 1565 kg (3451 lbs)\n• Weight to torque ratio: 4 kg per 1 Nm\n• Weight to length ratio: 2.9 mm per 1 kg\n• Engine capacity to weight: 2.3 cc per 1 kg\n• Pounds per 1 kW: 12 lbs/kW\n• Weightly rating: 8 / 10\n\n## 2006 BMW Z4 curb weight\n\n• 3.2 —1415 kg (3120 lbs)\n\n## 2006 BMW Z4 weight to consumption ratio\n\n• 3.2 is 4.6% lighter than average\n• Vehicle Curb weight Difference from world's smallest Weight to power ratio 0—60 mph acceleration ratio Consumption ratio\n3.2 1415 kg /\n3120 lbs\n990 kg (2183 lbs) heavier 4 kg to 1 hp 295 kg/s (650 lbs/s) -\nVehicle 3.2\nCurb weight 1415 kg /\n3120 lbs\nDifference from world's smallest 990 kg (990 lbs) heavier\nWeight to power ratio 4 kg to 1 hp\n0—60 mph acceleration ratio 295 kg/s (650 lbs/s)\nConsumption ratio -", null, "## Quick notes on BMW Z4 weight\n\n• Average weight for generation: 1425 kg (3142 lbs)\n• Difference from world average: 58 kg or 128 lbs lighter\n• Difference from world's heaviest: 3075 kg or 6781 lbs lighter\n• Load to one wheel: 356 kg (786 lbs)\n• Maximum allowable weight: 1575 kg (3473 lbs)\n• Weight to torque ratio: 4 kg per 1 Nm\n• Weight to length ratio: 2.9 mm per 1 kg\n• Engine capacity to weight: 2.3 cc per 1 kg\n• Pounds per 1 kW: 12 lbs/kW\n• Weightly rating: 8 / 10\n\n## 2006 BMW Z4 curb weight\n\n• 3.2 —1425 kg (3142 lbs)\n\n## 2006 BMW Z4 weight to consumption ratio\n\n• 3.2 —75 kg/mpg (165 lbs/mpg)\n\n## 2006 BMW Z4 weight to consumption ratio\n\n• 3.2 is 3.9% lighter than average\n• Vehicle Curb weight Difference from world's smallest Weight to power ratio 0—60 mph acceleration ratio Consumption ratio\n3.2 1425 kg /\n3142 lbs\n1000 kg (2205 lbs) heavier 4 kg to 1 hp 297 kg/s (655 lbs/s) 118 kg/L\n(260 lbs/L)\nVehicle 3.2\nCurb weight 1425 kg /\n3142 lbs\nDifference from world's smallest 1000 kg (1000 lbs) heavier\nWeight to power ratio 4 kg to 1 hp\n0—60 mph acceleration ratio 297 kg/s (655 lbs/s)\nConsumption ratio 118 kg/L\n(260 lbs/L)", null, "## Quick notes on BMW Z4 weight\n\n• Average weight for generation: 1342 kg (2959 lbs)\n• Difference from world average: 141 kg or 311 lbs lighter\n• Difference from world's heaviest: 3135 kg or 6913 lbs lighter\n• Load to one wheel: 336 kg (740 lbs)\n• Maximum allowable weight: 1492 kg (3290 lbs)\n• Weight to torque ratio: 5 kg per 1 Nm\n• Weight to length ratio: 3 mm per 1 kg\n• Engine capacity to weight: 1.9 cc per 1 kg\n• Pounds per 1 kW: 20 lbs/kW\n• Weightly rating: 8 / 10\n\n## 2002 BMW Z4 curb weight\n\n• 2.2i —1325 kg (2922 lbs)\n• 2.5i —1335 kg (2944 lbs)\n• 3.0i —1365 kg (3010 lbs)\n\n## 2002 BMW Z4 weight to consumption ratio\n\n• 2.2i —41 kg/mpg (90 lbs/mpg)\n• 2.5i —42 kg/mpg (93 lbs/mpg)\n• 3.0i —44 kg/mpg (97 lbs/mpg)\n\n## 2002 BMW Z4 weight to consumption ratio\n\n• 2.2i is 10.7% lighter than average\n• 2.5i is 10% lighter than average\n• 3.0i is 8% lighter than average\n• Vehicle Curb weight Difference from world's smallest Weight to power ratio 0—60 mph acceleration ratio Consumption ratio\n2.2i 1325 kg /\n2922 lbs\n900 kg (1985 lbs) heavier 8 kg to 1 hp 182 kg/s (401 lbs/s) 182 kg/L\n(401 lbs/L)\n2.5i 1335 kg /\n2944 lbs\n910 kg (2007 lbs) heavier 7 kg to 1 hp 199 kg/s (439 lbs/s) 180 kg/L\n(397 lbs/L)\n3.0i 1365 kg /\n3010 lbs\n940 kg (2073 lbs) heavier 6 kg to 1 hp 244 kg/s (538 lbs/s) 182 kg/L\n(401 lbs/L)\nVehicle 2.2i\nCurb weight 1325 kg /\n2922 lbs\nDifference from world's smallest 900 kg (900 lbs) heavier\nWeight to power ratio 8 kg to 1 hp\n0—60 mph acceleration ratio 182 kg/s (401 lbs/s)\nConsumption ratio 182 kg/L\n(401 lbs/L)\nVehicle 2.5i\nCurb weight 1335 kg /\n2944 lbs\nDifference from world's smallest 910 kg (910 lbs) heavier\nWeight to power ratio 7 kg to 1 hp\n0—60 mph acceleration ratio 199 kg/s (439 lbs/s)\nConsumption ratio 180 kg/L\n(397 lbs/L)\nVehicle 3.0i\nCurb weight 1365 kg /\n3010 lbs\nDifference from world's smallest 940 kg (940 lbs) heavier\nWeight to power ratio 6 kg to 1 hp\n0—60 mph acceleration ratio 244 kg/s (538 lbs/s)\nConsumption ratio 182 kg/L\n(401 lbs/L)" ]	[ null, "https://weightle.com/images/search.png", null, "https://weightle.com/images/close.png", null, "https://weightle.com/images/menu.png", null, "https://weightle.com/images/next-white.png", null, "https://weightle.com/images/next-white.png", null, "https://weightle.com/images/autowebp/bmw-z4-2018-g29.webp", null, "https://weightle.com/images/autowebp/bmw-z4-2013-e89-facelift-2013.webp", null, "https://weightle.com/images/autowebp/bmw-z4-2009-e89-2011.webp", null, "https://weightle.com/images/autowebp/bmw-z4-2006-e85-facelift-2006.webp", null, "https://weightle.com/images/autowebp/bmw-z4-2006-coupe-e86.webp", null, "https://weightle.com/images/autowebp/bmw-z4-2006-m-e85.webp", null, 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https://kr.mathworks.com/matlabcentral/answers/158402-plot-with-different-symbols	[ "plot with different symbols\n\n조회 수: 66(최근 30일)\nNiki 2014년 10월 13일\n편집: Stephen 2014년 10월 13일\nI have two vectors with 1000 length each. for example\nr1 = rand(1000,1); r2 = rand(1000,1); then I want to plot a scatter which shows r1 versus r2 as follows:\nplot(r1, r2) I want to show each two values of r1 and 2 with the same symbol but different from the rest. any suggestion ?\n댓글 수: 1표시숨기기 없음\nStephen 2014년 10월 13일\nMATLAB has thirteen different plot symbols. How do you wish to divide up 1000 points?\n\n댓글을 달려면 로그인하십시오.\n\n답변(1개)\n\nIain 2014년 10월 13일\nr1 = rand(1,1000);\nr2 = rand(1,1000);\nplot(1:1000,r1,'bx',1:1000,r2,'kx')\nChange the x to +, d, s, o for other symbols....\n댓글 수: 1표시숨기기 없음\nNiki 2014년 10월 13일\nThanks for your comment. But not really if I wanted to do such time consuming way to plot, it was much easier to do it in other ways. I am more thinking to find a more automatic way\n\n댓글을 달려면 로그인하십시오.\n\nCommunity Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7010583,"math_prob":0.9471821,"size":627,"snap":"2022-05-2022-21","text_gpt3_token_len":240,"char_repetition_ratio":0.10593901,"word_repetition_ratio":0.0,"special_character_ratio":0.37161085,"punctuation_ratio":0.19875777,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9770921,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-27T06:30:29Z\",\"WARC-Record-ID\":\"<urn:uuid:a00ba323-c589-4d5c-b395-3841f1a1205d>\",\"Content-Length\":\"113158\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:77e8eaa7-2fb0-4eff-9d4e-fb58c4936e12>\",\"WARC-Concurrent-To\":\"<urn:uuid:2ce823c2-9817-412a-9f00-6600625a8f79>\",\"WARC-IP-Address\":\"104.68.243.15\",\"WARC-Target-URI\":\"https://kr.mathworks.com/matlabcentral/answers/158402-plot-with-different-symbols\",\"WARC-Payload-Digest\":\"sha1:YXWSMIE2X3QAYYUBMCKZ76ILOD5HMAE4\",\"WARC-Block-Digest\":\"sha1:DEV4NHBRZT6ZRH3222MJPQEDSEDKG3CX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320305141.20_warc_CC-MAIN-20220127042833-20220127072833-00651.warc.gz\"}"}
http://erlang.org/pipermail/erlang-questions/2009-May/043844.html	[ "[erlang-questions] At what point am I \"playing compiler\"\n\nPer Melin <", null, ">\nSun May 17 22:40:18 CEST 2009\n\n```Dennis Byrne:\n> The functions expressive/0 and efficient/0 have the same result.\n> Sometimes I prefer expressive syntax but I am concerned about\n> the compilers (or runtime) make these concerns obselete?\n>\n> expressive() ->\n> List = [1,2,3],\n> Last = lists:last(List),\n> Min = lists:foldl(fun min/2, Last, List),\n> Max = lists:foldl(fun max/2, Last, List),\n> Sum = lists:foldl(fun sum/2, 0, List),\n> {Min, Max, Sum}.\n>\n> efficient() ->\n> List = [1,2,3],\n> Last = lists:last(List),\n> lists:foldl(fun summary/2, {Last, Last, 0}, List).\n>\n> summary(X, {Min, Max, Total}) ->\n> {min(X, Min), max(X, Max), Total + X}.\n>\n> sum(X, Y) ->\n> X + Y.\n>\n> min(X, Y) when X < Y ->\n> X;\n> min(_, Y) ->\n> Y.\n>\n> max(X, Y) when X > Y ->\n> X;\n> max(_, Y) ->\n> Y.\n\nexpressive_and_efficient() ->\nList = [1,2,3],\n{lists:min(List), lists:max(List), lists:sum(List)}.\n\n:-)\n\nI run micro-benchmarks obsessively. On my machine expressive() is 70%\nslower than efficient() without HIPE and 150% slower with HIPE. But\nwe're talking fractions of a microsecond per execution. Should you\nbother?\n\nIf you're concerned with efficiency, timer:tc/3 is your friend. Stuff\nlike this you should obviously loop at least a few million times to\nget reliable times.\n\n```" ]	[ null, "http://erlang.org/pipermail/erlang-questions/emailaddrs/ema-4112.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.78046167,"math_prob":0.9413878,"size":1454,"snap":"2019-26-2019-30","text_gpt3_token_len":445,"char_repetition_ratio":0.13310345,"word_repetition_ratio":0.05668016,"special_character_ratio":0.35075653,"punctuation_ratio":0.2356688,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97507966,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-19T09:00:41Z\",\"WARC-Record-ID\":\"<urn:uuid:f78fe9f5-2bbf-49d6-81cd-6ad8673ff999>\",\"Content-Length\":\"5094\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7c9b4e63-5ec7-41fd-8815-0cf1e96163dd>\",\"WARC-Concurrent-To\":\"<urn:uuid:16485a43-3fae-4637-881b-2da40f0d8310>\",\"WARC-IP-Address\":\"192.121.151.106\",\"WARC-Target-URI\":\"http://erlang.org/pipermail/erlang-questions/2009-May/043844.html\",\"WARC-Payload-Digest\":\"sha1:6ZBC4R3U6SVVXGCKXZGWGQBB2TQSHWDL\",\"WARC-Block-Digest\":\"sha1:MFLHSRNHFBY3OQCEPGA4JFTWYMKX3NSJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627998943.53_warc_CC-MAIN-20190619083757-20190619105757-00531.warc.gz\"}"}
https://phys.org/tags/wavelength+of+light/	[ "# News tagged with wavelength of light\n\nRelated topics: light\n\npage 1 from 18\n\n## Wavelength\n\nIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves. Wavelength is commonly designated by the Greek letter lambda (λ). The concept can also be applied to periodic waves of non-sinusoidal shape. The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.\n\nAssuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.\n\nExamples of wave-like phenomena are sound waves, light, and water waves. A sound wave is a periodic variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary. Water waves are periodic variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary periodically in both lattice position and time.\n\nWavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in waves over deep water a particle in the water moves in a circle of the same diameter as the wave height, unrelated to wavelength.\n\nThis text uses material from Wikipedia, licensed under CC BY-SA" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9330816,"math_prob":0.98601973,"size":1608,"snap":"2021-21-2021-25","text_gpt3_token_len":307,"char_repetition_ratio":0.13902743,"word_repetition_ratio":0.0,"special_character_ratio":0.18221393,"punctuation_ratio":0.10380623,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96380806,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-11T21:14:17Z\",\"WARC-Record-ID\":\"<urn:uuid:c76b6a62-dd80-42e4-9fc0-ba6668866f1d>\",\"Content-Length\":\"65677\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:46e40d52-2baf-4ea8-92c7-b87d5abbed8d>\",\"WARC-Concurrent-To\":\"<urn:uuid:b355c953-aefa-475f-9452-aa22f38a9977>\",\"WARC-IP-Address\":\"72.251.236.55\",\"WARC-Target-URI\":\"https://phys.org/tags/wavelength+of+light/\",\"WARC-Payload-Digest\":\"sha1:WAADQKATZANNJZBF5VQZIYAEENPGV4TU\",\"WARC-Block-Digest\":\"sha1:MMDSLBQ6FDGAAUYGFCLZKMA4OIYPLH42\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989856.11_warc_CC-MAIN-20210511184216-20210511214216-00352.warc.gz\"}"}
http://bims.iranjournals.ir/article_364.html	[ "# The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2\n\nDocument Type: Research Paper\n\nAuthors\n\nAbstract\n\nLet $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$.\nAn $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($RAS =-A$).\nThe $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have\na number of special properties and widely used in engineering and\nscientific computating. Here, we introduce the necessary and\nsufficient conditions for the solvability of the pair of matrix\nequations $A_{1}XB_{1}=C_{1}$ and $A_{2}XB_{2}=C_{2}$, over $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices, and give the\ngeneral expressions of the solutions for the solvable cases.\nFinally, we give necessary and sufficient conditions for the\nexistence of $(R, S)$-symmetric and $(R, S)$-skew symmetric\nsolutions and representations of these solutions to the pair of\nmatrix equations in some special cases.\n\nKeywords\n\n### History\n\n• Receive Date: 03 February 2009\n• Revise Date: 15 March 2012\n• Accept Date: 17 March 2010" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7203532,"math_prob":0.9993986,"size":1826,"snap":"2020-24-2020-29","text_gpt3_token_len":601,"char_repetition_ratio":0.17837541,"word_repetition_ratio":0.33828998,"special_character_ratio":0.322563,"punctuation_ratio":0.18877551,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99997103,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-27T14:22:42Z\",\"WARC-Record-ID\":\"<urn:uuid:cd9aee0b-4a3a-45b5-ba37-51830752619a>\",\"Content-Length\":\"41869\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c4ee5e5b-bcd3-4364-ac20-fec2784bf079>\",\"WARC-Concurrent-To\":\"<urn:uuid:822e7298-557e-457a-a6a8-a99f49e7b43a>\",\"WARC-IP-Address\":\"217.182.166.236\",\"WARC-Target-URI\":\"http://bims.iranjournals.ir/article_364.html\",\"WARC-Payload-Digest\":\"sha1:2EJNWP74AARUSS6REJNPSTEMVENXLF6U\",\"WARC-Block-Digest\":\"sha1:2KCGIS6QCAWDRZBNHKX3SXJN53NCGPQC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347394756.31_warc_CC-MAIN-20200527141855-20200527171855-00579.warc.gz\"}"}
https://codekomusic.com/qa/is-vlookup-useful.html	[ "", null, "# Is Vlookup Useful?\n\n## Is Vlookup obsolete?\n\nVLOOKUP is an obsolete function inherited from Lotus-123.\n\nThere is much better in Excel, more powerful and less limited, it is INDEX/MATCH.\n\nINDEX/MATCH replaces all lookups functions (VLOOKUP, HLOOKUP and LOOKUP)..\n\n## What is pivoting in Excel?\n\nA Pivot Table is used to summarise, sort, reorganise, group, count, total or average data stored in a table. It allows us to transform columns into rows and rows into columns. It allows grouping by any field (column), and using advanced calculations on them.\n\n## Where is Vlookup in Excel?\n\nHow to use VLOOKUP in ExcelClick the cell where you want the VLOOKUP formula to be calculated. … Click “Formula” at the top of the screen. … Click “Lookup & Reference” on the Ribbon. … Click “VLOOKUP” at the bottom of the drop-down menu. … Specify the cell in which you will enter the value whose data you’re looking for.More items…•May 4, 2020\n\n## Can you use Vlookup and Hlookup together?\n\nVLOOKUP and HLOOKUP are two of the most popular formulas in Excel and using them together is one of the first formula combinations that people learn. … Both of these contexts make it worthwhile to learn VLOOKUP HLOOKUP.\n\n## What are the limitations of Vlookup?\n\nLimitations of VLOOKUP One major limitation of VLOOKUP is that it cannot look to the left. The values to lookup must always be on the left-most column of the range and the values to return must be on the right hand side. You cannot use the standard VLOOKUP to look at the columns and the rows to find an exact match.\n\n## What is better than Vlookup?\n\nWith sorted data and an approximate match, INDEX-MATCH is about 30% faster than VLOOKUP. With sorted data and a fast technique to find an exact match, INDEX-MATCH is about 13% faster than VLOOKUP. … If you use VLOOKUP you must look up the same SKU for each column of information you need.\n\n## What is pivot table in simple words?\n\nA pivot table is a table of statistics that summarizes the data of a more extensive table (such as from a database, spreadsheet, or business intelligence program). … Pivot tables are a technique in data processing. They arrange and rearrange (or “pivot”) statistics in order to draw attention to useful information.\n\n## Who invented Excel?\n\nMicrosoft ExcelA simple line chart being created in Excel, running on Windows 10Developer(s)MicrosoftInitial release1987Stable release2103 (16.0.13901.20336) / April 2, 2021Operating systemMicrosoft Windows6 more rows\n\n## Who invented Excel formulas?\n\nDan BricklinDan Bricklin invented the spreadsheet—but don’t hold that against him. The father of the spreadsheet. December 22, 2015 This article is more than 2 years old. You may not know Dan Bricklin, but you are almost certainly familiar with his work.\n\n## What is Hlookup formula in Excel?\n\nHLOOKUP in Excel stands for ‘Horizontal Lookup’. It is a function that makes Excel search for a certain value in a row (the so called ‘table array’), in order to return a value from a different row in the same column.\n\n## How use Vlookup step by step?\n\nHow to use VLOOKUP in ExcelStep 1: Organize the data. … Step 2: Tell the function what to lookup. … Step 3: Tell the function where to look. … Step 4: Tell Excel what column to output the data from. … Step 5: Exact or approximate match.\n\n## Who invented Vlookup?\n\nBill Jelen: “From 1979 – VisiCalc and LOOKUP”! In Bill’s last installment for VLOOKUP WEEK 2012, we go back to 1979…VisiCalc and the whole ’20 Functions’ available in that time! There were no IF statements and there was no VLOOKUP…but there was ‘LOOKUP’. Follow along and see where VLOOKUP began!\n\n## What is Vlookup in Excel example?\n\nThe VLOOKUP function in Excel performs a case-insensitive lookup. For example, the VLOOKUP function below looks up MIA (cell G2) in the leftmost column of the table. Explanation: the VLOOKUP function is case-insensitive so it looks up MIA or Mia or mia or miA, etc.\n\n## Why Hlookup is used in Excel?\n\nWhat is the HLOOKUP Function? HLOOKUP stands for Horizontal Lookup and can be used to retrieve information from a table by searching a row for the matching data and outputting from the corresponding column. While VLOOKUP searches for the value in a column, HLOOKUP searches for the value in a row.\n\n## How do I compare two lists in Excel?\n\nThe quickest way to find all about two lists is to select them both and them click on Conditional Formatting -> Highlight cells rules -> Duplicate Values (Excel 2007). The result is that it highlights in both lists the values that ARE the same.\n\n## How do I match data in Excel?\n\nCompare Two Columns and Highlight MatchesSelect the entire data set.Click the Home tab.In the Styles group, click on the ‘Conditional Formatting’ option.Hover the cursor on the Highlight Cell Rules option.Click on Duplicate Values.In the Duplicate Values dialog box, make sure ‘Duplicate’ is selected.More items…\n\n## What to do when Vlookup returns NA?\n\nProblem: The lookup column is not sorted in the ascending orderChange the VLOOKUP function to look for an exact match. To do that, set the range_lookup argument to FALSE. No sorting is necessary for FALSE.Use the INDEX/MATCH function to look up a value in an unsorted table.\n\n## Why would I use a Vlookup?\n\nWhen you need to find information in a large spreadsheet, or you are always looking for the same kind of information, use the VLOOKUP function. VLOOKUP works a lot like a phone book, where you start with the piece of data you know, like someone’s name, in order to find out what you don’t know, like their phone number.\n\nIt can not lookup and return a value which is to the left of the lookup value. It works only with data which is arranged vertically. VLOOKUP would give a wrong result if you add/delete a new column in your data (as the column number value now refers to the wrong column).\n\n## What is Vlookup in simple words?\n\nVLOOKUP stands for ‘Vertical Lookup’. It is a function that makes Excel search for a certain value in a column (the so called ‘table array’), in order to return a value from a different column in the same row.\n\n## What does Vlookup return?\n\nIn its simplest form, the VLOOKUP function says: =VLOOKUP(What you want to look up, where you want to look for it, the column number in the range containing the value to return, return an Approximate or Exact match – indicated as 1/TRUE, or 0/FALSE).\n\n## What is an Hlookup vs Vlookup?\n\nHLookup searches for a value in the top row of a table and then returns a value in the same column. The VLookup function displays the searched value in the same row but in the next column." ]	[ null, "https://mc.yandex.ru/watch/66676240", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8268373,"math_prob":0.6516607,"size":7186,"snap":"2021-21-2021-25","text_gpt3_token_len":1697,"char_repetition_ratio":0.16805904,"word_repetition_ratio":0.098101266,"special_character_ratio":0.22543836,"punctuation_ratio":0.112280704,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9554147,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-06T12:47:15Z\",\"WARC-Record-ID\":\"<urn:uuid:6e72faa2-1b50-4694-bce7-a8de5ca55eee>\",\"Content-Length\":\"48224\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ed36aaa8-391d-44cb-ada5-e311c5296fed>\",\"WARC-Concurrent-To\":\"<urn:uuid:15ef0311-cf4f-44bd-bc56-77e3bf5d845a>\",\"WARC-IP-Address\":\"87.236.16.235\",\"WARC-Target-URI\":\"https://codekomusic.com/qa/is-vlookup-useful.html\",\"WARC-Payload-Digest\":\"sha1:YRJVZW5YFURX7EN4IW53RM7XMZRZQXT6\",\"WARC-Block-Digest\":\"sha1:632HZCTXI5IJ5JF5LQ7XEX7HCAFJFX7O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988753.97_warc_CC-MAIN-20210506114045-20210506144045-00458.warc.gz\"}"}
https://zbmath.org/?q=an%3A1308.90166	[ "# zbMATH — the first resource for mathematics\n\nOn the use of iterative methods in cubic regularization for unconstrained optimization. (English) Zbl 1308.90166\nSummary: In this paper we consider the problem of minimizing a smooth function by using the adaptive cubic regularized (ARC) framework. We focus on the computation of the trial step as a suitable approximate minimizer of the cubic model and discuss the use of matrix-free iterative methods. Our approach is alternative to the implementation proposed in the original version of ARC, involving a linear algebra phase, but preserves the same worst-case complexity count. Further we introduce a new stopping criterion in order to properly manage the “over-solving” issue arising whenever the cubic model is not an adequate model of the true objective function. Numerical experiments conducted by using a nonmonotone gradient method as inexact solver are presented. The obtained results clearly show the effectiveness of the new variant of ARC algorithm.\n\n##### MSC:\n 90C30 Nonlinear programming" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6858097,"math_prob":0.88211906,"size":5290,"snap":"2021-31-2021-39","text_gpt3_token_len":1522,"char_repetition_ratio":0.13280363,"word_repetition_ratio":0.04607046,"special_character_ratio":0.31039697,"punctuation_ratio":0.2704692,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96428,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-24T14:27:15Z\",\"WARC-Record-ID\":\"<urn:uuid:edc21446-bb5c-4fbe-9fc3-a892aec28af5>\",\"Content-Length\":\"53805\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6e7fd211-3e5a-4f5e-8a37-2e1855f1487d>\",\"WARC-Concurrent-To\":\"<urn:uuid:1352ac4d-265c-45c4-9413-ec88e0837313>\",\"WARC-IP-Address\":\"141.66.194.2\",\"WARC-Target-URI\":\"https://zbmath.org/?q=an%3A1308.90166\",\"WARC-Payload-Digest\":\"sha1:EXCXOMIAD25U5246Y2BL6GBGJBFOI3IX\",\"WARC-Block-Digest\":\"sha1:WGKBM4VWSYMGG3JPLKBBMPTORR7BCQ5C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046150266.65_warc_CC-MAIN-20210724125655-20210724155655-00682.warc.gz\"}"}
https://rdrr.io/cran/compositions/man/biplot3d.html	[ "biplot3d: Three-dimensional biplots, based on package rgl In compositions: Compositional Data Analysis\n\nDescription\n\nPlots variables and cases in the same plot, based on a principal component analysis.\n\nUsage\n\n 1 2 3 4 5 6 7 8 9 10 11 biplot3D(x,...) ## Default S3 method: biplot3D(x,y,var.axes=TRUE,col=c(\"green\",\"red\"),cex=c(2,2), xlabs = NULL, ylabs = NULL, expand = 1,arrow.len = 0.1, ...,add=FALSE) ## S3 method for class 'princomp' biplot3D(x,choices=1:3,scale=1,..., comp.col=1,comp.labs=paste(\"Comp.\",1:3), scale.scores=lambda[choices]^(1-scale), scale.var=scale.comp, scale.comp=sqrt(lambda[choices]), scale.disp=1/scale.comp)\n\nArguments\n\n x princomp object or matrix of point locations to be drawn (typically, cases) choices Which principal components should be used? scale a scaling parameter like in biplot scale.scores a vector giving the scaling applied to the scores scale.var a vector giving the scaling applied to the variables scale.comp a vector giving the scaling applied to the unit length of each component scale.disp a vector giving the scaling of the display in the directions of the components comp.col color to draw the axes of the components, defaults to black comp.labs labels for the components ... further plotting parameters as defined in rgl::rgl.material y matrix of second point/arrow-head locations (typically, variables) var.axes logical, TRUE draws arrows and FALSE points for y col vector/list of two elements the first giving the color/colors for the first data set and the second giving color/colors for the second data set. cex vector/list of two elements the first giving the size for the first data set and the second giving size for the second data set. xlabs labels to be plotted at x-locations ylabs labels to be plotted at y-locations expand the relative expansion of the y data set with respect to x arrow.len The length of the arrows as defined in arrows3D add logical, adding to existing plot or making a new one?\n\nDetails\n\nThis \"biplot\" is a triplot, relating data, variables and principal components. The relative scaling of the components is still experimental, meant to mimic the behavior of classical biplots.\n\nValue\n\nthe 3D plotting coordinates of the tips of the arrows of the variables displayed, returned invisibly\n\nAuthor(s)\n\nK.Gerald v.d. Boogaart http://www.stat.boogaart.de" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.69823897,"math_prob":0.9713283,"size":2638,"snap":"2022-05-2022-21","text_gpt3_token_len":707,"char_repetition_ratio":0.12376613,"word_repetition_ratio":0.13447432,"special_character_ratio":0.2596664,"punctuation_ratio":0.16448598,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99191463,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-22T03:45:44Z\",\"WARC-Record-ID\":\"<urn:uuid:078b118f-8375-4f9f-a811-e96f4953683a>\",\"Content-Length\":\"57076\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:366eb632-c81b-4b93-aa9a-93acd5726a37>\",\"WARC-Concurrent-To\":\"<urn:uuid:18daf129-38f3-4fe8-ad75-3a04bf38919d>\",\"WARC-IP-Address\":\"51.81.83.12\",\"WARC-Target-URI\":\"https://rdrr.io/cran/compositions/man/biplot3d.html\",\"WARC-Payload-Digest\":\"sha1:F7U4EMTIRFSBQWOFFWUWAUCTSFXHAMHG\",\"WARC-Block-Digest\":\"sha1:K2TYSTP4Q2AXA2PC3VRUKBPPUZGETRXO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320303729.69_warc_CC-MAIN-20220122012907-20220122042907-00059.warc.gz\"}"}
https://rd.springer.com/chapter/10.1007%2F978-3-030-11566-1_6	[ "# Inference of a Dyadic Measure and Its Simplicial Geometry from Binary Feature Data and Application to Data Quality\n\nChapter\nPart of the Association for Women in Mathematics Series book series (AWMS, volume 17)\n\n## Abstract\n\nWe propose a new method for representing data sets with an ordered set of binary features which summarizes both measure-theoretic and topological properties. The method does not require any assumption of metric space properties for the data. A data set with an ordered set of binary features is viewed as a dyadic set with a dyadic measure. We prove that dyadic sets with dyadic measures have a canonical set of binary features and determine canonical nerve simplicial complexes. The method computes the two related representations: multiscale parameters for the dyadic measure and the Betti numbers of the simplicial complex. The dyadic product formula representation formulated in previous work is exploited. The parameters characterize the relative skewness of the measure at dyadic scales and localities. The more abstract Betti number statistics summarize the simplicial geometry of the support of the measure. We prove that they provide a simple privacy property. Our methods are compared with other results for measures on sets with tree structures, recent multi-resolution theory, and computational topology. We illustrate the method on a data quality data set and propose future research directions.\n\n## References\n\n1. 1.\nL. Ahlfors, Lectures on Quasi-Conformal Mappings, vol. 10 (van Nostrand Mathematical Studies, Princeton, 1966)\n2. 2.\nD. Bassu, P.W. Jones, L. Ness, D. Shallcross, Product Formalisms for Measures on Spaces with Binary Tree Structures: Representation, Visualization and Multiscale Noise, submitted to SIGMA Forum of Maths (under revision) (2016). https://arxiv.org/abs/1601.02946\n3. 3.\nA. Beurling, L. Ahlfors, The boundary correspondence under quasi-conformal mappings. Acta Math. 96, 125–142 (1956)\n4. 4.\nL. Billera, S. Holmes, K. Vogtmann, Geometry of the space of phylogenetic trees. Adv. Appl. Math. 27, 733–767 (2001)\n5. 5.\nC. Dwork, A. Roth, The algorithmic foundations of differential privacy. Found. Trends Theor. Comput. Sci. 9, 211–401 (2014)\n6. 6.\nH. Edelsbrunner, J. Harer, Persistent homology—a survey. Contemp. Math. 453, 257–282 (2008)\n7. 7.\nF. Fasy, B. Lecci, A. Rinaldo, L. Wasserman, S. Balakrishnan, A. Singh, Confidence sets for persistence diagrams. Ann. Stat. 42, 2301–2339 (2014)\n8. 8.\nR. Fefferman, C. Kenig, J. Pipher, The theory of weights and the Dirichlet problem for elliptical equations. Ann. Math. 134, 65–124 (1991)\n9. 9.\nM. Gavish, B. Nadler, R. Coifman, Multiscale wavelets on trees, graphs and high dimensional data: theory and applications to semi supervised learning, in Proceedings of the 27th International Conference on Machine Learning (Omnipress, Madison, 2010), pp. 367–374Google Scholar\n10. 10.\nS. Harker, K. Mischaikow, M. Mrozek, V. Nanda, Discrete Morse theoretic algorithms for computing homology of complexes and maps. Found. Comput. Math. 14, 151–184 (2014)\n11. 11.\nM.T. Kaczynski, M.K. Mrozek, Computational Homology in Applied Mathematical Sciences 157 (Springer, New York, 2004)Google Scholar\n12. 12.\nJ.-P. Kahane, Sur le chaos multiplicative. Ann. Sci. Math. 9, 105–150 (1985)\n13. 13.\nE. Kolaczyk, R. Nowak, Multiscale likelihood analysis and complexity penalized estimation. Ann. Stat. 32, 500–527 (2004)\n14. 14.\nX. Meng, A trio of inference problems that could win you a Nobel Prize in statistics (if you help fund it), in Past, Present, Future Stat. Sci. (CRC Press, Boca Raton, 2014), pp. 537–562Google Scholar\n15. 15.\nL. Ness, Dyadic product formula representations of confidence measures and decision rules for dyadic data set samples, in MISNC SI DS 201 (ACM, New York, 2016)Google Scholar\n16. 16.\nR. Rhodes, V. Vargas, Gaussian multiplicative chaos and applications: a review. Probab. Surv. 11, 315–392 (2014)\n17. 17.\nK. Turner, S. Mukhurjee, D. Boyer, Persistent homology transform modeling shapes and surfaces. Inf. Inf. 3, 310–344 (2014)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7658743,"math_prob":0.8406682,"size":4914,"snap":"2019-43-2019-47","text_gpt3_token_len":1264,"char_repetition_ratio":0.13034624,"word_repetition_ratio":0.00882353,"special_character_ratio":0.24664225,"punctuation_ratio":0.21818182,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9743175,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-19T11:44:11Z\",\"WARC-Record-ID\":\"<urn:uuid:7b4314cb-f225-4838-b018-ddc315b7cd90>\",\"Content-Length\":\"168160\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f3e09004-f974-45b4-8d7c-8b57188737dc>\",\"WARC-Concurrent-To\":\"<urn:uuid:6b6f0661-5085-4c2b-b34a-9e393def4b5e>\",\"WARC-IP-Address\":\"151.101.248.95\",\"WARC-Target-URI\":\"https://rd.springer.com/chapter/10.1007%2F978-3-030-11566-1_6\",\"WARC-Payload-Digest\":\"sha1:QKI4NGPKKVLFBONDK2LKUFDIKSTCPL4R\",\"WARC-Block-Digest\":\"sha1:J2OEN7AUIYVKGPTPDRXIWZUR6JNTVBTT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496670135.29_warc_CC-MAIN-20191119093744-20191119121744-00471.warc.gz\"}"}
https://math.stackexchange.com/questions/3142713/how-do-we-get-from-ln-a-ln-prn-to-a-pern-and-similar-logarithmic-equat	[ "# How do we get from $\\ln A=\\ln P+rn$ to $A=Pe^{rn}$ and similar logarithmic equations?\n\nI've been self-studying from the amazing \"Engineering Mathematics\" by Stroud and Booth, and am currently learning about algebra, particularly logarithms.\n\nThere is a question which I don't understand who they've solved. Namely, I'm supposed to express the following equations without logs:\n\n$$\\ln A = \\ln P + rn$$\n\nThe solution they provide is:\n\n$$A = Pe^{rn}$$\n\nBut I absolutely have no idea how they got to these solutions. (I managed to \"decipher\" some of the similar ones piece by piece by studying the rules of logarithms).\n\nThe basic idea behind all basic algebraic manipulations is that you are trying to isolate some variable or expression from the rest of the equation (that is, you are trying to \"solve\" for $$A$$ in this equation by putting it on one side of the equality by itself).\n\nFor this particular example (and indeed, most questions involving logarithms), you will have to know that the logarithm is \"invertible\"; just like multiplying and dividing by the same non-zero number changes nothing, taking a logarithm and then an exponential of a positive number changes nothing.\n\nSo, when we see $$\\ln(A)=\\ln(P)+rn$$, we can \"undo\" the logarithm by taking an exponential. However, what we do to one side must also be done to the other, so we are left with the following after recalling our basic rules of exponentiation: $$A=e^{\\ln(A)}=e^{\\ln(P)+rn}=e^{\\ln(P)}\\cdot e^{rn}=Pe^{rn}$$\n\nA key intuition behind logarithms is that multiplication translates to addition, i.e.\n\n$$\\ln(A*B)=\\ln(A)+\\ln(P)\\qquad$$ and $$\\qquad\\ln(A/B)=\\ln(A)-\\ln(P)$$\n\nWe can use this to solve your equation\n\n\\begin{align} \\ln(A)&=\\ln(P)+rn\\newline \\ln(A)-\\ln(P)&=rn\\newline \\ln(A/P)&=rn\\newline A/P&=e^{rn}\\newline A&=Pe^{rn} \\end{align}\n\nHint: Write $$e^{\\ln(A)}=e^{\\ln(P)+rn}$$ and use that $$e^{\\ln(x)}=x$$\n\nThere are a couple of things you must know about logarithms to understand that piece of mathematics.\n\nFirst of all, you need to know that $$\\ln{e}=1$$. It follows directly from the fact that $$e^1=e$$.\n\nSecondly, you need to know the fact that you can slide whatever you've got in front of the logarithm up and make it an exponent on the thing that's inside the logarithm: $$x\\ln{y}=\\ln{y^x}$$.\n\nAlso, when you add logarithms, you multiply whatever you have under the logarithm signs together as long as the product is a number that's greater than zero: $$\\ln{x}+\\ln{y}=\\ln{(xy)},\\ xy>0$$. (You can only take the logarithm of a positive number)\n\nAnd the last fact you're going to need is the fact that $$\\ln{x}=\\ln{y}\\implies x=y$$.\n\n\\begin{align} \\ln{A}&=\\ln{P}+rn\\cdot 1\\\\ \\ln{A}&=\\ln{P}+rn\\cdot \\ln{e}\\\\ \\ln{A}&=\\ln{P}+\\ln{e^{rn}}\\\\ \\ln{A}&=\\ln{(Pe^{rn})}\\\\ A&=Pe^{rn} \\end{align}" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9809102,"math_prob":0.9992791,"size":523,"snap":"2022-05-2022-21","text_gpt3_token_len":123,"char_repetition_ratio":0.09055877,"word_repetition_ratio":0.0,"special_character_ratio":0.23135756,"punctuation_ratio":0.095744684,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999951,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-16T11:09:09Z\",\"WARC-Record-ID\":\"<urn:uuid:2882051e-65f4-495b-a9d8-97fbaeb7b63e>\",\"Content-Length\":\"248165\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f4b3b826-2492-46e9-ba40-9fae1860f55e>\",\"WARC-Concurrent-To\":\"<urn:uuid:d86880c5-3460-44bb-b8fc-c13f0838b506>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/3142713/how-do-we-get-from-ln-a-ln-prn-to-a-pern-and-similar-logarithmic-equat\",\"WARC-Payload-Digest\":\"sha1:AYQC2GXJHYV2PJMUGFR62QD5OY2DDRXR\",\"WARC-Block-Digest\":\"sha1:ADVCI2LNAHAR3647SKPUBKCJZ43IJRVM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662510117.12_warc_CC-MAIN-20220516104933-20220516134933-00140.warc.gz\"}"}
https://www.djangospin.com/python-generating-random-elements-random-module/	[ "", null, "# Python: Generating random elements with the random module\n\nGenerating random elements with the random module in Python\n\n## Generating random elements with the random module in Python\n\nThe standard library called random helps the user to inject simulation into your Python programs. Its randint(x, y) function gives a random integer in the range marked by its arguments, inclusive of both end points. If you do not want the upper bound to be inclusive in the range, you can use the randrange(x, b) function, which even offers a step argument just like range().\n\n```>>> import random\n>>> random.randint(0, 5)\t\t\t# random number from 1-5\n3\n>>> random.randint(0, 5)\n5\n>>> random.randint(0, 5)\n3\n\n>>> random.randrange(0, 5)\t\t\t# random number from 1-4\n1\n>>> random.randrange(0, 5)\n4\n>>> random.randrange(0, 5)\n0\n\n>>> random.randrange(0, 5, 2)\t\t# random number from 1-4 & step = 2\n2\n>>> random.randrange(0, 5, 2)\n0\n>>> random.randrange(0, 5, 2)\n2\n>>> random.randrange(0, 5, 2)\n4\n```\n\nTo generate random elements other than integers, we have a method called choice(), which accepts an iterable and returns a random element from it.\n\n```>>> random.choice( ['a', 'b'] )\n'a'\n>>> random.choice( ['a', 'b'] )\n'a'\n>>> random.choice( ['a', 'b'] )\n'b'\n>>> random.choice( ['a', 'b'] )\n'a'\n>>> random.choice( ['a', 'b'] )\n'b'\n```" ]	[ null, "https://www.djangospin.com/wp-content/uploads/2015/12/py_logo.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6298764,"math_prob":0.9605993,"size":1186,"snap":"2019-51-2020-05","text_gpt3_token_len":347,"char_repetition_ratio":0.250423,"word_repetition_ratio":0.15463917,"special_character_ratio":0.35328835,"punctuation_ratio":0.18548387,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98465663,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-16T10:26:03Z\",\"WARC-Record-ID\":\"<urn:uuid:5feaee23-998c-4e63-8b30-60eec751cd0a>\",\"Content-Length\":\"50243\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0e3663bf-61cd-4a04-bff5-45da136cb1f3>\",\"WARC-Concurrent-To\":\"<urn:uuid:a4092a0f-27c0-43ce-8411-fd4ccb9e09d6>\",\"WARC-IP-Address\":\"69.163.162.247\",\"WARC-Target-URI\":\"https://www.djangospin.com/python-generating-random-elements-random-module/\",\"WARC-Payload-Digest\":\"sha1:O6M6TJZGMXRNDUIMAICSQ6DEU2DIZU3I\",\"WARC-Block-Digest\":\"sha1:EFY4SXTKWXCXWO5KY7M2B4W3YUX2LQC2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575541319511.97_warc_CC-MAIN-20191216093448-20191216121448-00439.warc.gz\"}"}
https://schoolbag.info/mathematics/idiots/34.html	[ " Points, Lines, Planes, and Angles - Basics of Geometry - The Shape of the World - Basic Math and Pre-Algebra\n\n## Basic Math and Pre-Algebra\n\nPART 3. The Shape of the World\n\nAny world tour must include seeing the sights, having a look at the shape of things. Whether it’s a natural formation like a mountain or a canyon, or a famous building or monument, by the end of a journey, your scrapbook will certainly have some examples of great geometry.\n\nThis part of our journey is devoted to looking at the geometry of the mathematical world. You’ll learn the basic vocabulary you need to describe what you see and how to identify the polygons, circles, polyhedrals, and other solids that form the architecture of the mathematical world.\n\nWe won’t abandon numbers completely as we look at these shapes, but for a while numbers will be a lesser focus. There’s still a place for calculating, but we’ll investigate relationships between shapes as well.\n\nCHAPTER 12. Basics of Geometry\n\nGeometry begins with a few undefined terms—point, line, and plane—and logically builds a system that describes many physical objects. The word “geometry” means “earth measuring,” and geometry had its beginnings in the work of dividing land up among farmers. Doing that requires lines, angles, and many different shapes.\n\nIn this chapter, you’ll lay the foundation on which to build your knowledge of geometry. Starting from those undefined terms, you’ll learn about portions of lines and combining lines to make angles. You’ll measure and classify angles, explore relationships between them, and bisect segments and angles. Parallel and perpendicular lines are the building blocks of many figures and create many angle relationships. Last of all, you’ll take many of these ideas onto the coordinate plane and see how they connect back to algebra.\n\nPoints, Lines, Planes, and Angles\n\nThe undefined terms of geometry are a curious mix of things you know and things you can only imagine. A point can be thought of as a dot, a tiny spot, or a position. That’s the familiar part. The part that requires imagination is the idea that a point doesn’t take up any space. It has no size and no dimension. You can’t measure it. You can draw a dot to represent a point, even though your dot does take up some space, and you label points with uppercase letters.\n\nYou know what a line is. You see lines all the time. But geometry asks you to use your imagination here, too. A line is a set of points—an infinite string of points—that goes on forever in both directions. It has length, in fact it has infinite length, but it has no width and no height. It’s only one point wide or high, and points don’t take up space. And yet, somehow, you can string points together to make something that has infinite length.\n\nPeople often say, “a straight line,” but in geometry that phrase is redundant. All lines are straight. If it curves or bends, it’s not a line.\n\nWhen you draw a picture to represent a line, even though your picture does have some width and can’t actually go on forever, you put arrows on the ends to show that it keeps going. You can label the line with one script letter, like line l, or by placing two points on the line and writing those two points with a line over the top, like this:", null, ".\n\nDEFINITION\n\nA point is a position in space that has no length, width, or height. A line is a set of points that has length but no width or height. A plane is a flat surface that has length and width but no thickness. Space is the set of all points.\n\nIs your imagination still working? Where do these points and lines live? Where would you draw a point or a line? Perhaps on a sheet of paper or the chalkboard? Those surfaces are the images that help you imagine a plane. A plane is a flat surface that has infinite length and infinite width but no height or thickness. It’s an endless sheet of paper that’s only one point deep.\n\nAnd where do the points and the lines and the planes live? In space! No, not outer space, at least not exactly. Space, in geometry, is the set of all points, everywhere.\n\nBasic Geometry Terms\n\nBefore your imagination is completely exhausted, let’s look at some parts of a line that don’t require so much imagination. A ray, sometimes called a half-line, is a portion of a line from one point, called the endpoint, going on forever in one direction. You can’t measure the length of a ray because, like a line, it goes on forever. A ray looks like an arrow, and you name it by naming its endpoint and then another point on the ray, with an arrow over the top, like this:", null, ".\n\nMore familiar, if only because it can really fit on your paper is a line segment, literally, part of a line. A line is a portion of a line between two endpoints. (Finally, something you can measure!) Name it by its endpoints, with a segment over the top, like this:", null, ".", null, "Lines contain infinitely many points, but they are named by any two points on the line. A line that contains the two points A and B can be named", null, "or", null, ". In the same way, a line segment can be named by its endpoints in either order, but for rays, the order makes a difference. The rays", null, "and", null, "are shown and are two different rays.\n\nDEFINITION\n\nA ray is a portion of a line from one endpoint, going on forever through another point.\n\nA line segment is a point of a line made up of two endpoints and all the points of the line between the endpoints.\n\nWhen you put two rays together, you create a new figure called an angle. An angle is a figure formed by two rays with a common endpoint, called the vertex. The two rays are the sides of the angle. You’ll often see angles whose sides are line segments, but you can think of those segments as parts of rays. (By the way, you can measure angles, too.)\n\nDEFINITION\n\nAn angle is two rays with a common endpoint, called the vertex. The rays are the sides of the angle.", null, "In the angle XYZ, the vertex is Y, and the sides are rays", null, "and", null, ". You can name angles by three letters, one on one side, the vertex, and one on the other side. XYZ and ZYX are both names for this angle. An angle can be named by just its vertex, for example, Y, as long as it is the only angle with that vertex.\n\nCHECK POINT\n\nDraw and label each figure described.\n\n1. Line segment", null, "2. Ray", null, "3. Angle DEF\n\n4. Rays", null, "and", null, "5. Angles PQR and RQT\n\nLength and Angle Measure\n\nWell, you found things you can measure: a line segment or an angle. They don’t go on forever. You can measure them and actually stop somewhere. So how do you do it?\n\nMeasuring just means assigning a number to something to give an indication of its size. The number depends on the ruler you’re using. Feet? Inches? Centimeters? Furlongs? They all measure length (although you don’t see furlongs used much outside of horse racing).\n\nA ruler is just a line or line segment that you’ve broken up into smaller segments, all the same size, and numbered. You could even use a number line, and many times we will.\n\nIf you place a ruler next to a line segment, each endpoint of the segment will line up with some number on the ruler (even if it’s one of the little fraction lines in between the whole numbers).\n\nThe numbers that correspond to the endpoints are called coordinates, and the length of the line segment is the difference between the coordinates. Technically, the length is the absolute value of the difference, because direction doesn’t matter.\n\nDEFINITION\n\nA ruler is a line or segment divided into sections of equal size, labeled with numbers, called coordinates, used to measure the length of a line segment.", null, "A number line like this can be used to measure line segments.\n\nFor example, the length of line segment AB is equal to the distance between coordinates -7 and -2, or five units.\n\nYou can also measure angles. Angles are measured by the amount of rotation from one side to the other. Picture the hands of a clock rotating, creating angles of different sizes. It is important to remember that the lengths of the sides have no effect on the measurement of the angle. The hands of the famous clock known as Big Ben are much longer than the hands of your wrist watch or alarm clock, but they all make the same angle at 9 o’clock.\n\nSo how do you put a ruler on an angle? For starters, it’s not a ruler. A ruler is a line you use to measure parts of lines. Angles aren’t parts of lines. They’re more like wedges from a circle. So to measure them you create an instrument called a protractor, a circle broken into 360 little sections, each called a degree.\n\nIn geometry, angles are measured in degrees. When you put the protractor over the angle with the center of the circle on the vertex of the angle, the sides fall on numbers, called coordinates. The measure of the angle is the absolute value of the difference of the coordinates.\n\nDEFINITION\n\nA protractor is a circle whose circumference is divided into 360 units, called degrees, which is used to measure angles.", null, "A protractor can be created using any circle, but most people are familiar with the plastic half-circle tool shown here.\n\nWhen two segments have the same length, they are called congruent segments. In symbols, you could write", null, "to say that the segment connecting A to B is the same length as the segment connecting X to Y. You could also write AB = XY to say the measurements—the lengths—are the same. With the little segment above the letters, you’re talking about the segment. Without it, you’re talking about the length, a number. Segments are congruent. Lengths are equal.\n\nDEFINITION\n\nTwo segments are congruent if they are the same length. Two angles are congruent if they have the same measure.\n\nThe same is true of angles and their measures. The symbol A refers to the actual angle, and the symbol mA denotes the measure of that angle. If you write XYZ ≅ ∠RST, you’re saying the two angles have the same measure. You could also write mXYZ = mRST. Angles are congruent; measures are equal.\n\nA full rotation all the way around the circle is 360°. Half of that, or 180°, is the measure of a straight angle. The straight angle takes its name from the fact that it looks like a line.\n\nAn angle of 90°, or a quarter rotation, is called a right angle. If one side of a right angle is on the floor, the other side stands upright. Angles between 0° and 90° are called acute angles.\n\nAngles whose measurement in greater than 90° but less that 180° are obtuse angles.\n\nDEFINITION\n\nA straight angle is an angle that measures 180°. A right angle is an angle that measures 90°.\n\nAn angle that measures less than 90° is an acute angle. An obtuse angle is an angle that measures more than 90° but less than 180°.\n\nYou can classify angles one by one, according to their size, but you can also label angles based on their relationship to one another. Sometimes the relationship is about position or location or what the angles look like. Other times it’s just about measurements.\n\nTwo angles whose measurements total to 90° are called complementary angles. If two angles are complementary, each is the complement of the other.\n\nThe complement of an angle of 25° can be found by subtracting the known angle, 25°, from 90°. 90° - 25° = 65°, so an angle of 25° and an angle of 65° are complementary. To find the measure of the complement of an angle of 12°, subtract 90° - 12° = 78°. An angle of 12° and an angle of 78° are complementary angles.\n\nTwo angles whose measurements total to 180° are called supplementary angles. If two angles are supplementary, each is the supplement of the other.\n\nDEFINITION\n\nComplementary angles are a pair of angles whose measurements total 90°.\n\nSupplementary angles are a pair of angles whose measurements total 180°.\n\nTo find the supplement of an angle of 132°, 180° - 132° = 48°. The measure of the supplement of an angle of 103° is 180 - 103 = 77°.\n\nWhen two lines intersect, the lines make an X and four angles are formed. Each pair of angles across the X from one another is a pair of vertical angles. Vertical angles are always congruent; they always have the same measurement.", null, "The angles AED and CEB are vertical angles, as are the angles DEC and AEB.\n\nTwo angles that have the same vertex and share a side but don’t overlap are called adjacent angles. Two adjacent angles whose exterior sides (the ones they don’t share) make a line are called a linear pair Linear pairs are always supplementary.\n\nDEFINITION\n\nVertical angles are a pair of angles both of which have their vertices at the point where two lines intersect and do not share a side.\n\nAdjacent angles are a pair of angles that have the same vertex and share a side but do not overlap one another.\n\nA linear pair is made up of two adjacent angles whose unshared sides form a straight angle.", null, "Angles RPQ and SPQare adjacent. Angles ABD and CBD are both adjacent and linear.\n\nCHECK POINT\n\n6. If mX = 174°, then X is a(n) ____________ angle.\n\n7. If mT = 38°, then T is a(n) ____________.\n\n8. If X and Y are supplementary, and mX = 174°, then mY = ____________.\n\n9. If R and T are complementary, and mT = 38°, then mR = ____________.\n\n10. Lines", null, "and", null, "intersect at point Y. If mPYR = 51°, then mRYA = ____________, and mTYA = ____________.\n\nMidpoints and Bisectors\n\nWhile you’re in the middle of all these lines and segments and rays and angles, it’s a good time to talk about middles. Because lines and rays go on forever, you can’t talk about the middle of a line or the middle of a ray. To say where the middle of something is, you have to be able to measure it. Until you can assign a length to an object, you can’t say where halfway is.\n\nA midpoint is a point on a line segment that divides it into two segments of equal length, two congruent segments. If M is the midpoint of", null, ", then", null, "Each of the little pieces is the same length (AM = MB), and each of them is half as long as", null, ". Only segments have midpoints.\n\nA line or ray or segment that passes through the midpoint of a segment is a segment bisector.\n\nAngles don’t have midpoints, but they can have bisectors. An angle bisector is a ray from the vertex of the angle that divides the angle into two congruent angles.\n\nDEFINITION\n\nThe midpoint of a line segment is a point on the segment that divides it into two segments of equal length.\n\nA segment bisector is a line, ray, or segment that divides a segment into two congruent segments.\n\nAn angle bisector is a line, ray, or segment that passes through the vertex of an angle and cuts it into two angles of equal size.\n\nCHECK POINT\n\n11. M is the midpoint of segment", null, "If PM = 3 cm, MQ= _____ cm and PQ = _____ cm.\n\n12. H is the midpoint of", null, "If XY = 28 inches, then XH = _____ inches.\n\n13. Ray", null, "bisects CAT. If mCAT = 86°, then mHAT = _____.\n\n14. If mAXB = 27° and mBXC = 27°, then _____ bisects AXC.\n\n15. mPYQ= 13°, mQYR = 12°, mRYS = 5°, and mSYT = 20°. True or False:", null, "bisects PYT.\n\n" ]	[ null, "https://schoolbag.info/mathematics/idiots/idiots.files/image198.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image199.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image200.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image201.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image200.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image202.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image199.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image203.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image204.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image205.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image206.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image207.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image208.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image209.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image210.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image211.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image212.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image213.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image214.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image215.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image216.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image217.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image218.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image219.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image220.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image221.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image222.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image223.jpg", null, "https://schoolbag.info/mathematics/idiots/idiots.files/image224.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93619764,"math_prob":0.97856146,"size":14586,"snap":"2023-40-2023-50","text_gpt3_token_len":3485,"char_repetition_ratio":0.16918118,"word_repetition_ratio":0.048363097,"special_character_ratio":0.23721376,"punctuation_ratio":0.118331715,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.9913376,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58],"im_url_duplicate_count":[null,3,null,6,null,6,null,3,null,6,null,3,null,6,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-04T17:16:45Z\",\"WARC-Record-ID\":\"<urn:uuid:9d66ec96-df4d-420d-85d9-4e6e368d4ad5>\",\"Content-Length\":\"37036\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:73204ae5-afa0-498a-aa23-570df1bac679>\",\"WARC-Concurrent-To\":\"<urn:uuid:0b9975cf-d1dd-4ed8-ba98-8c4c2845572f>\",\"WARC-IP-Address\":\"31.131.26.27\",\"WARC-Target-URI\":\"https://schoolbag.info/mathematics/idiots/34.html\",\"WARC-Payload-Digest\":\"sha1:EZK6PLNSC43JCK2GV3GOFNHVPNIZ77JD\",\"WARC-Block-Digest\":\"sha1:AFY4BMYDN45ORHCPMULG7GRGAHA2ALPX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100531.77_warc_CC-MAIN-20231204151108-20231204181108-00265.warc.gz\"}"}
https://slideplayer.com/slide/6885776/	[ "", null, "# Math notes and tips.\n\n## Presentation on theme: \"Math notes and tips.\"— Presentation transcript:\n\nMath notes and tips\n\nMultiplying decimals 4.376 X2.1 ----------------\nDon’t worry about lining up the decimals. However many numbers are behind the decimals then that is how many are in your answer!\n\nDividing decimals 6.625 ÷ 0.53 0 53 /6 625 ------------------------\nMove the decimal so that the outside number is a whole number What ever you do with the decimal on the out side you need to do to the decimal on the inside\n\nM.A.D M – multiply A – add D – denominator stays the same\n\nYou have to make the bottom number (the denominator) the same in the fractions\nSubtracting Adding 1 ¼ - 1/3= The smallest common multiple for 4 and 3 is 12 So 1 ¼ = 1 3/12 and 1/3 = 4/12 You also need to make 1 3/12 in to an improper fraction(use MAD) so it is 15/12 You can now subtract them and you get 11/12 1 + 1 3 The smallest common multiple for 2 and 3 is 6 So: 1 = 3 2 = 6 1 = 2 3 = 6 You can now add them and you get 5/6\n\nMultiplying fractions\nRegular Mixed numbers 2/4 x 1/3 = Multiply the top number (numerator) and the bottom number (denominator) So multiply 2 and 1 and also 4 and 3 to get 2/12 1 2/4 x 1/3 = You must get rid of the whole number by multiplying the 1 by the 4 and adding 2 then you keep the denominator (use MAD) 4x Then multiply like regular 6/4 x 1/3 = 6/12 = = Use order of operations\n\nDividing fractions Keep Change Flip 1÷2 3 4 1 X 4 3 2\n3 4 Keep Change Flip Keep 1st fraction the same change the ÷ to x flip the 2nd fraction X Now you multiply it like regular Answer: 4 2 6 reduced 3\n\nSame sign – find the “sum” Add #’s keep the sign Ex: -6 + (-2) = -8 Ex: -6 – (+2) = -8 + (-2) Different signs – find the difference Subtract the #’s and keep the sign of the # with the higher value. Ex: -8 + (2) = -6 Ex: = 3 Ex: -6 – (-2) = -4 + (+2) Remember: when it shows subtraction – change to addition and flip the sign behind the sign\n\nMultiplying and Dividing Integers\nSame sign – ALWAYS POSITIVE Ex: -5 x -4 = 20 Ex: -36 ÷ -6 = 6 Different signs – ALWAYS NEGATIVE Ex: -3 x 4 = -12 Ex: 30 ÷ -5 = -6\n\nOrder of Operations Order of operations () X2 x / + - P E M D A S\nL X Y E U A E C A N L A U R T L S S Y E E Multiplication and division are equal and opposite operations. Work left to right! Addition and subtraction are equal and opposite operations. Work left to right! Multiply Divide Add Subtract Parentheses Exponents\n\nConverting Fractions/Decimals/Percents\n\nNumber Line -4 -3 -2 -1 0 1 2 3 4 Moving to the left\nMoving to the left #’s decrease in value Negative # look like they get larger, but they are really getting smaller in value. Moving to the right #’s increasing in value Positive # get larger,\n\n0.6 = 2/3 = 66.6% = 33 2/3% (0.66666) Repeating Decimals\n0.3 = 1/3 = 33.3% = 33 1/3% ( ) 0.6 = 2/3 = 66.6% = 33 2/3% ( )\n\nFractions to remember Fraction Decimal Percent ½ .50 50% ¼ .25 25% 1/8\n.125 12.5% 1/16 .0625 6.25% 1/3 .3333 33.3% 2/3 .6666 66.6% 1/12 .08333 8.3% 1/24 .04166 4.16% 1/5 .20 20%" ]	[ null, "https://slideplayer.com/static/blue_design/img/slide-loader4.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83280087,"math_prob":0.9953833,"size":3122,"snap":"2022-40-2023-06","text_gpt3_token_len":1053,"char_repetition_ratio":0.13790892,"word_repetition_ratio":0.03081664,"special_character_ratio":0.38597053,"punctuation_ratio":0.07614943,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9986504,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-05T16:32:22Z\",\"WARC-Record-ID\":\"<urn:uuid:9d52a9f2-c4f3-47a0-8979-2b42b4663bf3>\",\"Content-Length\":\"177112\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a02498de-8631-4db3-ad10-765241d6db7c>\",\"WARC-Concurrent-To\":\"<urn:uuid:8663038f-8a4c-4976-927b-d5d019cbce61>\",\"WARC-IP-Address\":\"138.201.58.10\",\"WARC-Target-URI\":\"https://slideplayer.com/slide/6885776/\",\"WARC-Payload-Digest\":\"sha1:ZXUWJYSAGVXKHLNUUJKFBFP5F4PPD5LN\",\"WARC-Block-Digest\":\"sha1:VRPWYC2JJOGO7ZLURFTXFAUZK76HI5Z2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500273.30_warc_CC-MAIN-20230205161658-20230205191658-00528.warc.gz\"}"}
https://www.physicsforums.com/threads/vacuum-travel-formula-creation.466031/	[ "# Vacuum travel formula creation\n\n## Main Question or Discussion Point\n\nSay we have a maglev train travelling i a vacuum. The only thing limiting its speed is the g-force tolerance of the passengers.\n\nThe train would therefore accelerate at a certain rate until halfway, and then decelerate until it reached its destination.\n\nWhat would be the travelling time of such a train as a function of the distance?\n\nRelated Other Physics Topics News on Phys.org\n$$t=\\sqrt{\\frac{4s}{g}}$$\nwhere t is the time, s is the distance and g is the accelleration.\nCalculated using the fact that distance travelled is the area underneath a velocity-time graph.\n\nThank you.\n\nWhat acceleration value g should I use? I'm looking for an acceleration/deceleration that is hardly noticeable for the passengers, making the journey comfortable.\n\nWith an acceleration of 0.5m/s^2 you can cross the USA in 1.5h in a straight line, which is pretty good...\n\nThe chairs could turn 180 degrees when the train is going to decelerate. The top speed would be 2.7km/s.\n\nThe usual problem with trains is that they start and stop at all the intermediate stations...\n\nSay we have a maglev train travelling i a vacuum. The only thing limiting its speed is the g-force tolerance of the passengers.\n\nThe train would therefore accelerate at a certain rate until halfway, and then decelerate until it reached its destination.\n\nWhat would be the travelling time of such a train as a function of the distance?\nAt the distance x the train is accelerated until x/2 so the time is expressed as:\nx/2=gt²/2\nt=√x/g" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9513865,"math_prob":0.98001266,"size":586,"snap":"2020-24-2020-29","text_gpt3_token_len":124,"char_repetition_ratio":0.13573883,"word_repetition_ratio":0.6138614,"special_character_ratio":0.20648465,"punctuation_ratio":0.07272727,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9914889,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-27T22:31:12Z\",\"WARC-Record-ID\":\"<urn:uuid:969e0919-2ca2-4652-8c06-6c641a29bcb5>\",\"Content-Length\":\"78779\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:044e2d3c-059b-471f-9d2f-86fef1407e0d>\",\"WARC-Concurrent-To\":\"<urn:uuid:5af8ea99-7560-4e0d-9e86-a3657f991613>\",\"WARC-IP-Address\":\"23.111.143.85\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/vacuum-travel-formula-creation.466031/\",\"WARC-Payload-Digest\":\"sha1:D22B4ZMB66EHFVGCJSNJID73B6EC3YM6\",\"WARC-Block-Digest\":\"sha1:S5QYA4JPQP4B6H6NMIJBRDOW4MNPPHJH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347396163.18_warc_CC-MAIN-20200527204212-20200527234212-00304.warc.gz\"}"}
https://tools.carboncollective.co/compound-interest/59209-at-6-percent-in-20-years/	[ "# What is the compound interest on $59209 at 6% over 20 years? If you want to invest$59,209 over 20 years, and you expect it will earn 6.00% in annual interest, your investment will have grown to become $189,891.28. If you're on this page, you probably already know what compound interest is and how a sum of money can grow at a faster rate each year, as the interest is added to the original principal amount and recalculated for each period. The actual rate that$59,209 compounds at is dependent on the frequency of the compounding periods. In this article, to keep things simple, we are using an annual compounding period of 20 years, but it could be monthly, weekly, daily, or even continuously compounding.\n\nThe formula for calculating compound interest is:\n\n$$A = P(1 + \\dfrac{r}{n})^{nt}$$\n\n• A is the amount of money after the compounding periods\n• P is the principal amount\n• r is the annual interest rate\n• n is the number of compounding periods per year\n• t is the number of years\n\nWe can now input the variables for the formula to confirm that it does work as expected and calculates the correct amount of compound interest.\n\nFor this formula, we need to convert the rate, 6.00% into a decimal, which would be 0.06.\n\n$$A = 59209(1 + \\dfrac{ 0.06 }{1})^{ 20}$$\n\nAs you can see, we are ignoring the n when calculating this to the power of 20 because our example is for annual compounding, or one period per year, so 20 × 1 = 20.\n\n## How the compound interest on $59,209 grows over time The interest from previous periods is added to the principal amount, and this grows the sum a rate that always accelerating. The table below shows how the amount increases over the 20 years it is compounding: Start Balance Interest End Balance 1$59,209.00 $3,552.54$62,761.54\n2 $62,761.54$3,765.69 $66,527.23 3$66,527.23 $3,991.63$70,518.87\n4 $70,518.87$4,231.13 $74,750.00 5$74,750.00 $4,485.00$79,235.00\n6 $79,235.00$4,754.10 $83,989.10 7$83,989.10 $5,039.35$89,028.44\n8 $89,028.44$5,341.71 $94,370.15 9$94,370.15 $5,662.21$100,032.36\n10 $100,032.36$6,001.94 $106,034.30 11$106,034.30 $6,362.06$112,396.36\n12 $112,396.36$6,743.78 $119,140.14 13$119,140.14 $7,148.41$126,288.55\n14 $126,288.55$7,577.31 $133,865.86 15$133,865.86 $8,031.95$141,897.81\n16 $141,897.81$8,513.87 $150,411.68 17$150,411.68 $9,024.70$159,436.38\n18 $159,436.38$9,566.18 $169,002.57 19$169,002.57 $10,140.15$179,142.72\n20 $179,142.72$10,748.56 $189,891.28 We can also display this data on a chart to show you how the compounding increases with each compounding period. As you can see if you view the compounding chart for$59,209 at 6.00% over a long enough period of time, the rate at which it grows increases over time as the interest is added to the balance and new interest calculated from that figure.\n\n## How long would it take to double $59,209 at 6% interest? Another commonly asked question about compounding interest would be to calculate how long it would take to double your investment of$59,209 assuming an interest rate of 6.00%.\n\nWe can calculate this very approximately using the Rule of 72.\n\nThe formula for this is very simple:\n\n$$Years = \\dfrac{72}{Interest\\: Rate}$$\n\nBy dividing 72 by the interest rate given, we can calculate the rough number of years it would take to double the money. Let's add our rate to the formula and calculate this:\n\n$$Years = \\dfrac{72}{ 6 } = 12$$\n\nUsing this, we know that any amount we invest at 6.00% would double itself in approximately 12 years. So $59,209 would be worth$118,418 in ~12 years.\n\nWe can also calculate the exact length of time it will take to double an amount at 6.00% using a slightly more complex formula:\n\n$$Years = \\dfrac{log(2)}{log(1 + 0.06)} = 11.9\\; years$$\n\nHere, we use the decimal format of the interest rate, and use the logarithm math function to calculate the exact value.\n\nAs you can see, the exact calculation is very close to the Rule of 72 calculation, which is much easier to remember.\n\nHopefully, this article has helped you to understand the compound interest you might achieve from investing \\$59,209 at 6.00% over a 20 year investment period." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91771835,"math_prob":0.9987763,"size":4132,"snap":"2023-40-2023-50","text_gpt3_token_len":1306,"char_repetition_ratio":0.13880815,"word_repetition_ratio":0.01490313,"special_character_ratio":0.410697,"punctuation_ratio":0.19242273,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999114,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-01T16:13:01Z\",\"WARC-Record-ID\":\"<urn:uuid:bcdd1982-1d0e-41e9-8e8b-6efab991d5cb>\",\"Content-Length\":\"28083\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3c93bb72-e94a-4926-9cdc-95c1db5a93da>\",\"WARC-Concurrent-To\":\"<urn:uuid:045e1100-49a9-432c-b7b6-3415bd3f016a>\",\"WARC-IP-Address\":\"138.197.3.89\",\"WARC-Target-URI\":\"https://tools.carboncollective.co/compound-interest/59209-at-6-percent-in-20-years/\",\"WARC-Payload-Digest\":\"sha1:4CJPEPGU52N6OQXHW5ATZ4KL4F7B326C\",\"WARC-Block-Digest\":\"sha1:XOJE5OWVYMIWNPP2NLVPSVCZZHZILCBM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510903.85_warc_CC-MAIN-20231001141548-20231001171548-00149.warc.gz\"}"}
https://help.nrl.com/exportword?pageId=28672493	[ "Date: Tue, 18 May 2021 14:19:23 +1000 (AEST) Message-ID: <2059320466.1327.1621311563580@rlc-syd-cfl01.rlc.local> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary=\"----=_Part_1326_577914541.1621311563579\" ------=_Part_1326_577914541.1621311563579 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html I am trying to play Fantasy and am experiencing issues with my a= ccount setup...\n\n# I am trying to play Fantasy and am experiencing issues with my acco= unt setup...\n\n=20\n=20\n=20\n=20\n\n=20\n=20 =20\n=20\n=20\n\nBefore you can set up your Fantasy team, you need to sign up for an NRL = Account and verify the email that you used to sign up.\n\nYou can sign up from the Fantasy site, the NRL site or any Club/State si= te. You can sign up to an NRL Account anytime.", null, "=20\n=20\n=20\n=20 =20\nFinal step to co= mplete your Fantasy Registration\n=20\n=20\n\nEnter the Country you are in. If Australia is selected,= please tell us your State.\n\nAccept the Terms and Conditions by placing a tick in th= e box - if you want to read them click on Terms and Conditions and they wil= l be displayed to you.\n\nLet us know if you would like to hear from the great folks at Youi by pl= acing a tick in the box.\n\nClick Play Now.", null, "=20\n=20\n=20\n=20 =20\n=20\n=20\n\nTell us the game you want to play.\n\nClick Play Fantasy or Play Draft to be= gin setting up your team for this year.", null, "=20\n=20\n=20\n\n=20\n=20\n=20\n=20\n\n=20 =20 =20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n=20\n\n=20\n=20\nMore Insight\n=20\n\n=20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n• =20\n=20 Page:= =20\n=20\n• =20\n=20\n\n=20\n\n=20\n=20\n=20" ]	[ null, "https://help.nrl.com/3D\"2a95aaf79be0c0f6dded4085a45a29c0\"", null, "https://help.nrl.com/3D\"70d1=", null, "https://help.nrl.com/3D\"43f8=", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5863046,"math_prob":0.7119014,"size":461,"snap":"2021-21-2021-25","text_gpt3_token_len":148,"char_repetition_ratio":0.12691467,"word_repetition_ratio":0.0,"special_character_ratio":0.44251627,"punctuation_ratio":0.2840909,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99988496,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-18T04:19:25Z\",\"WARC-Record-ID\":\"<urn:uuid:e273d0f6-61db-4808-bd4e-fe009da3b2ab>\",\"Content-Length\":\"478523\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e4b19f43-c537-4f59-ab83-b073045d5b22>\",\"WARC-Concurrent-To\":\"<urn:uuid:49e401f6-9822-40b5-b539-08ddfdb93e79>\",\"WARC-IP-Address\":\"203.42.16.85\",\"WARC-Target-URI\":\"https://help.nrl.com/exportword?pageId=28672493\",\"WARC-Payload-Digest\":\"sha1:WLD4LXP3Y7YPKCGXYU5TPFYF6L6G4WLM\",\"WARC-Block-Digest\":\"sha1:YAGWECHKKWOW6LZA4D6ONJZCOPJ4M55D\",\"WARC-Identified-Payload-Type\":\"message/rfc822\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989820.78_warc_CC-MAIN-20210518033148-20210518063148-00454.warc.gz\"}"}
https://sh-tsang.medium.com/review-adanorm-adaptive-normalization-73865be8d522?source=read_next_recirc---------3---------------------6fd9c622_99ce_433f_860a_142b608646ff-------	[ "## Improve LayerNorm (Layer Normalization)\n\nUnderstanding and Improving Layer Normalization\n2019 NeurIPS, Over 50 Citations (Sik-Ho Tsang @ Medium)\nMachine Translation, Language Model, Image Classification, Layer Normalization\n\n• By understanding LayerNorm (Layer Normalization), a step further is made to improve LayerNorm as AdaNorm (Adaptive Normalization).\n\n# Outline\n\n1. LayerNorm\n2. LayerNorm-simple\n3. DetachNorm\n\n# 1. LayerNorm\n\n• Let x=(x1, x2, …, xH) be the vector representation of an input of size H to normalization layers. LayerNorm re-centers and re-scales input x as:\n• where h is the output of a LayerNorm layer. ⊙ is a dot production operation. μ\u0016 and σ are the mean and standard deviation of input. Bias b and gain g are parameters with the same dimension H.\n• LayerNorm is a default setting in Transformer and Transformer-XL.\n\n# 2. LayerNorm-simple\n\n• For machine translation, Transformer is re-implemented.\n• For language model, 12-layer Transformer-XL is used.\n• For text classification, Transformer with a 4-layer encoder is used.\n• For image classification, 3-layer CNN is used.\n• For parsing, MLP-based parser is used.\n\nThe bias and gain do NOT work on six out of eight datasets.\n\n# 3. DetachNorm\n\n• Detaching derivatives means treating the mean and variance as changeable constants, rather than variables, which do not require gradients in backward propagation.\n• The function θ(.) can be seen as a special copy function, which copies the values of μ\u0016 and σ into constants ^μ\u0016\u0016 and ^σ\u001b.\n\nIn all, DetachNorm keeps the same forward normalization fact as LayerNorm does, but cuts offs the derivatives of the mean and variance.\n\n• DetachNorm performs worse than “w/o Norm”, showing that forward normalization has little to do with the success of LayerNorm.\n\nDetachNorm performs worse than LayerNorm-simple on six datasets. The derivatives of the mean and variance bring higher improvements than forward normalization does.\n\n• In AdaNorm, Φ(y), a function with respect to input x, is used to replace the bias and gain with the following equation:\n\nUnlike the bias and gain being fixed in LayerNorm, Φ(y) can adaptively adjust scaling weights based on inputs.\n\n• To keep the training stability, some constraints are made. (1) First, Φ(y) must be differentiable. (2) Second, the average scaling weight is expected to be fixed, namely the average of Φ(y) is a constant C where C > 0. (3) Third, it is expected that the average of z is bounded, which can avoid the problem of exploding loss.\n• By considering above constraints and based on Chebyshev’s Inequality, finally, Φ(y) is:\n• (Please feel free to read the paper if interested for this proof.)\n• Given an input vector x, the complete calculation process of AdaNorm is:\n• where C is a hyper-parameter, k=1/10.\n• In implementation, the gradient of C(1-ky) is detached and it is only treated as a changeable constant.\n• AdaNorm outperforms LayerNorm on seven datasets, with 0.2 BLEU on En-De, 0.1 BLEU on De-En, 0.2 BLEU on En-Vi, 0.29 ACC on RT, 1.31 ACC on SST, 0.22 ACC on MNIST, and 0.11 UAC on PTB.\n\nUnlike LayerNorm-simple only performing well on bigger models, AdaNorm achieves more balanced results.\n\n• The above figure shows the loss curves of LayerNorm and AdaNorm on the validation set of En-Vi, PTB, and De-En.\n• Compared to AdaNorm, LayerNorm has lower training loss but higher validation loss. Lower validation loss proves that AdaNorm has better convergence." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.84101903,"math_prob":0.9237179,"size":3667,"snap":"2023-40-2023-50","text_gpt3_token_len":1001,"char_repetition_ratio":0.12012012,"word_repetition_ratio":0.0070546735,"special_character_ratio":0.25579494,"punctuation_ratio":0.12992701,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9807799,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-02T09:09:31Z\",\"WARC-Record-ID\":\"<urn:uuid:d4126cfc-e975-4bb9-81d4-36f40f377fea>\",\"Content-Length\":\"270954\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:952efa81-22d8-48ab-8906-d72ad343aefa>\",\"WARC-Concurrent-To\":\"<urn:uuid:6614eb76-141e-4447-a1e8-2e791c15bc00>\",\"WARC-IP-Address\":\"162.159.152.4\",\"WARC-Target-URI\":\"https://sh-tsang.medium.com/review-adanorm-adaptive-normalization-73865be8d522?source=read_next_recirc---------3---------------------6fd9c622_99ce_433f_860a_142b608646ff-------\",\"WARC-Payload-Digest\":\"sha1:4ARTXBPXLZOWUCY637RWC375QNGVDT2D\",\"WARC-Block-Digest\":\"sha1:LQGANFUCGMHYDICBDATGDPD64U3UZ2BC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510983.45_warc_CC-MAIN-20231002064957-20231002094957-00890.warc.gz\"}"}
https://graph-tool.skewed.de/static/doc/centrality.html	[ "graph_tool.centrality - Centrality measures¶\n\nThis module includes centrality-related algorithms.\n\nSummary¶\n\n pagerank Calculate the PageRank of each vertex. betweenness Calculate the betweenness centrality for each vertex and edge. central_point_dominance Calculate the central point dominance of the graph, given the betweenness centrality of each vertex. closeness Calculate the closeness centrality for each vertex. eigenvector Calculate the eigenvector centrality of each vertex in the graph, as well as the largest eigenvalue. katz Calculate the Katz centrality of each vertex in the graph. hits Calculate the authority and hub centralities of each vertex in the graph. eigentrust Calculate the eigentrust centrality of each vertex in the graph. trust_transitivity Calculate the pervasive trust transitivity between chosen (or all) vertices in the graph.\n\nContents¶\n\ngraph_tool.centrality.pagerank(g, damping=0.85, pers=None, weight=None, prop=None, epsilon=1e-06, max_iter=None, ret_iter=False)[source]\n\nCalculate the PageRank of each vertex.\n\nParameters\ngGraph\n\nGraph to be used.\n\ndampingfloat, optional (default: 0.85)\n\nDamping factor.\n\npersVertexPropertyMap, optional (default: None)\n\nPersonalization vector. If omitted, a constant value of $$1/N$$ will be used.\n\nweightEdgePropertyMap, optional (default: None)\n\nEdge weights. If omitted, a constant value of 1 will be used.\n\npropVertexPropertyMap, optional (default: None)\n\nVertex property map to store the PageRank values. If supplied, it will be used uninitialized.\n\nepsilonfloat, optional (default: 1e-6)\n\nConvergence condition. The iteration will stop if the total delta of all vertices are below this value.\n\nmax_iterint, optional (default: None)\n\nIf supplied, this will limit the total number of iterations.\n\nret_iterbool, optional (default: False)\n\nIf true, the total number of iterations is also returned.\n\nReturns\npagerankVertexPropertyMap\n\nA vertex property map containing the PageRank values.\n\nbetweenness\n\nbetweenness centrality\n\neigentrust\n\neigentrust centrality\n\neigenvector\n\neigenvector centrality\n\nhits\n\nauthority and hub centralities\n\ntrust_transitivity\n\npervasive trust transitivity\n\nNotes\n\nThe value of PageRank [pagerank-wikipedia] of vertex v, $$PR(v)$$, is given iteratively by the relation:\n\n$PR(v) = \\frac{1-d}{N} + d \\sum_{u \\in \\Gamma^{-}(v)} \\frac{PR (u)}{d^{+}(u)}$\n\nwhere $$\\Gamma^{-}(v)$$ are the in-neighbors of v, $$d^{+}(u)$$ is the out-degree of u, and d is a damping factor.\n\nIf a personalization property $$p(v)$$ is given, the definition becomes:\n\n$PR(v) = (1-d)p(v) + d \\sum_{u \\in \\Gamma^{-}(v)} \\frac{PR (u)}{d^{+}(u)}$\n\nIf edge weights are also given, the equation is then generalized to:\n\n$PR(v) = (1-d)p(v) + d \\sum_{u \\in \\Gamma^{-}(v)} \\frac{PR (u) w_{u\\to v}}{d^{+}(u)}$\n\nwhere $$d^{+}(u)=\\sum_{y}A_{u,y}w_{u\\to y}$$ is redefined to be the sum of the weights of the out-going edges from u.\n\nIf a node has out-degree zero, it is assumed to connect to every other node with a weight proportional to $$p(v)$$ or a constant if no personalization is given.\n\nThe implemented algorithm progressively iterates the above equations, until it no longer changes, according to the parameter epsilon. It has a topology-dependent running time.\n\nIf enabled during compilation, this algorithm runs in parallel.\n\nReferences\n\npagerank-wikipedia(1,2)\n\nhttp://en.wikipedia.org/wiki/Pagerank\n\nlawrence-pagerank-1998\n\nP. Lawrence, B. Sergey, M. Rajeev, W. Terry, “The pagerank citation ranking: Bringing order to the web”, Technical report, Stanford University, 1998\n\nLangville-survey-2005\n\nA. N. Langville, C. D. Meyer, “A Survey of Eigenvector Methods for Web Information Retrieval”, SIAM Review, vol. 47, no. 1, pp. 135-161, 2005, DOI: 10.1137/S0036144503424786 [sci-hub, @tor]\n\nL. A. Adamic and N. Glance, “The political blogosphere and the 2004 US Election”, in Proceedings of the WWW-2005 Workshop on the Weblogging Ecosystem (2005). DOI: 10.1145/1134271.1134277 [sci-hub, @tor]\n\nExamples\n\n>>> g = gt.collection.data[\"polblogs\"]\n>>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))\n>>> pr = gt.pagerank(g)\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=pr,\n... vertex_size=gt.prop_to_size(pr, mi=5, ma=15),\n... vorder=pr, vcmap=matplotlib.cm.gist_heat,\n... output=\"polblogs_pr.pdf\")\n<...>", null, "PageRank values of the a political blogs network of [adamic-polblogs].\n\nNow with a personalization vector, and edge weights:\n\n>>> d = g.degree_property_map(\"total\")\n>>> periphery = d.a <= 2\n>>> p = g.new_vertex_property(\"double\")\n>>> p.a[periphery] = 100\n>>> pr = gt.pagerank(g, pers=p)\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=pr,\n... vertex_size=gt.prop_to_size(pr, mi=5, ma=15),\n... vorder=pr, vcmap=matplotlib.cm.gist_heat,\n... output=\"polblogs_pr_pers.pdf\")\n<...>", null, "Personalized PageRank values of the a political blogs network of [adamic-polblogs], where vertices with very low degree are given artificially high scores.\n\ngraph_tool.centrality.betweenness(g, pivots=None, vprop=None, eprop=None, weight=None, norm=True)[source]\n\nCalculate the betweenness centrality for each vertex and edge.\n\nParameters\ngGraph\n\nGraph to be used.\n\npivotslist or ndarray, optional (default: None)\n\nIf provided, the betweenness will be estimated using the vertices in this list as pivots. If the list contains all nodes (the default) the algorithm will be exact, and if the vertices are randomly chosen the result will be an unbiased estimator.\n\nvpropVertexPropertyMap, optional (default: None)\n\nVertex property map to store the vertex betweenness values.\n\nepropEdgePropertyMap, optional (default: None)\n\nEdge property map to store the edge betweenness values.\n\nweightEdgePropertyMap, optional (default: None)\n\nEdge property map corresponding to the weight value of each edge.\n\nnormbool, optional (default: True)\n\nWhether or not the betweenness values should be normalized.\n\nReturns\nvertex_betweennessA vertex property map with the vertex betweenness values.\nedge_betweennessAn edge property map with the edge betweenness values.\n\ncentral_point_dominance\n\ncentral point dominance of the graph\n\npagerank\n\nPageRank centrality\n\neigentrust\n\neigentrust centrality\n\neigenvector\n\neigenvector centrality\n\nhits\n\nauthority and hub centralities\n\ntrust_transitivity\n\npervasive trust transitivity\n\nNotes\n\nBetweenness centrality of a vertex $$C_B(v)$$ is defined as,\n\n$C_B(v)= \\sum_{s \\neq v \\neq t \\in V \\atop s \\neq t} \\frac{\\sigma_{st}(v)}{\\sigma_{st}}$\n\nwhere $$\\sigma_{st}$$ is the number of shortest paths from s to t, and $$\\sigma_{st}(v)$$ is the number of shortest paths from s to t that pass through a vertex $$v$$. This may be normalised by dividing through the number of pairs of vertices not including v, which is $$(n-1)(n-2)/2$$, for undirected graphs, or $$(n-1)(n-2)$$ for directed ones.\n\nThe algorithm used here is defined in [brandes-faster-2001], and has a complexity of $$O(VE)$$ for unweighted graphs and $$O(VE + V(V+E)\\log V)$$ for weighted graphs. The space complexity is $$O(VE)$$.\n\nIf the pivots parameter is given, the complexity will be instead $$O(PE)$$ for unweighted graphs and $$O(PE + P(V+E)\\log V)$$ for weighted graphs, where $$P$$ is the number of pivot vertices.\n\nIf enabled during compilation, this algorithm runs in parallel.\n\nReferences\n\nbetweenness-wikipedia\n\nhttp://en.wikipedia.org/wiki/Centrality#Betweenness_centrality\n\nbrandes-faster-2001(1,2)\n\nU. Brandes, “A faster algorithm for betweenness centrality”, Journal of Mathematical Sociology, 2001, DOI: 10.1080/0022250X.2001.9990249 [sci-hub, @tor]\n\nbrandes-centrality-2007\n\nU. Brandes, C. Pich, “Centrality estimation in large networks”, Int. J. Bifurcation Chaos 17, 2303 (2007). DOI: 10.1142/S0218127407018403 [sci-hub, @tor]\n\nL. A. Adamic and N. Glance, “The political blogosphere and the 2004 US Election”, in Proceedings of the WWW-2005 Workshop on the Weblogging Ecosystem (2005). DOI: 10.1145/1134271.1134277 [sci-hub, @tor]\n\nExamples\n\n>>> g = gt.collection.data[\"polblogs\"]\n>>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))\n>>> vp, ep = gt.betweenness(g)\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=vp,\n... vertex_size=gt.prop_to_size(vp, mi=5, ma=15),\n... edge_pen_width=gt.prop_to_size(ep, mi=0.5, ma=5),\n... vcmap=matplotlib.cm.gist_heat,\n... vorder=vp, output=\"polblogs_betweenness.pdf\")\n<...>", null, "Betweenness values of the a political blogs network of [adamic-polblogs].\n\ngraph_tool.centrality.closeness(g, weight=None, source=None, vprop=None, norm=True, harmonic=False)[source]\n\nCalculate the closeness centrality for each vertex.\n\nParameters\ngGraph\n\nGraph to be used.\n\nweightEdgePropertyMap, optional (default: None)\n\nEdge property map corresponding to the weight value of each edge.\n\nsourceVertex, optional (default: None)\n\nIf specified, the centrality is computed for this vertex alone.\n\nvpropVertexPropertyMap, optional (default: None)\n\nVertex property map to store the vertex centrality values.\n\nnormbool, optional (default: True)\n\nWhether or not the centrality values should be normalized.\n\nharmonicbool, optional (default: False)\n\nIf true, the sum of the inverse of the distances will be computed, instead of the inverse of the sum.\n\nReturns\nvertex_closenessVertexPropertyMap\n\nA vertex property map with the vertex closeness values.\n\ncentral_point_dominance\n\ncentral point dominance of the graph\n\npagerank\n\nPageRank centrality\n\neigentrust\n\neigentrust centrality\n\neigenvector\n\neigenvector centrality\n\nhits\n\nauthority and hub centralities\n\ntrust_transitivity\n\npervasive trust transitivity\n\nNotes\n\nThe closeness centrality of a vertex $$i$$ is defined as,\n\n$c_i = \\frac{1}{\\sum_j d_{ij}}$\n\nwhere $$d_{ij}$$ is the (possibly directed and/or weighted) distance from $$i$$ to $$j$$. In case there is no path between the two vertices, here the distance is taken to be zero.\n\nIf harmonic == True, the definition becomes\n\n$c_i = \\sum_j\\frac{1}{d_{ij}},$\n\nbut now, in case there is no path between the two vertices, we take $$d_{ij} \\to\\infty$$ such that $$1/d_{ij}=0$$.\n\nIf norm == True, the values of $$c_i$$ are normalized by $$n_i-1$$ where $$n_i$$ is the size of the (out-) component of $$i$$. If harmonic == True, they are instead simply normalized by $$V-1$$.\n\nThe algorithm complexity of $$O(V(V + E))$$ for unweighted graphs and $$O(V(V+E) \\log V)$$ for weighted graphs. If the option source is specified, this drops to $$O(V + E)$$ and $$O((V+E)\\log V)$$ respectively.\n\nIf enabled during compilation, this algorithm runs in parallel.\n\nReferences\n\ncloseness-wikipedia\n\nhttps://en.wikipedia.org/wiki/Closeness_centrality\n\nopsahl-node-2010\n\nOpsahl, T., Agneessens, F., Skvoretz, J., “Node centrality in weighted networks: Generalizing degree and shortest paths”. Social Networks 32, 245-251, 2010 DOI: 10.1016/j.socnet.2010.03.006 [sci-hub, @tor]\n\nL. A. Adamic and N. Glance, “The political blogosphere and the 2004 US Election”, in Proceedings of the WWW-2005 Workshop on the Weblogging Ecosystem (2005). DOI: 10.1145/1134271.1134277 [sci-hub, @tor]\n\nExamples\n\n>>> g = gt.collection.data[\"polblogs\"]\n>>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))\n>>> c = gt.closeness(g)\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=c,\n... vertex_size=gt.prop_to_size(c, mi=5, ma=15),\n... vcmap=matplotlib.cm.gist_heat,\n... vorder=c, output=\"polblogs_closeness.pdf\")\n<...>", null, "Closeness values of the a political blogs network of [adamic-polblogs].\n\ngraph_tool.centrality.central_point_dominance(g, betweenness)[source]\n\nCalculate the central point dominance of the graph, given the betweenness centrality of each vertex.\n\nParameters\ngGraph\n\nGraph to be used.\n\nbetweennessVertexPropertyMap\n\nVertex property map with the betweenness centrality values. The values must be normalized.\n\nReturns\ncpfloat\n\nThe central point dominance.\n\nbetweenness\n\nbetweenness centrality\n\nNotes\n\nLet $$v^$$ be the vertex with the largest relative betweenness centrality; then, the central point dominance [freeman-set-1977] is defined as:\n\n$C'_B = \\frac{1}{\|V\|-1} \\sum_{v} C_B(v^) - C_B(v)$\n\nwhere $$C_B(v)$$ is the normalized betweenness centrality of vertex v. The value of $$C_B$$ lies in the range [0,1].\n\nThe algorithm has a complexity of $$O(V)$$.\n\nReferences\n\nfreeman-set-1977(1,2)\n\nLinton C. Freeman, “A Set of Measures of Centrality Based on Betweenness”, Sociometry, Vol. 40, No. 1, pp. 35-41, 1977, DOI: 10.2307/3033543 [sci-hub, @tor]\n\nExamples\n\n>>> g = gt.collection.data[\"polblogs\"]\n>>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))\n>>> vp, ep = gt.betweenness(g)\n>>> print(gt.central_point_dominance(g, vp))\n0.105683...\ngraph_tool.centrality.eigenvector(g, weight=None, vprop=None, epsilon=1e-06, max_iter=None)[source]\n\nCalculate the eigenvector centrality of each vertex in the graph, as well as the largest eigenvalue.\n\nParameters\ngGraph\n\nGraph to be used.\n\nweightEdgePropertyMap (optional, default: None)\n\nEdge property map with the edge weights.\n\nvpropVertexPropertyMap, optional (default: None)\n\nVertex property map where the values of eigenvector must be stored. If provided, it will be used uninitialized.\n\nepsilonfloat, optional (default: 1e-6)\n\nConvergence condition. The iteration will stop if the total delta of all vertices are below this value.\n\nmax_iterint, optional (default: None)\n\nIf supplied, this will limit the total number of iterations.\n\nReturns\neigenvaluefloat\n\nThe largest eigenvalue of the (weighted) adjacency matrix.\n\neigenvectorVertexPropertyMap\n\nA vertex property map containing the eigenvector values.\n\nbetweenness\n\nbetweenness centrality\n\npagerank\n\nPageRank centrality\n\nhits\n\nauthority and hub centralities\n\ntrust_transitivity\n\npervasive trust transitivity\n\nNotes\n\nThe eigenvector centrality $$\\mathbf{x}$$ is the eigenvector of the (weighted) adjacency matrix with the largest eigenvalue $$\\lambda$$, i.e. it is the solution of\n\n$\\mathbf{A}\\mathbf{x} = \\lambda\\mathbf{x},$\n\nwhere $$\\mathbf{A}$$ is the (weighted) adjacency matrix and $$\\lambda$$ is the largest eigenvalue.\n\nThe algorithm uses the power method which has a topology-dependent complexity of $$O\\left(N\\times\\frac{-\\log\\epsilon}{\\log\|\\lambda_1/\\lambda_2\|}\\right)$$, where $$N$$ is the number of vertices, $$\\epsilon$$ is the epsilon parameter, and $$\\lambda_1$$ and $$\\lambda_2$$ are the largest and second largest eigenvalues of the (weighted) adjacency matrix, respectively.\n\nIf enabled during compilation, this algorithm runs in parallel.\n\nReferences\n\neigenvector-centrality\n\nhttp://en.wikipedia.org/wiki/Centrality#Eigenvector_centrality\n\npower-method\n\nhttp://en.wikipedia.org/wiki/Power_iteration\n\nlangville-survey-2005\n\nA. N. Langville, C. D. Meyer, “A Survey of Eigenvector Methods for Web Information Retrieval”, SIAM Review, vol. 47, no. 1, pp. 135-161, 2005, DOI: 10.1137/S0036144503424786 [sci-hub, @tor]\n\nL. A. Adamic and N. Glance, “The political blogosphere and the 2004 US Election”, in Proceedings of the WWW-2005 Workshop on the Weblogging Ecosystem (2005). DOI: 10.1145/1134271.1134277 [sci-hub, @tor]\n\nExamples\n\n>>> g = gt.collection.data[\"polblogs\"]\n>>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))\n>>> w = g.new_edge_property(\"double\")\n>>> w.a = np.random.random(len(w.a)) * 42\n>>> ee, x = gt.eigenvector(g, w)\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=x,\n... vertex_size=gt.prop_to_size(x, mi=5, ma=15),\n... vcmap=matplotlib.cm.gist_heat,\n... vorder=x, output=\"polblogs_eigenvector.pdf\")\n<...>", null, "Eigenvector values of the a political blogs network of [adamic-polblogs], with random weights attributed to the edges.\n\ngraph_tool.centrality.katz(g, alpha=0.01, beta=None, weight=None, vprop=None, epsilon=1e-06, max_iter=None, norm=True)[source]\n\nCalculate the Katz centrality of each vertex in the graph.\n\nParameters\ngGraph\n\nGraph to be used.\n\nweightEdgePropertyMap (optional, default: None)\n\nEdge property map with the edge weights.\n\nalphafloat, optional (default: 0.01)\n\nFree parameter $$\\alpha$$. This must be smaller than the inverse of the largest eigenvalue of the adjacency matrix.\n\nbetaVertexPropertyMap, optional (default: None)\n\nVertex property map where the local personalization values. If not provided, the global value of 1 will be used.\n\nvpropVertexPropertyMap, optional (default: None)\n\nVertex property map where the values of eigenvector must be stored. If provided, it will be used uninitialized.\n\nepsilonfloat, optional (default: 1e-6)\n\nConvergence condition. The iteration will stop if the total delta of all vertices are below this value.\n\nmax_iterint, optional (default: None)\n\nIf supplied, this will limit the total number of iterations.\n\nnormbool, optional (default: True)\n\nWhether or not the centrality values should be normalized.\n\nReturns\ncentralityVertexPropertyMap\n\nA vertex property map containing the Katz centrality values.\n\nbetweenness\n\nbetweenness centrality\n\npagerank\n\nPageRank centrality\n\neigenvector\n\neigenvector centrality\n\nhits\n\nauthority and hub centralities\n\ntrust_transitivity\n\npervasive trust transitivity\n\nNotes\n\nThe Katz centrality $$\\mathbf{x}$$ is the solution of the nonhomogeneous linear system\n\n$\\mathbf{x} = \\alpha\\mathbf{A}\\mathbf{x} + \\mathbf{\\beta},$\n\nwhere $$\\mathbf{A}$$ is the (weighted) adjacency matrix and $$\\mathbf{\\beta}$$ is the personalization vector (if not supplied, $$\\mathbf{\\beta} = \\mathbf{1}$$ is assumed).\n\nThe algorithm uses successive iterations of the equation above, which has a topology-dependent convergence complexity.\n\nIf enabled during compilation, this algorithm runs in parallel.\n\nReferences\n\nkatz-centrality\n\nhttp://en.wikipedia.org/wiki/Katz_centrality\n\nkatz-new\n\nL. Katz, “A new status index derived from sociometric analysis”, Psychometrika 18, Number 1, 39-43, 1953, DOI: 10.1007/BF02289026 [sci-hub, @tor]\n\nL. A. Adamic and N. Glance, “The political blogosphere and the 2004 US Election”, in Proceedings of the WWW-2005 Workshop on the Weblogging Ecosystem (2005). DOI: 10.1145/1134271.1134277 [sci-hub, @tor]\n\nExamples\n\n>>> g = gt.collection.data[\"polblogs\"]\n>>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))\n>>> w = g.new_edge_property(\"double\")\n>>> w.a = np.random.random(len(w.a))\n>>> x = gt.katz(g, weight=w)\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=x,\n... vertex_size=gt.prop_to_size(x, mi=5, ma=15),\n... vcmap=matplotlib.cm.gist_heat,\n... vorder=x, output=\"polblogs_katz.pdf\")\n<...>", null, "Katz centrality values of the a political blogs network of [adamic-polblogs], with random weights attributed to the edges.\n\ngraph_tool.centrality.hits(g, weight=None, xprop=None, yprop=None, epsilon=1e-06, max_iter=None)[source]\n\nCalculate the authority and hub centralities of each vertex in the graph.\n\nParameters\ngGraph\n\nGraph to be used.\n\nweightEdgePropertyMap (optional, default: None)\n\nEdge property map with the edge weights.\n\nxpropVertexPropertyMap, optional (default: None)\n\nVertex property map where the authority centrality must be stored.\n\nypropVertexPropertyMap, optional (default: None)\n\nVertex property map where the hub centrality must be stored.\n\nepsilonfloat, optional (default: 1e-6)\n\nConvergence condition. The iteration will stop if the total delta of all vertices are below this value.\n\nmax_iterint, optional (default: None)\n\nIf supplied, this will limit the total number of iterations.\n\nReturns\neigfloat\n\nThe largest eigenvalue of the cocitation matrix.\n\nxVertexPropertyMap\n\nA vertex property map containing the authority centrality values.\n\nyVertexPropertyMap\n\nA vertex property map containing the hub centrality values.\n\nbetweenness\n\nbetweenness centrality\n\neigenvector\n\neigenvector centrality\n\npagerank\n\nPageRank centrality\n\ntrust_transitivity\n\npervasive trust transitivity\n\nNotes\n\nThe Hyperlink-Induced Topic Search (HITS) centrality assigns hub ($$\\mathbf{y}$$) and authority ($$\\mathbf{x}$$) centralities to the vertices, following:\n\n\\begin{split}\\begin{align} \\mathbf{x} &= \\alpha\\mathbf{A}\\mathbf{y} \\\\ \\mathbf{y} &= \\beta\\mathbf{A}^T\\mathbf{x} \\end{align}\\end{split}\n\nwhere $$\\mathbf{A}$$ is the (weighted) adjacency matrix and $$\\lambda = 1/(\\alpha\\beta)$$ is the largest eigenvalue of the cocitation matrix, $$\\mathbf{A}\\mathbf{A}^T$$. (Without loss of generality, we set $$\\beta=1$$ in the algorithm.)\n\nThe algorithm uses the power method which has a topology-dependent complexity of $$O\\left(N\\times\\frac{-\\log\\epsilon}{\\log\|\\lambda_1/\\lambda_2\|}\\right)$$, where $$N$$ is the number of vertices, $$\\epsilon$$ is the epsilon parameter, and $$\\lambda_1$$ and $$\\lambda_2$$ are the largest and second largest eigenvalues of the (weighted) cocitation matrix, respectively.\n\nIf enabled during compilation, this algorithm runs in parallel.\n\nReferences\n\nhits-algorithm\n\nhttp://en.wikipedia.org/wiki/HITS_algorithm\n\nkleinberg-authoritative\n\nJ. Kleinberg, “Authoritative sources in a hyperlinked environment”, Journal of the ACM 46 (5): 604-632, 1999, DOI: 10.1145/324133.324140 [sci-hub, @tor].\n\npower-method\n\nhttp://en.wikipedia.org/wiki/Power_iteration\n\nL. A. Adamic and N. Glance, “The political blogosphere and the 2004 US Election”, in Proceedings of the WWW-2005 Workshop on the Weblogging Ecosystem (2005). DOI: 10.1145/1134271.1134277 [sci-hub, @tor]\n\nExamples\n\n>>> g = gt.collection.data[\"polblogs\"]\n>>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))\n>>> ee, x, y = gt.hits(g)\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=x,\n... vertex_size=gt.prop_to_size(x, mi=5, ma=15),\n... vcmap=matplotlib.cm.gist_heat,\n... vorder=x, output=\"polblogs_hits_auths.pdf\")\n<...>\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=y,\n... vertex_size=gt.prop_to_size(y, mi=5, ma=15),\n... vcmap=matplotlib.cm.gist_heat,\n... vorder=y, output=\"polblogs_hits_hubs.pdf\")\n<...>", null, "HITS authority values of the a political blogs network of [adamic-polblogs].", null, "HITS hub values of the a political blogs network of [adamic-polblogs].\n\ngraph_tool.centrality.eigentrust(g, trust_map, vprop=None, norm=False, epsilon=1e-06, max_iter=0, ret_iter=False)[source]\n\nCalculate the eigentrust centrality of each vertex in the graph.\n\nParameters\ngGraph\n\nGraph to be used.\n\ntrust_mapEdgePropertyMap\n\nEdge property map with the values of trust associated with each edge. The values must lie in the range [0,1].\n\nvpropVertexPropertyMap, optional (default: None)\n\nVertex property map where the values of eigentrust must be stored.\n\nnormbool, optional (default: False)\n\nNorm eigentrust values so that the total sum equals 1.\n\nepsilonfloat, optional (default: 1e-6)\n\nConvergence condition. The iteration will stop if the total delta of all vertices are below this value.\n\nmax_iterint, optional (default: None)\n\nIf supplied, this will limit the total number of iterations.\n\nret_iterbool, optional (default: False)\n\nIf true, the total number of iterations is also returned.\n\nReturns\neigentrustVertexPropertyMap\n\nA vertex property map containing the eigentrust values.\n\nbetweenness\n\nbetweenness centrality\n\npagerank\n\nPageRank centrality\n\ntrust_transitivity\n\npervasive trust transitivity\n\nNotes\n\nThe eigentrust [kamvar-eigentrust-2003] values $$t_i$$ correspond the following limit\n\n$\\mathbf{t} = \\lim_{n\\to\\infty} \\left(C^T\\right)^n \\mathbf{c}$\n\nwhere $$c_i = 1/\|V\|$$ and the elements of the matrix $$C$$ are the normalized trust values:\n\n$c_{ij} = \\frac{\\max(s_{ij},0)}{\\sum_{j} \\max(s_{ij}, 0)}$\n\nThe algorithm has a topology-dependent complexity.\n\nIf enabled during compilation, this algorithm runs in parallel.\n\nReferences\n\nkamvar-eigentrust-2003(1,2)\n\nS. D. Kamvar, M. T. Schlosser, H. Garcia-Molina “The eigentrust algorithm for reputation management in p2p networks”, Proceedings of the 12th international conference on World Wide Web, Pages: 640 - 651, 2003, DOI: 10.1145/775152.775242 [sci-hub, @tor]\n\nL. A. Adamic and N. Glance, “The political blogosphere and the 2004 US Election”, in Proceedings of the WWW-2005 Workshop on the Weblogging Ecosystem (2005). DOI: 10.1145/1134271.1134277 [sci-hub, @tor]\n\nExamples\n\n>>> g = gt.collection.data[\"polblogs\"]\n>>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))\n>>> w = g.new_edge_property(\"double\")\n>>> w.a = np.random.random(len(w.a)) * 42\n>>> t = gt.eigentrust(g, w)\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=t,\n... vertex_size=gt.prop_to_size(t, mi=5, ma=15),\n... vcmap=matplotlib.cm.gist_heat,\n... vorder=t, output=\"polblogs_eigentrust.pdf\")\n<...>", null, "Eigentrust values of the a political blogs network of [adamic-polblogs], with random weights attributed to the edges.\n\ngraph_tool.centrality.trust_transitivity(g, trust_map, source=None, target=None, vprop=None)[source]\n\nCalculate the pervasive trust transitivity between chosen (or all) vertices in the graph.\n\nParameters\ngGraph\n\nGraph to be used.\n\ntrust_mapEdgePropertyMap\n\nEdge property map with the values of trust associated with each edge. The values must lie in the range [0,1].\n\nsourceVertex (optional, default: None)\n\nSource vertex. All trust values are computed relative to this vertex. If left unspecified, the trust values for all sources are computed.\n\ntargetVertex (optional, default: None)\n\nThe only target for which the trust value will be calculated. If left unspecified, the trust values for all targets are computed.\n\nvpropVertexPropertyMap (optional, default: None)\n\nA vertex property map where the values of transitive trust must be stored.\n\nReturns\ntrust_transitivityVertexPropertyMap or float\n\nA vertex vector property map containing, for each source vertex, a vector with the trust values for the other vertices. If only one of source or target is specified, this will be a single-valued vertex property map containing the trust vector from/to the source/target vertex to/from the rest of the network. If both source and target are specified, the result is a single float, with the corresponding trust value for the target.\n\neigentrust\n\neigentrust centrality\n\nbetweenness\n\nbetweenness centrality\n\npagerank\n\nPageRank centrality\n\nNotes\n\nThe pervasive trust transitivity between vertices i and j is defined as\n\n$t_{ij} = \\frac{\\sum_m A_{m,j} w^2_{G\\setminus\\{j\\}}(i\\to m)c_{m,j}} {\\sum_m A_{m,j} w_{G\\setminus\\{j\\}}(i\\to m)}$\n\nwhere $$A_{ij}$$ is the adjacency matrix, $$c_{ij}$$ is the direct trust from i to j, and $$w_G(i\\to j)$$ is the weight of the path with maximum weight from i to j, computed as\n\n$w_G(i\\to j) = \\prod_{e\\in i\\to j} c_e.$\n\nThe algorithm measures the transitive trust by finding the paths with maximum weight, using Dijkstra’s algorithm, to all in-neighbors of a given target. This search needs to be performed repeatedly for every target, since it needs to be removed from the graph first. For each given source, the resulting complexity is therefore $$O(V^2\\log V)$$ for all targets, and $$O(V\\log V)$$ for a single target. For a given target, the complexity for obtaining the trust from all given sources is $$O(kV\\log V)$$, where $$k$$ is the in-degree of the target. Thus, the complexity for obtaining the complete trust matrix is $$O(EV\\log V)$$, where $$E$$ is the number of edges in the network.\n\nIf enabled during compilation, this algorithm runs in parallel.\n\nReferences\n\nrichters-trust-2010\n\nOliver Richters and Tiago P. Peixoto, “Trust Transitivity in Social Networks,” PLoS ONE 6, no. 4: e1838 (2011), DOI: 10.1371/journal.pone.0018384 [sci-hub, @tor]\n\nL. A. Adamic and N. Glance, “The political blogosphere and the 2004 US Election”, in Proceedings of the WWW-2005 Workshop on the Weblogging Ecosystem (2005). DOI: 10.1145/1134271.1134277 [sci-hub, @tor]\n\nExamples\n\n>>> g = gt.collection.data[\"polblogs\"]\n>>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))\n>>> g = gt.Graph(g, prune=True)\n>>> w = g.new_edge_property(\"double\")\n>>> w.a = np.random.random(len(w.a))\n>>> t = gt.trust_transitivity(g, w, source=g.vertex(42))\n>>> gt.graph_draw(g, pos=g.vp[\"pos\"], vertex_fill_color=t,\n... vertex_size=gt.prop_to_size(t, mi=5, ma=15),\n... vcmap=matplotlib.cm.gist_heat,\n... vorder=t, output=\"polblogs_trust_transitivity.pdf\")\n<...>", null, "Trust transitivity values from source vertex 42 of the a political blogs network of [adamic-polblogs], with random weights attributed to the edges." ]	[ null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_pr.png", null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_pr_pers.png", null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_betweenness.png", null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_closeness.png", null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_eigenvector.png", null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_katz.png", null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_hits_auths.png", null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_hits_hubs.png", null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_eigentrust.png", null, "https://graph-tool.skewed.de/static/doc/_images/polblogs_trust_transitivity.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.60019433,"math_prob":0.9791077,"size":26851,"snap":"2019-43-2019-47","text_gpt3_token_len":7632,"char_repetition_ratio":0.14422467,"word_repetition_ratio":0.42213348,"special_character_ratio":0.2838628,"punctuation_ratio":0.20477612,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99882495,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,3,null,4,null,3,null,1,null,4,null,4,null,3,null,1,null,3,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-18T23:18:52Z\",\"WARC-Record-ID\":\"<urn:uuid:2427f0bd-fd19-4ea9-8cc9-dd460a755f0c>\",\"Content-Length\":\"118110\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:30d68720-3842-4ac0-8ed8-c450ecb8afe6>\",\"WARC-Concurrent-To\":\"<urn:uuid:40b19b23-419b-45ab-8ef6-a4675dad48c0>\",\"WARC-IP-Address\":\"74.50.54.68\",\"WARC-Target-URI\":\"https://graph-tool.skewed.de/static/doc/centrality.html\",\"WARC-Payload-Digest\":\"sha1:LOYGDYS7IXG3L7J2QUTX2JC5CQZQR5Z3\",\"WARC-Block-Digest\":\"sha1:IPAR2LRDV6BUJGYEMYSJ74ON7C7FTS6A\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986685915.43_warc_CC-MAIN-20191018231153-20191019014653-00264.warc.gz\"}"}
https://socratic.org/questions/5340858702bf3429e1cd603e	[ "# Question #d603e\n\nApr 28, 2015\n\nFor a simple pendulum, it's is not often easy to find potential.\n\nOn the other hand, it is easier and for most cases, more useful to find the change in potential energy", null, "That is, $\\Delta \\text{Pe}$ instead of just $\\text{Pe}$\n\n$\\Delta \\text{Pe} = m g \\Delta h$\n$m =$ mass\n$g =$ acceleration due to gravity\n$\\Delta h =$ change in height above the ground\n\nBut in fact, if we know the position of the ball above the ground, them we can calculate the Potential energy as $\\text{Pe} = m g {x}_{1}$ for example!\n\n$\\Delta \\text{Pe}$ is more of interest because we can conserve energy.\nLike this,\n$m g \\Delta h = \\frac{1}{2} m \\Delta {v}^{2}$" ]	[ null, "https://useruploads.socratic.org/CDFyxx5TRBLgA5cT1Xg2_7C267876-0B87-4FD3-AB36-D8050DCCADFA.PNG", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.82254064,"math_prob":0.9997907,"size":465,"snap":"2020-45-2020-50","text_gpt3_token_len":112,"char_repetition_ratio":0.10412148,"word_repetition_ratio":0.0,"special_character_ratio":0.23225807,"punctuation_ratio":0.095744684,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999671,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-26T07:18:42Z\",\"WARC-Record-ID\":\"<urn:uuid:0040783b-e3b5-4fa7-956e-83ea2b9a1b1f>\",\"Content-Length\":\"33479\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1b8f24f0-0a8d-4b7b-9b1f-8c810fcf4ee9>\",\"WARC-Concurrent-To\":\"<urn:uuid:4d65d5a9-28e3-498b-be51-97ec8a0ed24e>\",\"WARC-IP-Address\":\"216.239.32.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/5340858702bf3429e1cd603e\",\"WARC-Payload-Digest\":\"sha1:4IILYJIO34HLHCUSZH2K73UFHIK4TNGA\",\"WARC-Block-Digest\":\"sha1:ZO32UAP4A2ABWBIEFCZCYYBQECEO5IJ5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141186761.30_warc_CC-MAIN-20201126055652-20201126085652-00704.warc.gz\"}"}
https://nrich.maths.org/funnyfactorisation	[ "#### You may also like", null, "Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!", null, "### Multiplication Magic\n\nGiven any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). The question asks you to explain the trick.", null, "### N000ughty Thoughts\n\nHow many noughts are at the end of these giant numbers?\n\n# Funny Factorisation\n\n##### Age 11 to 16 Challenge Level:\n\nSome 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using each of the digits $1$ to $9$ once, and only once.\n\nThe number $4396$ can be written as just such a product.", null, "Can you find the factors?\n\nMaths is full of surprises!\nThe numbers $5796$ and $5346$ can each be written as a product like this in two different ways.", null, "Can you find these four funny factorisations?\n\nExtension\n\nThere are two more funny factorisations to find, using each of the digits $1$ to $9$ once, and only once.\nCan you fill in the blanks in the multiplication below to find one of them?", null, "If you know a bit about computer programming, you may wish to write a program to find the final funny factorisation." ]	[ null, "https://nrich.maths.org/content/01/09/bbprob1/icon.png", null, "https://nrich.maths.org/content/99/03/15plus1/icon.jpg", null, "https://nrich.maths.org/content/01/03/15plus3/icon.jpg", null, "https://nrich.maths.org/content/00/11/six3/funnyfact1.png", null, "https://nrich.maths.org/content/00/11/six3/funnyfact2.png", null, "https://nrich.maths.org/content/00/11/six3/funnyfact3.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9008027,"math_prob":0.9869808,"size":710,"snap":"2020-34-2020-40","text_gpt3_token_len":173,"char_repetition_ratio":0.12606232,"word_repetition_ratio":0.122137405,"special_character_ratio":0.2535211,"punctuation_ratio":0.08783784,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99163115,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,null,null,8,null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-18T14:51:47Z\",\"WARC-Record-ID\":\"<urn:uuid:a1de3b80-3273-42b2-883a-1bfd9cabf268>\",\"Content-Length\":\"15075\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f5647536-828f-42f7-a87a-696d5762d895>\",\"WARC-Concurrent-To\":\"<urn:uuid:aa012201-b9ee-45a3-8047-bbd70d12b6b6>\",\"WARC-IP-Address\":\"131.111.18.195\",\"WARC-Target-URI\":\"https://nrich.maths.org/funnyfactorisation\",\"WARC-Payload-Digest\":\"sha1:FYY6GF2P3JPU57AD3VEENEYTEROZMXUX\",\"WARC-Block-Digest\":\"sha1:DDZNPBQM5XZSGZD3SU6MJRUZJ2A6FQTT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400187899.11_warc_CC-MAIN-20200918124116-20200918154116-00404.warc.gz\"}"}
https://dsp.stackexchange.com/questions/47604/when-listening-in-to-an-am-signals-of-various-frequencies-how-do-we-exactly-tun	[ "# When listening in to an AM signals of various frequencies, how do we exactly tune in?\n\nAlright, so I read on AM and Double Sideband AM, but I don't the more fundamental idea - the frequencies.\n\nFrequency is just: $\\frac{1}{T}$, where T is period\n\nSo difference between 5 Hz and 30 Hz is that period of 1st signal is $\\frac{1}{5}$ = 0.2 seconds, and of 2nd signal = $\\frac{1}{30} = 0.03 seconds$\n\nand I know in AM you need to demodulate by multiplying by cos(wt) to bring message to lower frequency and then low pass filter to only have message signal etc\n\nbut for simplicity sake, let's assume two signals are transmitted, one is at 5Hz the other one is at 30Hz\n\nHow do you \"listen in\"? Because the frequency spectrum, where frequency is x-axis is a bit misleading!", null, "It shows that you can magically shift to the right and just listen in to the needed signal! That's not the case! Frequency is just how fast a signal repeats. Amplitude is changing according to sine function.\n\nSo if you have two signals, one at 5Hz and second one at 30Hz, then they both \"are in the air\", you can't just magically listen in every $\\frac{1}{30Hz} = 0.03 seconds$ and only get signal at 30Hz, you'll also be getting the signal at 5Hz, they'll be overlapping because frequency is just how fast signal is changing.\n\nSo how do you listen in? Do you just listen in for everything?\n\nThen you have a signal that's changing every \"0.2 seconds (5Hz)\" and another one every \"0.03 seconds\", they'll overlap of course. The only way they don't is if there's only one signal is in the air. I don't see how different frequencies allow to fine tune to one particular signal and ignore others.\n\nBesides, even if there's just one signal in the air, say it's the 5Hz signal, how do you \"listen in\"? Do you just \"listen in\" continuously, or a receiver just turns on and shuts off every $\\frac{1}{5Hz} = 0.2 sec$????", null, "• Trigonometric sum and difference formulas are “just the case”, even if you think the math is “magic”. Also, sampling needs to be done somewhat above twice the highest frequency. Mar 6, 2018 at 11:17\n• I don't really understand what the confusion is, but something that you might be missing is this: before receiving an AM signal, you need to get rid of everything else in the spectrum: IOW, you need a bandpass filter centered around the carrier you're interested in, and that covers both SB, and nothing else.\n– MBaz\nMar 6, 2018 at 13:06\n\nOk, I think here is a good point to introduce equivalent baseband, because you implicitly are already using it!\n\nSo, what does your cosine 5Hz audio signal look like, if you were to set $f_c=0$, in spectrum?\n\nExactly, one dirac at +5 Hz, and one at -5 Hz! Hence, when you mix that up to $f_c\\ne 0$, you get symmetric sidebands. That works for any real signals (ie. for any audio signal) – and even when you add them. That's where your two sidebands come from – positive and (hermitian) symmetrical negative components of any real-valued signal.\n\nSo, in baseband, your sum of 5 and 30 Hz cosines have four spectral components – at -30, -5, +5 and +30 Hz, and mixed up to the carrier frequency you get the same discrete spectral components, but added to $\\pm f_c$. (your figure also shows a component at $f_c$, but that's only there if you got a DC component in your baseband signal, and/or you're not suppressing the carrier)\n\nNow, there's very different receiver architectures for AM-modulated audio. None of them \"just looks every 1/(audio period)\". \"Looking every so often\" presumes you're building something digital. Most AM receivers (most AM being pretty obsolete by now) are not digital. The simplest detector methods really are just rectifying diodes and a low pass filter to get rid of the RF content – I'll leave googling for \"AM diode detector\" up to you; there's a plethora of good articles on that out there. This is all continuous-time, so there's no \"looking that often\" there – it all happens by electronically processing the continuous signal.\n\nNow, assuming we're really aiming for digital here:\n\nThat 1/(audio period) wouldn't even make sense for audio – it breaks Nyquist; you need at least twice the audio bandwidth as sampling rate to be able to reconstruct the signal.\n\nWhat one can build is simply a mixer with $f_c$, which will first (continuous-time!) multiply with a harmonic of that frequency (effectively, a complex sinusoid), and then sample (that's the act of looking only every so often) that, and then you get a digital signal that's basically nothing but your original audio sum.\n\nNote that you've been asking about \"how to deal with the fact that you add two sines of different frequencies\", but that question is totally independent from the AM aspect of that: you just can. Under the Fourier Transform, i.e. in the spectrum, these are orthogonal, i.e. you can perfectly separate them, both in a computer, in a circuit, or with your ear. That's why you're hopefully able to listen to sounds that aren't made of a single tone. In fact, in reality, single-tone sounds are extremely rare.\n\n• >\"The simplest detector methods really are just rectifying diodes and a low pass filter to get rid of the RF content\" How does it receive the signal? And when it is send at a high frequency through air... how is it being transmitted to tower? How does it \"propagate\"?\n– Jack\nMar 7, 2018 at 0:09\n• I said \"I leave googling for diode receivers up to you\" in the very next sentence, with the hint that there's good material out there. I can't take reading what's available off your shoulders. Mar 7, 2018 at 0:35" ]	[ null, "https://i.stack.imgur.com/95LcJ.png", null, "https://i.stack.imgur.com/Yvn21.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.96246386,"math_prob":0.8827668,"size":1874,"snap":"2023-40-2023-50","text_gpt3_token_len":487,"char_repetition_ratio":0.14331551,"word_repetition_ratio":0.0,"special_character_ratio":0.26894343,"punctuation_ratio":0.117794484,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95020616,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-22T16:02:29Z\",\"WARC-Record-ID\":\"<urn:uuid:7cc4466d-6793-443f-9a23-8c2413d353c5>\",\"Content-Length\":\"162929\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5bb5baa9-f7dc-4e39-8e43-58449cb080f6>\",\"WARC-Concurrent-To\":\"<urn:uuid:ec8cd066-87b7-401b-94db-012da1589001>\",\"WARC-IP-Address\":\"104.18.11.86\",\"WARC-Target-URI\":\"https://dsp.stackexchange.com/questions/47604/when-listening-in-to-an-am-signals-of-various-frequencies-how-do-we-exactly-tun\",\"WARC-Payload-Digest\":\"sha1:7PJKD2XREQKI5TLI7YNJ5XOKQSB6TAJ5\",\"WARC-Block-Digest\":\"sha1:DCFXS6KZDT7ZNGXJM33OX2JNW77EUSLO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506420.84_warc_CC-MAIN-20230922134342-20230922164342-00681.warc.gz\"}"}
https://physics.stackexchange.com/questions/151317/minimum-angular-velocity-for-circular-motion-pendulum/151322	[ "# Minimum angular velocity for circular motion (pendulum)\n\nHow can I show that there is a minimum angular velocity $\\omega_{min}$, different from zero, such that if we chose an $\\omega$ smaller than $\\omega_{min}$, then it is not possible to have a circular motion as in the picture?", null, "• Why does it merit a bounty? It looks straight forward. Are we missing something? Is this a quantum mechanics question, where there is a minimum energy level? – mmesser314 Dec 9 '14 at 5:35\n• They convinced me they were right!, the correct answer is that there is a minimum $\\omega_{min}$, which is the one requires for an angle $\\theta=0$ – Wolphram jonny Dec 9 '14 at 17:53\n\n## 3 Answers\n\nIf you solve the problem for the two forces the vertical and the horizontal force (which is required for the circular motion) you obtain the relation\n\n$$\\omega^2=\\frac{g}{L\\cos\\theta}$$\n\nHence the minimum required $\\omega$ is $\\sqrt{g/l}$, the same as the angular frequency for motion of a bob in a plane.\n\n• this answer is wrong, why do you think that w is a minimum one instead to that corresponding to circular moption for a given angle? remember that given an angle, there is only one possible omega, there is NOT a range of possible omegas. – Wolphram jonny Dec 9 '14 at 4:38\n• The minimum occurs when $cos \\theta$ equals 1, or $\\theta$ equals 0. Which means there is no circular motion. – LDC3 Dec 9 '14 at 4:39\n• OK, then you agree, there is no minimum for circular motion, just that at theta=0 there is no motion at all! – Wolphram jonny Dec 9 '14 at 4:47\n• No value smaller than w=√g/L can lead to circular motion for simple reason. – SAKhan Dec 9 '14 at 5:07\n\nExpanding the correct answer of @SAKhan:\n\nAssume that the conical pendulum is rotating at an angle $\\theta$ at an angular velocity $\\omega$.\n\nNote also that the radius of the circle is given by $$r=L\\sin(\\theta)$$\n\nFor the point mass to move in a horizontal circle, the total vertical force is zero:$$T\\cos(\\theta)=mg$$\n\nThe net horizontal force must supply the needed centripetal force:$$T\\sin(\\theta)=m\\omega^2r=m\\omega^2L\\sin(\\theta)$$Combining these two equations to eliminate $T$, we get:$$\\omega^2=\\frac{g}{L\\cos(\\theta)}$$\n\nThe maximum value of $\\cos(\\theta)$ is $1$, when $\\theta=0$, so $$\\omega_{minimum}=\\sqrt{\\frac{g}{L}}$$\n\nEdited for clarity:\n\nSo, what does this math mean?\n\nAssume for the sake of simplicity that the length, $L$ of the pendulum is $9.8$ meters, Then the equation for $\\omega$ reduces to$$\\omega = \\sqrt{\\frac{1}{\\cos(\\theta)}}$$ Now, we repeatedly start the pendulum into circular motion, each time at a some different angle $\\theta$. (This could take some fiddling!) For each of these set-ups, once we are sure that the pendulum is moving in a circle, we measure the angle $\\theta$ and the angular velocity $\\omega$. This angular velocity can be measured by taking the period of the circular motion, and dividing it into $2\\pi$.\n\nIf we took all the data and plot them, we would obtain graph that shows that the value of $\\omega$ approaches $1$ as $\\theta$ approaches $0$. Strictly speaking, $\\omega=1$ is a lower limit (rather than a minimum) that is approached asymptotically as the angle $\\theta$ approaches zero.", null, "The vertical axis is $\\omega$, in radians, and the horizontal axis is $\\theta$ in degrees\n\n• why you conlcude that this be the minimum omega for circular motion instead of conlcusing that it is the omega required for circular motion at angle theta? – Wolphram jonny Dec 9 '14 at 4:33\n• The minimum occurs when θ equals 0; which means the pendulum is hanging vertically. – LDC3 Dec 9 '14 at 4:42\n• The graph nicely demonstrates that there is one value of $\\omega$ for each value of $\\theta$, and that this value tends to a non-zero value when the circular motion becomes very small. I wish you had labeled the vertical axis in units of $\\frac{L}{g}$ rather than showing that $\\omega$ tends to $1$ which is slightly misleading. Perhaps define $\\omega_0=\\sqrt{L/g}$ and plot $\\frac{\\omega}{\\omega_0}$ ... – Floris Dec 9 '14 at 14:15\n• Nicely explained – SAKhan Oct 1 '17 at 6:25\n\nThere is such minimun agngular speed: You will always find an an angle that results in circular motion for any given angular speed. The angle is given by:\n\n$$\\cos \\theta=\\frac{g}{L \\omega^2}$$\n\nUpdate: I got to this expression by using the equations of motion:\n\n$m\\omega^2L \\sin \\theta=T\\sin\\theta$\n\nand\n\n$T\\cos\\theta=mg$\n\nWhat this means is that the minimum speed is reached for $\\theta=0$, where \\omega_min=\\sqrt{L/g}. Any other circular motion will require a larger angular velocity. Thus, if we give the pendulum a spees less that the minimum, it will not be able to undergo a circular motion and starts to oscilate.\n\n• @Floris I updated my answer, are you sure I forgot some force? – Wolphram jonny Dec 9 '14 at 3:37\n• Have you forgotten that the bob will move like a regular pendulum below its natural frequency? There is a restoring force proportional to $\\sin\\theta$ when there is no rotation. I believe that sets the lower limit on $\\omega$ – Floris Dec 9 '14 at 3:41\n• Yes, thanks! I missed a sin (theta) when I updated the answer, I'll correct it (but the solution is correct) – Wolphram jonny Dec 9 '14 at 3:41\n• @Wolphramjonny great! But now your equation contradicts your sentence \"There is no such minimun agngular speed\" (meaning, what if $g/L\\omega^2>1$?) – user12029 Dec 9 '14 at 4:33\n• But the question is asking the opposite: for a given $\\omega$ can you always find an angle? (or rather, the question is presenting the assertion that you cannot, and asking for a proof) – David Z Dec 9 '14 at 8:13" ]	[ null, "https://i.stack.imgur.com/9kZyY.jpg", null, "https://i.stack.imgur.com/1mcDo.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86518997,"math_prob":0.9988743,"size":5888,"snap":"2019-35-2019-39","text_gpt3_token_len":1623,"char_repetition_ratio":0.17046227,"word_repetition_ratio":0.052083332,"special_character_ratio":0.28125,"punctuation_ratio":0.09290096,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99993384,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-18T13:29:08Z\",\"WARC-Record-ID\":\"<urn:uuid:085d5f4a-df2a-45c6-9228-039fbd8251bb>\",\"Content-Length\":\"165111\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7e5fe439-11c3-4cb1-8dde-b304836d8095>\",\"WARC-Concurrent-To\":\"<urn:uuid:29d5b992-9d1c-4bd9-99e6-3326476b72c6>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/151317/minimum-angular-velocity-for-circular-motion-pendulum/151322\",\"WARC-Payload-Digest\":\"sha1:BUANKSGF5HHTBFBDBV6RTRXZXEBZS232\",\"WARC-Block-Digest\":\"sha1:OL5D2JJVRV63IG52QM2URCYEQAGB2BP7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027313889.29_warc_CC-MAIN-20190818124516-20190818150516-00081.warc.gz\"}"}
https://answers.everydaycalculation.com/simplify-fraction/280-1350	[ "Solutions by everydaycalculation.com\n\n## Reduce 280/1350 to lowest terms\n\nThe simplest form of 280/1350 is 28/135.\n\n#### Steps to simplifying fractions\n\n1. Find the GCD (or HCF) of numerator and denominator\nGCD of 280 and 1350 is 10\n2. Divide both the numerator and denominator by the GCD\n280 ÷ 10/1350 ÷ 10\n3. Reduced fraction: 28/135\nTherefore, 280/1350 simplified to lowest terms is 28/135.\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]	[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.723005,"math_prob":0.7858586,"size":390,"snap":"2023-40-2023-50","text_gpt3_token_len":132,"char_repetition_ratio":0.15803109,"word_repetition_ratio":0.0,"special_character_ratio":0.47179487,"punctuation_ratio":0.08219178,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9535244,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-05T08:13:21Z\",\"WARC-Record-ID\":\"<urn:uuid:c82392ff-e953-4577-a37c-a7f45d323071>\",\"Content-Length\":\"6736\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:adf12cae-6baa-4806-9f8d-03ca70eb508a>\",\"WARC-Concurrent-To\":\"<urn:uuid:564fc824-e534-41a8-9463-97cb9d9df69f>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/simplify-fraction/280-1350\",\"WARC-Payload-Digest\":\"sha1:L7EQRGQZWQIZ3J524ZNADPKO6B2PUTEH\",\"WARC-Block-Digest\":\"sha1:2R5UT4T3QQ7YTNTZSICXWKOFMRMA76F4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100550.40_warc_CC-MAIN-20231205073336-20231205103336-00442.warc.gz\"}"}