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https://facebook.github.io/prophet/docs/non-daily_data.html	[ "## Sub-daily data\n\nProphet can make forecasts for time series with sub-daily observations by passing in a dataframe with timestamps in the `ds` column. The format of the timestamps should be YYYY-MM-DD HH:MM:SS - see the example csv here. When sub-daily data are used, daily seasonality will automatically be fit. Here we fit Prophet to data with 5-minute resolution (daily temperatures at Yosemite):\n\n``````1\n2\n3\n4\n5\n6\n# R\nm <- prophet(df, changepoint.prior.scale=0.01)\nfuture <- make_future_dataframe(m, periods = 300, freq = 60 * 60)\nfcst <- predict(m, future)\nplot(m, fcst)\n``````\n``````1\n2\n3\n4\n5\n6\n# Python\nm = Prophet(changepoint_prior_scale=0.01).fit(df)\nfuture = m.make_future_dataframe(periods=300, freq='H')\nfcst = m.predict(future)\nfig = m.plot(fcst)\n``````", null, "The daily seasonality will show up in the components plot:\n\n``````1\n2\n# R\nprophet_plot_components(m, fcst)\n``````\n``````1\n2\n# Python\nfig = m.plot_components(fcst)\n``````", null, "## Data with regular gaps\n\nSuppose the dataset above only had observations from 12a to 6a:\n\n``````1\n2\n3\n4\n5\n6\n7\n8\n# R\ndf2 <- df %>%\nmutate(ds = as.POSIXct(ds, tz=\"GMT\")) %>%\nfilter(as.numeric(format(ds, \"%H\")) < 6)\nm <- prophet(df2)\nfuture <- make_future_dataframe(m, periods = 300, freq = 60 * 60)\nfcst <- predict(m, future)\nplot(m, fcst)\n``````\n``````1\n2\n3\n4\n5\n6\n7\n8\n# Python\ndf2 = df.copy()\ndf2['ds'] = pd.to_datetime(df2['ds'])\ndf2 = df2[df2['ds'].dt.hour < 6]\nm = Prophet().fit(df2)\nfuture = m.make_future_dataframe(periods=300, freq='H')\nfcst = m.predict(future)\nfig = m.plot(fcst)\n``````", null, "The forecast seems quite poor, with much larger fluctuations in the future than were seen in the history. The issue here is that we have fit a daily cycle to a time series that only has data for part of the day (12a to 6a). The daily seasonality is thus unconstrained for the remainder of the day and is not estimated well. The solution is to only make predictions for the time windows for which there are historical data. Here, that means to limit the `future` dataframe to have times from 12a to 6a:\n\n``````1\n2\n3\n4\n5\n# R\nfuture2 <- future %>%\nfilter(as.numeric(format(ds, \"%H\")) < 6)\nfcst <- predict(m, future2)\nplot(m, fcst)\n``````\n``````1\n2\n3\n4\n5\n# Python\nfuture2 = future.copy()\nfuture2 = future2[future2['ds'].dt.hour < 6]\nfcst = m.predict(future2)\nfig = m.plot(fcst)\n``````", null, "The same principle applies to other datasets with regular gaps in the data. For example, if the history contains only weekdays, then predictions should only be made for weekdays since the weekly seasonality will not be well estimated for the weekends.\n\n## Monthly data\n\nYou can use Prophet to fit monthly data. However, the underlying model is continuous-time, which means that you can get strange results if you fit the model to monthly data and then ask for daily forecasts. Here we forecast US retail sales volume for the next 10 years:\n\n``````1\n2\n3\n4\n5\n6\n# R\nm <- prophet(df, seasonality.mode = 'multiplicative')\nfuture <- make_future_dataframe(m, periods = 3652)\nfcst <- predict(m, future)\nplot(m, fcst)\n``````\n``````1\n2\n3\n4\n5\n6\n# Python\nm = Prophet(seasonality_mode='multiplicative').fit(df)\nfuture = m.make_future_dataframe(periods=3652)\nfcst = m.predict(future)\nfig = m.plot(fcst)\n``````", null, "This is the same issue from above where the dataset has regular gaps. When we fit the yearly seasonality, it only has data for the first of each month and the seasonality components for the remaining days are unidentifiable and overfit. This can be clearly seen by doing MCMC to see uncertainty in the seasonality:\n\n``````1\n2\n3\n4\n# R\nm <- prophet(df, seasonality.mode = 'multiplicative', mcmc.samples = 300)\nfcst <- predict(m, future)\nprophet_plot_components(m, fcst)\n``````\n``````1\n2\n3\n4\n# Python\nm = Prophet(seasonality_mode='multiplicative', mcmc_samples=300).fit(df, show_progress=False)\nfcst = m.predict(future)\nfig = m.plot_components(fcst)\n``````\n``````1\n2\nWARNING:pystan:481 of 600 iterations saturated the maximum tree depth of 10 (80.2 %)\nWARNING:pystan:Run again with max_treedepth larger than 10 to avoid saturation\n``````", null, "The seasonality has low uncertainty at the start of each month where there are data points, but has very high posterior variance in between. When fitting Prophet to monthly data, only make monthly forecasts, which can be done by passing the frequency into `make_future_dataframe`:\n\n``````1\n2\n3\n4\n# R\nfuture <- make_future_dataframe(m, periods = 120, freq = 'month')\nfcst <- predict(m, future)\nplot(m, fcst)\n``````\n``````1\n2\n3\n4\n# Python\nfuture = m.make_future_dataframe(periods=120, freq='MS')\nfcst = m.predict(future)\nfig = m.plot(fcst)\n``````", null, "In Python, the frequency can be anything from the pandas list of frequency strings here: https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#timeseries-offset-aliases . Note that `MS` used here is month-start, meaning the data point is placed on the start of each month.\n\nIn monthly data, yearly seasonality can also be modeled with binary extra regressors. In particular, the model can use 12 extra regressors like `is_jan`, `is_feb`, etc. where `is_jan` is 1 if the date is in Jan and 0 otherwise. This approach would avoid the within-month unidentifiability seen above. Be sure to use `yearly_seasonality=False` if monthly extra regressors are being added.\n\n## Holidays with aggregated data\n\nHoliday effects are applied to the particular date on which the holiday was specified. With data that has been aggregated to weekly or monthly frequency, holidays that don’t fall on the particular date used in the data will be ignored: for example, a Monday holiday in a weekly time series where each data point is on a Sunday. To include holiday effects in the model, the holiday will need to be moved to the date in the history dataframe for which the effect is desired. Note that with weekly or monthly aggregated data, many holiday effects will be well-captured by the yearly seasonality, so added holidays may only be necessary for holidays that occur in different weeks throughout the time series.\n\nEdit on GitHub" ]	[ null, "https://facebook.github.io/prophet/static/non-daily_data_files/non-daily_data_4_0.png", null, "https://facebook.github.io/prophet/static/non-daily_data_files/non-daily_data_7_0.png", null, "https://facebook.github.io/prophet/static/non-daily_data_files/non-daily_data_10_0.png", null, "https://facebook.github.io/prophet/static/non-daily_data_files/non-daily_data_13_0.png", null, "https://facebook.github.io/prophet/static/non-daily_data_files/non-daily_data_16_0.png", null, "https://facebook.github.io/prophet/static/non-daily_data_files/non-daily_data_19_1.png", null, "https://facebook.github.io/prophet/static/non-daily_data_files/non-daily_data_22_0.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8234726,"math_prob":0.96399236,"size":6227,"snap":"2023-40-2023-50","text_gpt3_token_len":1634,"char_repetition_ratio":0.1275912,"word_repetition_ratio":0.13748658,"special_character_ratio":0.26577806,"punctuation_ratio":0.1312709,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9929797,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null,3,null,2,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-09T21:39:42Z\",\"WARC-Record-ID\":\"<urn:uuid:49bcc390-1c25-40fb-b47e-b66317f5ec71>\",\"Content-Length\":\"53533\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ec1c2431-4178-4ad1-9748-7e1087597087>\",\"WARC-Concurrent-To\":\"<urn:uuid:94ce73d5-7102-4153-bf5d-535a2eefb873>\",\"WARC-IP-Address\":\"185.199.109.153\",\"WARC-Target-URI\":\"https://facebook.github.io/prophet/docs/non-daily_data.html\",\"WARC-Payload-Digest\":\"sha1:JRE6GABY5PDTYK33FQJNMH4AO5LR77GN\",\"WARC-Block-Digest\":\"sha1:GCR2MIX6KTCXE2IO4VHCNIDO4ANDAXVE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100972.58_warc_CC-MAIN-20231209202131-20231209232131-00610.warc.gz\"}"}
http://intellectualmathematics.com/blog/critique-of-langes-theory-of-explanation/	[ "# Critique of Lange’s theory of explanation\n\nNon-explanatory proofs are typically brute-force computations that do not illuminate why the theorem holds, but rather “makes it seem like an accident of algebra, as it were” (16), “supplies ‘little understanding’ and fails to show ‘what’s going on’” (20). Everyone agrees thus far.\n\nExplanatory proofs tend to be more conceptual, as Lange's examples show. In my view, the right way to characterise how these proofs differ from the non-explanatory ones are in terms of cognisability, as I have argued elsewhere.\n\nBut Lange has a different proposal. He argues that if a result has a notable symmetry to it then an explanatory proof must itself involve this symmetry in an essential way: “A proof that exploits the symmetry of the setup is privileged as explanatory” (18) and “only a proof exploiting such a symmetry in the problem is recognized as explaining why the solution holds” (19). Lange later generalises from this to allow any “salient feature” of the theorem to take the role of symmetry in this argument (28).\n\nIn my view this proposal is off the mark. I say that if a proof is cognisable it would typically count as explanatory, regardless of whether it exploits symmetry properties of the result or not.\n\nAn example illustrating this is the proof of the equality of the coordinate and cosine forms of the scalar product.\n\nIn my calculus book I prove this in a cognisable way. I start with the geometrical idea of a projection, and I show through intuitive-visual reasoning how this leads to the coordinate form. This is an explanatory proof, in my opinion.\n\nThe standard proof in other textbooks is to start with the coordinate form and derive the cosine form using the law of cosines. This is obviously extremely unsatisfactory, since the law of cosines is a “black-box,” algebraic hocus-pocus result. This is a prototypically non-explanatory proof, in the sense of the quotations from Lange above.\n\nYet according to Lange’s proposal it is the latter proof that is the explanatory one. For the result is certainly symmetric, and the standard proof likewise respects this symmetry throughout.\n\nMy proof, on the other hand, is most definitely asymmetrical: it involves the projection of one vector onto another, an asymmetrical relation. Thus my proof actually introduces an asymmetry that was not in the result itself. And it was precisely this move that made the proof congnisable, and thereby explanatory, in my view. Which is the exact opposite of what Lange’s proposal says should happen." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93874866,"math_prob":0.83864623,"size":2599,"snap":"2021-31-2021-39","text_gpt3_token_len":537,"char_repetition_ratio":0.14759152,"word_repetition_ratio":0.0,"special_character_ratio":0.19969219,"punctuation_ratio":0.08902691,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9779658,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-24T05:29:00Z\",\"WARC-Record-ID\":\"<urn:uuid:41eb2b67-5e16-480f-b9ec-b9231cb86d32>\",\"Content-Length\":\"28891\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2e44c6f8-bd7b-421f-8c17-3dd6d42506d6>\",\"WARC-Concurrent-To\":\"<urn:uuid:c5e6f9ab-64f2-4604-86fc-19a4c7ef23db>\",\"WARC-IP-Address\":\"198.46.81.182\",\"WARC-Target-URI\":\"http://intellectualmathematics.com/blog/critique-of-langes-theory-of-explanation/\",\"WARC-Payload-Digest\":\"sha1:RUMOKNCMJ27CJU6OXYQNNR2YJEJ7IODS\",\"WARC-Block-Digest\":\"sha1:MAFPR75LPFMVTXRODOQUMB3BC7LIVFAW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057504.60_warc_CC-MAIN-20210924050055-20210924080055-00276.warc.gz\"}"}
http://slideplayer.com/slide/4626559/	[ "", null, "Measurement Notes Chapter 2 Length Scientist use the metric system—a standard measurement system based on the #10. The meter is the basic unit. millimeter.\n\nPresentation on theme: \"Measurement Notes Chapter 2 Length Scientist use the metric system—a standard measurement system based on the #10. The meter is the basic unit. millimeter.\"— Presentation transcript:\n\nMeasurement Notes Chapter 2\n\nLength Scientist use the metric system—a standard measurement system based on the #10. The meter is the basic unit. millimeter = mmKingKilo (100 centi) centimeter = cmHenryHecto (10 deci) decimeter = dmDiedDeca meter = mWhileWhole (1,000 kilo) kilometer = kmDrinkingDeci 10 mm = 1 cmChocolateCenti 10 cm = 1 dmMilkMilli 100 cm = 1m 1000 m = 1 km\n\nMetric Units Mass refers to the amount of matter in an object. The base unit of mass in the metric system in the gram and is represented by g. Standard: 1 kilogram is equal to the mass of the International Prototype Kilogram (IPK), a platinum-iridium cylinder kept by the BIPM at Sèvres, France. Metric Units 1 Kilogram (kg) = 1000 Grams (g) 1 Gram (g) = 1000 Milligrams (mg) Which is larger? A. 1 kilogram or 1500 grams B. 1200 milligrams or 1 gram C. 12 milligrams or 12 kilograms D. 4 kilograms or 4500 grams Kilogram Prototype\n\nBalance Rules In order to protect the balances and ensure accurate results, a number of rules should be followed:  Always check that the balance is level and zeroed before using it.  Do not weigh hot or cold objects.  Clean up any spills around the balance immediately.\n\nMeasuring Mass Top Image: http://www.southwestscales.com/Ohaus_Triple_Beam_750-SO.jpg Bottom Image: http://www.regentsprep.org/Regents/biology/units/laboratory/graphics/triplebeambalance.jpg We will be using triple- beam balances to find the mass of various objects. The objects are placed on the scale and then you move the weights on the beams until you get the lines on the right-side of the scale to match up. Once you have balanced the scale, you add up the amounts on each beam to find the total mass. What would be the mass of the object measured in the picture? _______ + ______ + _______ = ________ g\n\nMeasuring Mass – Triple-Beam Balance 1 st – Place the film canister on the scale. 2 nd – Slide the large weight to the right until the arm drops below the line. Move the rider back one groove. Make sure it “locks” into place. 3 rd – Repeat this process with the top weight. When the arm moves below the line, back it up one groove. 4 th – Slide the small weight on the front beam until the lines match up. 5 th – Add the amounts on each beam to find the total mass to the nearest tenth of a gram.\n\nCheck to see that the balance scale is at zero\n\nVolume Volume is the amount of space a substance occupies The liter (L) is the base unit Tools: metric ruler is used to measure regular solids v=l x w x h (cm3) or a graduated cylinder for liquids and irregular solids (mL) Meniscus- the curved surface of liquid resulting from surface tension\n\nGraduated Cylinders The glass cylinder has etched marks to indicate volumes, a pouring lip, and quite often, a plastic bumper to prevent breakage.\n\nReading the Meniscus Always read volume from the bottom of the meniscus. The meniscus is the curved surface of a liquid in a narrow cylindrical container.\n\nTry to avoid parallax errors. Parallax errors arise when a meniscus or needle is viewed from an angle rather than from straight-on at eye level. Correct: Viewing the meniscus at eye level Incorrect: viewing the meniscus from an angle\n\nSignificant Figures  Significant figures in measurement include the all certain digits and one uncertain digit.  Significant figures communicate how precise measurements are.  Certain digits are determined from the calibration marks on the cylinder.  The uncertain digit (the last digit of the reading) is estimated.\n\nUse the graduations to find all certain digits There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are… 52 mL.\n\nEstimate the uncertain digit and take a reading The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is The volume in the graduated cylinder is 0.8 mL 52.8 mL.\n\nSelf Test Examine the meniscus below and determine the volume of liquid contained in the graduated cylinder. The cylinder contains: _ _. _ mL 760\n\nIrregular Volume A solid with an irregular volume will be measured using the displacement method 1.Measure and record an amount of water 2.Drop the irregular object in the cylinder 3.Read the cylinder again and record the amount 4.Subtract the two measurements and the result is the volume of the irregular object in ml\n\nThe Thermometer o Determine the temperature by reading the scale on the thermometer at eye level. o Read the temperature by using all certain digits and one uncertain digit. o Certain digits are determined from the calibration marks on the thermometer. o The uncertain digit (the last digit of the reading) is estimated. o On most thermometers encountered in a general chemistry lab, the tenths place is the uncertain digit.\n\nDo not allow the tip to touch the walls or the bottom of the flask. If the thermometer bulb touches the flask, the temperature of the glass will be measured instead of the temperature of the solution. Readings may be incorrect, particularly if the flask is on a hotplate or in an ice bath.\n\nReading the Thermometer Determine the readings as shown below on Celsius thermometers: _ _. _  C 874350\n\nMass Mass is the amount of matter in an object It is determined by using a balance The unit for mass is grams.\n\nEnglish vs. Metric Units Which is larger? 1. 1 Pound or 100 Grams 2. 1 Kilogram or 1 Pound 3. 1 Ounce or 1000 Milligrams 1 pound = 453.6 grams 100 kilogram = 220 pounds 1 ounce of gold = 28,349.5 milligrams\n\nDensity The measure of how much mass is contained in a given volume.\n\nThe formula of density is: Density = Mass / Volume\n\nComparing Densities - Inferring: Which item has the greater density? The bowling ball Since the bowling bowl has a greater mass, it has a greater density, even though both balls have the same volume\n\nWhy is density expressed as a combination of two different units? Because density is actually made up of two other measurements – mass and volume – an objects density is expressed as a combination of two units.\n\nTwo Common Units For Density Grams per cubic centimeter (g/cm³) Grams per milliliter (g/mL)\n\nMath Practice: What is the density of a wood block with a volume of 125 cm³ and a mass of 57 g? Density = mass / volume Density = 57 g / 125 cm³ Density = 0.46 g/ cm³\n\nMath Practice: What is the density of a liquid with a mass of 45 g and a volume of 48 mL? Density = mass / volume Density = 45 g / 48 mL Density = 0.94 g/mL\n\nThe density of a substance is the ______for all samples of that substance. Same\n\nAn object will float if it is _____ _____ than a surrounding liquid. Less dense\n\nApplying Concepts: How could you use density to determine whether a bar of metal is pure gold? If the bar of gold has a density that is greater than or less than 19.3 g/cm³, then the sample is not pure gold. Densities of Some Common Substances SubstanceDensity (g/cm³) Air0.001 Ice0.9 Water1.0 Aluminum2.7 Gold19.3\n\nWill an object with a density of 0.7 g/cm³ float or sink in water? An object that has a density of 0.7 g/cm³ will float in water (1 g/cm³) because it is less dense than water\n\nDownload ppt \"Measurement Notes Chapter 2 Length Scientist use the metric system—a standard measurement system based on the #10. The meter is the basic unit. millimeter.\"\n\nSimilar presentations" ]	[ null, "http://slideplayer.com/static/blue_design/img/slide-loader4.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8312506,"math_prob":0.9653847,"size":7336,"snap":"2019-43-2019-47","text_gpt3_token_len":1811,"char_repetition_ratio":0.12629569,"word_repetition_ratio":0.050574712,"special_character_ratio":0.24931844,"punctuation_ratio":0.08833678,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98532796,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-23T11:39:03Z\",\"WARC-Record-ID\":\"<urn:uuid:709f1ee8-07c0-45e9-a9dd-dee8b133e1b5>\",\"Content-Length\":\"180833\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c11feb0f-8aaa-4a98-a36c-2f2f7b3735ee>\",\"WARC-Concurrent-To\":\"<urn:uuid:b5699b2b-4b99-4407-974b-80807bddee20>\",\"WARC-IP-Address\":\"88.99.70.210\",\"WARC-Target-URI\":\"http://slideplayer.com/slide/4626559/\",\"WARC-Payload-Digest\":\"sha1:LFZVQTKUE6G7NVHGGDUZG6QJBSLJJE25\",\"WARC-Block-Digest\":\"sha1:WL5455AAJGKIG5QPNNA53RJUP2CEYJRT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987833089.90_warc_CC-MAIN-20191023094558-20191023122058-00133.warc.gz\"}"}
https://math.stackexchange.com/questions/1955833/number-of-homomorphisms-from-a-finite-group-to-an-infinite-group	[ "# Number of homomorphisms from a finite group to an infinite group\n\nI am starting to self-study abstract algebra, and came across, in my humble opinion, a fairly difficult question. More specifically, the question I was trying to answer is along the lines of:\n\n\"Let $G$ a finite group, and $Hom(G,\\Bbb C^\\times)$ the set of all group homomorphisms $\\phi:G\\rightarrow\\Bbb C^\\times$, where $\\Bbb C^\\times$ is the multiplicative group of the non-zero complex numbers. Prove that $Hom(G,\\Bbb C^\\times)$ is finite.\"\n\nI found many answers for the case where both groups were finite, but didn't have much success in this case.\n\nI was trying to think about $G$ having a finite number of generators might lead to some brute-force technique, or maybe induction on the order of $G$, but no success up to now. I suspect there is something very basic I'm forgetting, so please go easy on me if that's the case.\n\nI would be glad if you could give some insights about finding all group homomorphisms between groups too. What kind of facts are normally used to prove such a thing?\n\nThanks in advance.\n\n• Take a look at Alekseev's \"Abel's Theorem in Problems and Solutions\". A great way to get into groups and complex numbers. – user8960 Oct 6 '16 at 0:41\n\n## 2 Answers\n\nFor any $g \\in G$, $g^{\|G\|} = 1$, so for any homomorphism $\\phi \\in \\text{Hom}(G, \\mathbb{C}^ \\times)$, $\\phi(g)^{\|G\|} = 1$. This means that $\\phi$ is a map from the finite set $G$ to the finite set of $\|G\|$-th roots of unity in $\\mathbb{C}$. There are only finitely many maps between two finite sets, hence $\|\\text{Hom}(G, \\mathbb{C}^ \\times)\|$ is finite.\n\n• I feel kinda dumb now that I see it was so simple... Guess I still need to study much more. I had another question, but your argument about the roots of unity applies for it too, so two birds, one stone. Thanks! – AspiringMathematician Oct 6 '16 at 14:23\n\nThe circle group has only a single subgroup of any given finite order. If $f: G \\to H$ is a surjective homomorphism, the order of $H$ divides the order of $G$. Therefore there are only a finite number of subsets of $\\Bbb{C}^{\\times}$ that a homomorphism can map $G$ to, and since there are only a finite number of functions from $G$ to any one of those sets the total number of homomorphisms from $G$ to $\\Bbb{C}^{\\times}$ is finite." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9716915,"math_prob":0.9899256,"size":1011,"snap":"2019-13-2019-22","text_gpt3_token_len":243,"char_repetition_ratio":0.102284014,"word_repetition_ratio":0.0,"special_character_ratio":0.23046489,"punctuation_ratio":0.11057692,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99973506,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-24T09:05:59Z\",\"WARC-Record-ID\":\"<urn:uuid:96f703fa-dc0d-4692-afb2-3aae6e67f59f>\",\"Content-Length\":\"137170\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c790dfba-169d-40ec-9d83-513c104f853e>\",\"WARC-Concurrent-To\":\"<urn:uuid:bf0574ba-29f6-4fe3-bb3a-c0315d00e309>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/1955833/number-of-homomorphisms-from-a-finite-group-to-an-infinite-group\",\"WARC-Payload-Digest\":\"sha1:BHQ6L7ZQEGGI547UZRG5LSHWKGEEY3OH\",\"WARC-Block-Digest\":\"sha1:Q2ZOKGW2HT3VK7ZVFHN6BIXRJQE26TCO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232257601.8_warc_CC-MAIN-20190524084432-20190524110432-00537.warc.gz\"}"}
https://www.maa.org/press/maa-reviews/number-theory-concepts-and-problems	[ "", null, "# Number Theory: Concepts and Problems", null, "###### Titu Andreescu, Gabriel Dospinescu, and Oleg Mushkarov\nPublisher:\nXYZ Press\nPublication Date:\n2017\nNumber of Pages:\n686\nFormat:\nHardcover\nPrice:\n79.95\nISBN:\n9780988562202\nCategory:\nProblem Book\n[Reviewed by\nMark Hunacek\n, on\n10/12/2017\n]\n\nXYZ Press is a small publishing company whose books are distributed by the American Mathematical Society, and which specializes in texts that are designed to teach mathematical problem solving and competition preparation. It was established by Titu Andreescu, who is also the editor, author or co-author of many of the roughly two dozen texts published by this company, including the one now under review, which deals with problems in number theory.\n\nI have seen a good many problem books over the years, and must admit that after a while many of them tend to blur together in my mind. This one, however, is something of an exception, and stands out more vividly from the crowd, both because of its heft (at almost 700 pages, it is quite thick) and, more significantly, because of its content: in addition to setting out problems and solutions, it actually develops a substantial amount of elementary undergraduate number theory, and therefore seems more textbook-oriented than many other problem-style books. As a result, it is, I think, more versatile, with a larger target audience, than is typical of such books.\n\nChapter 1 of the text is just a two-page preface, summarizing the origins and contents of the text. Chapters 2 through 7, which comprise roughly two thirds of the text, deal with substantive number theory, covering most of the “usual suspects” of a standard undergraduate course (divisibility, primes, the Fundamental theorem of arithmetic, congruences, quadratic residues and nonresidues, some Diophantine equations, and arithmetic functions), along with a number of topics that are not typically covered in such a course (for example: Bertrand’s postulate and the distribution of primes, a brief discussion of the abc conjecture, and p-adic valuations).\n\nAs noted above, each of these six chapters focuses both on the development of the underlying theory and on problems. Basic definitions are provided, theorems are stated precisely, and proofs are given, including of such results as the law of quadratic reciprocity. In addition to this, however, many solved problems (“examples”) appear in the text, and in addition each of these chapters ends with a section consisting of a substantial number, typically 50 or more per chapter, of “practice problems”. These practice problems often seem to have a somewhat different flavor than standard textbook homework problems (they are more in the nature of competition problems than homework problems, and hence more difficult), but there is some occasional overlap. Solutions to these practice problems constitute chapter 8 of the text, which is more than 200 pages long.\n\nBecause of the format of the book, and specifically because number theory is developed pretty much from scratch rather than just assumed, this book should be of interest to people who are taking or teaching a basic undergraduate number theory course, even if they have no interest in ever entering a mathematics Olympiad-style competition. Certainly any faculty member teaching such a course would likely find this book a treasure trove of interesting and challenging problems for use as homework or (if the students are unlucky!) exam questions. (Since a number of the problems have a combinatorial flavor, people taking or teaching a course in combinatorics might also find something useful here.)\n\nThe book could also potentially serve as the main text for a course in number theory, although in some respects this might be problematic. For one thing, some topics that are fairly standard fare in a number theory course are not covered here. Continued fractions are not discussed, and there is also no discussion of applications of number theory to cryptography, a topic that I think students in a basic number theory course really enjoy seeing. In addition, the last time I taught number theory I also spent a few weeks on quadratic rings where unique factorization fails, both to illustrate the importance and significance of the fundamental theorem of arithmetic, and to give the students at least a glimpse of algebraic numbers. This book doesn’t include such material, either. (Books that do discuss this material include Stillwell’s Elements of Number Theory and An Introduction to Number Theory and Cryptography by Kraft and Washington.)\n\nThe most negative feature of this book, one that also militates against its use as an actual text for a number theory course, is the total lack of an index. It is incomprehensible to me how a book intended for college students can be published without one, but this seems to be fairly common for books published by XYZ Press: although I have not reviewed the contents of every book published by XYZ, I did glance at the Table of Contents for about half a dozen chosen at random, and none of them indicated the presence of an Index.\n\nBut let us not end this review on a sour note. This book is a valuable collection of problems in elementary number theory; if I ever teach the course again, I will keep it close at hand.\n\nMark Hunacek (mhunacek@iastate.edu) teaches mathematics at Iowa State University.\n\n## Dummy View - NOT TO BE DELETED\n\n•", null, "•", null, "•", null, "•", null, "•", null, "" ]	[ null, "https://px.ads.linkedin.com/collect/", null, "https://www.maa.org/sites/default/files/NumberThyAndreescu.jpg", null, "https://www.maa.org/sites/default/files/styles/flexslider_full/public/20.09.25%20Sliffe%20Awards%20Announcement.png", null, "https://www.maa.org/sites/default/files/styles/flexslider_full/public/20.09.23%20Voting%20Journal_0.png", null, "https://www.maa.org/sites/default/files/styles/flexslider_full/public/20.09.21%20Awards%20nominations.png", null, "https://www.maa.org/sites/default/files/styles/flexslider_full/public/20.09.14%20AMC%20reg%20open.png", null, "https://www.maa.org/sites/default/files/styles/flexslider_full/public/20.09.09%20Sept.%20featured%20book.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9645925,"math_prob":0.7936657,"size":5081,"snap":"2020-34-2020-40","text_gpt3_token_len":1000,"char_repetition_ratio":0.12802836,"word_repetition_ratio":0.0,"special_character_ratio":0.19051369,"punctuation_ratio":0.10171306,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.959619,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,5,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-25T17:41:54Z\",\"WARC-Record-ID\":\"<urn:uuid:11be70b6-031c-4f72-8883-101f15d32d13>\",\"Content-Length\":\"105293\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f3afe796-5151-403c-b1d9-a07b9471b6c6>\",\"WARC-Concurrent-To\":\"<urn:uuid:9dec6a09-040e-48e8-bc30-44ce5c53f7bb>\",\"WARC-IP-Address\":\"192.31.143.111\",\"WARC-Target-URI\":\"https://www.maa.org/press/maa-reviews/number-theory-concepts-and-problems\",\"WARC-Payload-Digest\":\"sha1:G43PKJDTHYMU74SJYUYBKL56G4CXACLG\",\"WARC-Block-Digest\":\"sha1:OTGDPLEJE6OMAA54MVWWBNHNI6GBDKRN\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400227524.63_warc_CC-MAIN-20200925150904-20200925180904-00565.warc.gz\"}"}
https://solvedlib.com/homework-chapter-10-homework-save-5-of-8-0,403461	[ "# Homework: Chapter 10 Homework Save 5 of 8 (0 complete) HW Score: 0%, 0 of 8...\n\n###### Question:", null, "", null, "Homework: Chapter 10 Homework Save 5 of 8 (0 complete) HW Score: 0%, 0 of 8 pts Score: 0 of 1 pt P10-8 (similar to) Question Help O Depreclation expense. Richardses' Tree Farm, Inc. has just purchased a new serial tree trimmer for $88,000. Calculate the depreciation schedule using a seven-year life (for the property class category of a single-purpose agricultural and horticultural structure from Table 10.3) for both straight-line depreciation and MACRS, . Use the half-year convention for both methods. Compare the depreciation schedules before and after taxes using a 40% tax rate. What do you notice about the difference between these two methods? Using a seven-year life, straight-line depreciation, and the half-year convention for the first and last years, what is the annual depreciation of the trimmer? S (Round to the nearest dollar.) Enter your answer in the answer box and then click Check Answer. 10 parts Clear All Check Answer Check Answer IU remaining Homework: Chapter 10 Homework Save Score: 0 of 1 pt 5 of 8 (0 complete) HW Score: 0%, 0 of 8 pts P10-8 (similar to) Question Help Depreciation expense. Richardses' Tree Farm, Inc. has just purchased a new aerial tree trimmer for$68,000. Calculate the depreciation schedule using a seven-year life (for the property class category of a single-purpose agricultural and horticultural structure from Table 10.3) for both straight-line depreciation and MACRS. Use the half-year convention for both methods. Compare the depreciation schedules before and after taxes using a 40% tax rate. What do you notice about the difference between these two methods? Using a seven-year life, straight-line depreciation, and the half-year convention for the first and last years, what is the annual depreciation of the trimmer? S (Round to the nearest dollar.) í Data Table - X MACRS Fixed Annual Expense Percentages by Recovery Class Click on this icon to download the data from this table Year 3-Year 33.33% 44.45% 14.81% 7.41% 5-Year 20.00% 32.00% 19.20% 11.52% 11.52% 5.76% 7-Year 14.29% 24.49% 17.49% 12.49% 8.93% 8.93% A 93% 4.45% 10-Year 10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.55% 6.55% 3.28% 7 10 Print Done Enter your answer in the answer box and then click Check Answer. 10 parts IU remaining Clear All Check Answer\n\n#### Similar Solved Questions\n\n##### 2/6 polnts Prevlous AnswersLCalcCon5 1.2.013.For the function, do the followings(t) 1 + 0.5e (a) Describe the end behavior verbally Gecreeses Winout bound, the output values of $lepproach zerg}increases without bound, the output values cf$ approach a limibnavalre 055(b) Write limit notation for the end behavior.s(t)lim s(t)Write the equations for any horizonta asvmorotel5iansunot exist;DNE;)(smaller value)(larger value)\n2/6 polnts Prevlous Answers LCalcCon5 1.2.013. For the function, do the following s(t) 1 + 0.5e (a) Describe the end behavior verbally Gecreeses Winout bound, the output values of $lepproach zerg} increases without bound, the output values cf$ approach a limibnavalre 055 (b) Write limit notation f...\n##### Teuanilomauon shown liqur4uatintcoumTalltoDlamvenicu 0). (1. 0). (?. I) nd (1, !)fKKy) dA\nteuanilomauon shown liqur 4uat intcoum TalltoDlam venicu 0). (1. 0). (?. I) nd (1, !) fK Ky) dA...\n##### 148. A NURSE begins to bathe a newly admitted client who report that she has not...\n148. A NURSE begins to bathe a newly admitted client who report that she has not had anything to eat that day. The nurse interrupts the bath and obtains a healthy meal for the client. this action by the nurse is an example of which of the following? Boundary crossing Veracity Countertransference Pro...\n##### In a random sample of 1276 U.S. adults, 903 favor using mandatory testing to assess how...\nIn a random sample of 1276 U.S. adults, 903 favor using mandatory testing to assess how well schools are educating students. In another random sample of 1112 U.S. adults taken 9 years ago, 799 favored using mandatory testing to assess how well schools are educating students. At α = 0.05, can y...\n##### What is another name for an indirect fixed cost? Choices: A) a common fixed cost B)...\nWhat is another name for an indirect fixed cost? Choices: A) a common fixed cost B) a tracaeable fixed cost C) a controllable fixed cost D) a segment fixed cost...\n##### In an engine, an almost ideal gas is compressed adiabatically (see Note below) to half its...\nIn an engine, an almost ideal gas is compressed adiabatically (see Note below) to half its volume. In doing so, 2630 Joules of work is done on the gas. (a) How much heat flows into or out of the gas? (b) What is the change in internal energy of the gas? (c) Does its temperature rise or fall? Note: A...\n##### Constants A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The...\nConstants A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rocket's acceleration has components ax(t)=αt2 and ay(t)=β−γt, where α = 2.50 m/s4, β = 9.00 m/s2, and γ = 1.40 m/s3. At t=0 the rocket is at the ori...\n##### [0/1 Points]DETAILSPREVIOUS ANSWERSROGACALCET4 2.5.008.Evaluate the limit state that does not exist. (If an Anse does not exist, enter DNE: ) 14 x - 2 DNE\n[0/1 Points] DETAILS PREVIOUS ANSWERS ROGACALCET4 2.5.008. Evaluate the limit state that does not exist. (If an Anse does not exist, enter DNE: ) 14 x - 2 DNE...\n##### [W QUA 4 disk uith sadiu R Lu trbulid flu may Jiudiz diik fnto ixtitelt mawf ' intiwikly\" TaOl lonteuluc jt\" a) ExbJuy Mu Qa 9 erale Bttu Jiq ju Juumu i Yadiu b) Vst Onswrn (a) to Wlube dwn detinite inkgral suu tota Qua 9 fue disc t rebuuds\n[W QUA 4 disk uith sadiu R Lu trbulid flu may Jiudiz diik fnto ixtitelt mawf ' intiwikly\" TaOl lonteuluc jt\" a) ExbJuy Mu Qa 9 erale Bttu Jiq ju Juumu i Yadiu b) Vst Onswrn (a) to Wlube dwn detinite inkgral suu tota Qua 9 fue disc t rebuuds...\n##### Exercise 4-26 (Algorithmic) (LO. 4) Determine the taxable amount of Social Security benefits for the following...\nExercise 4-26 (Algorithmic) (LO. 4) Determine the taxable amount of Social Security benefits for the following situations. If required, round your answers to the nearest dollar. If an amount is zero, enter \"0\". a. Erwin and Eleanor are married and file a joint tax return. They have adjusted ...\n##### How do I evaluate sin from cos and use symmetry arguments?\nIf cos(theta)=0.8, and 270°< theta<360° a) evaluate sin(theta) and show it on a unit circle b) Using symmetry arguments evaluate cos(theta-180°) c) Confirm the result using the trigonometric identities...\n##### Consider the triangle with the given vertices. (0,0) . (5.6) . (-4,7)Use calculus to find the area S of this triangle. S\nConsider the triangle with the given vertices. (0,0) . (5.6) . (-4,7) Use calculus to find the area S of this triangle. S...\n##### Question 3CH; N-CH; CH?AN= CH; CH?Which molecule above Is the more soluble in water?\nQuestion 3 CH; N-CH; CH? AN= CH; CH? Which molecule above Is the more soluble in water?...\n##### Time Left Question 25 11 point) Bases on the EVU method, which decision alternative would you...\nTime Left Question 25 11 point) Bases on the EVU method, which decision alternative would you choose? Average Nature Od O 24 + Decision Alternative Poba bocion Amet Decon Amatve 2 becon Alternate 3 Decision Amatved 31 2 20 27 1 10 1) Decision Alternative 1 2) Decision Alternative 2 3) Decision Alter...\n##### Harold says, to find 6 x 8, I can use the facts for 5 x 4 and 1 x4\nHarold says, to find 6 x 8, I can use the facts for 5 x 4 and 1 x4. Do you agree? Explain...\n##### Sn9 LL.021Solution that contains 20 g of nonelectrolyte solute in 250 g water; freezes at 2.34 \"C, calculate the molar mass(g/mol) of the solute Kf for water= * 1.86 \"c/m)\nSn9 LL.0 21 Solution that contains 20 g of nonelectrolyte solute in 250 g water; freezes at 2.34 \"C, calculate the molar mass(g/mol) of the solute Kf for water= * 1.86 \"c/m)...\n##### Use the Taylor series for the integralto evaluateX1. (~k T = C 4.32k k! k=0 2. I = 2 44-32* K=0 (-1)* 1 = 4 . 32k+1 wQk +1) k=0 1 = (F1k4.32k+1 2k + 1 K=OI =4e-r\" dr4.32k+1 wQk +1) k=0\nUse the Taylor series for the integral to evaluate X1. (~k T = C 4.32k k! k=0 2. I = 2 44-32* K=0 (-1)* 1 = 4 . 32k+1 wQk +1) k=0 1 = (F1k4.32k+1 2k + 1 K=O I = 4e-r\" dr 4.32k+1 wQk +1) k=0...\n##### Suppose the curve â‚¬ = t8 _ 9,y = t+ 3 for 1 < t < 2 is rotated about the axis_ Set up (but do not evaluate) the integral for the surface area that is generated.\nSuppose the curve â‚¬ = t8 _ 9,y = t+ 3 for 1 < t < 2 is rotated about the axis_ Set up (but do not evaluate) the integral for the surface area that is generated....\n##### Use the following results from a test for marijuana use, which is provided by a certain...\nUse the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 149 subjects with positive test results, there are 29 false positive results; among 160 negative results, there are 5 false negative results. If one of the ...\n##### The inability to produce CDZ8 receptors on T (Ipts) A patient has genetic defect which results in cells, Which of the following would be consistent with this defect?The patient would have hyper (over) expression of cytokines produced by Helper T cells_ Helper T cells would be normal, but cytotoxic T cell function would be impaired Cytoxic T cells would be normal, but helper T cells would have impaired function Function of CDA+ and CD8+ cells would be impaired.\nthe inability to produce CDZ8 receptors on T (Ipts) A patient has genetic defect which results in cells, Which of the following would be consistent with this defect? The patient would have hyper (over) expression of cytokines produced by Helper T cells_ Helper T cells would be normal, but cytotoxic...\n##### Help with OChem HBC ROOR. & luetust hexane Antimarkamika's nile. 7. Draw the major organic product...\nHelp with OChem HBC ROOR. & luetust hexane Antimarkamika's nile. 7. Draw the major organic product generated in the reaction below.. 1. HgcOAc), H,0 2. NaBH Palkyl - i- butene 8. Provide the structure of the major organic product of the reaction below. 1. BH; THE 2. H.O, HO 9-10. Complete t...\n##### 6) Ethylene, 15.00 g, is reacted in water, 100.0 mL, and a phosphoric acid catalyst at...\n6) Ethylene, 15.00 g, is reacted in water, 100.0 mL, and a phosphoric acid catalyst at 250.0°C to give 8.500 g of ethanol. Calculate the percent yield for this reaction?...\n##### 7) A 67 y/o client has expressed an interest in reducing his dietary fat intake in...\n7) A 67 y/o client has expressed an interest in reducing his dietary fat intake in order to promote his heart health. Which of the following foods would you advise him to avoid? Margarine White fish Sunflower oil Olive oil 8) Which of the following foods is most likely to...\n##### AmeriPouer Curreni rininn Secundug Secundar 0._285 035a 0._us 0ao 0767525 0 75 7z 02478 01cs AldoVultaze Ideul W Culchalleu FrunAN ccconuurur SlrpNunibcr al Turot rmn EorundanAcluiiLnnu0584400SI00S760.6x:Mnor0nni6 Mnos 0.US 70,01497 Wln Mmao TESLn 0oisos U.0498 010mtna U.UUUS 6 70,0u699 UuuA Dontos UUI 00u7oo Uuubgb non @wuuI Mus Muuro Mons 0Ouusit 007yy momosDoI MerM0z 0oiy 0,017 0,0uS 0ouS 0o0S 0 Ms 0Mt Momaa086znanMSDoun moun MTMeLoouJ0OUS oos MOOSdeUUo: 02 0253200 3200 JZUU 320mMtucGWmo0rq\nAmeri Pouer Curreni rininn Secundug Secundar 0._285 035a 0._us 0ao 0767525 0 75 7z 02478 01cs Aldo Vultaze Ideul W Culchalleu FrunAN ccconuur ur Slrp Nunibcr al Turot rmn Eorundan Acluii Lnnu 05844 00SI 00S76 0.6x: Mnor 0nni6 Mnos 0.US 70,01497 Wln Mmao TESLn 0oisos U.0498 010mtna U.UUUS 6 70,0u69...\n##### 14. Money market assets typically are: a. for 20 years d. all of the above b....\n14. Money market assets typically are: a. for 20 years d. all of the above b. tax free e. none of the above C. sold at a discount with the capital gain the interest 15. Most businesses get funds by: a. issuing stock d. all of the above b. borrowing from banks e. none of the above c. raising funds in...\n##### Show that a Banach space $X$ is reflexive if and only if the closed unit ball of every equivalent norm on $X^{}$ is $w^{}$ -closed.\nShow that a Banach space $X$ is reflexive if and only if the closed unit ball of every equivalent norm on $X^{}$ is $w^{}$ -closed....\n##### At 25 \"C,an aqueous solution has an equilibrium concentration of 0.00317 M for generic cation, A?+(aq), and 0.00634 M for a generic anion , B (aq) . What the equilibrium constant; Kyp: Of the generic salt ABz (s)?Kp6.37 XiO-8Inconect\nAt 25 \"C,an aqueous solution has an equilibrium concentration of 0.00317 M for generic cation, A?+(aq), and 0.00634 M for a generic anion , B (aq) . What the equilibrium constant; Kyp: Of the generic salt ABz (s)? Kp 6.37 XiO-8 Inconect...\n##### Consider the set S = fp1; p2; p3; p4g, wherep1 = 1; p2 = 2x; p3 = -2 + 4x^2; p4 = -12x + 8x^3A) Show that this set of polynomials forms a basis for p3B) Find the coordinate vector of p = 1 + 2x - 4x^2 +8x^3relative to its basis\nConsider the set S = fp1; p2; p3; p4g, where p1 = 1; p2 = 2x; p3 = -2 + 4x^2; p4 = -12x + 8x^3 A) Show that this set of polynomials forms a basis for p3 B) Find the coordinate vector of p = 1 + 2x - 4x^2 +8x^3 relative to its basis...\n##### 7 his phenomenon is known as the thermic effect of food, and the effect (in kI per hollf) for one individual is F() = 9.76 + 170.Tle where t is the number of hours that have elapsed since and (=6.\n7 his phenomenon is known as the thermic effect of food, and the effect (in kI per hollf) for one individual is F() = 9.76 + 170.Tle where t is the number of hours that have elapsed since and (=6....\n##### Pb2t(aq) + 2 e Pb(s) Sn?t(aq) + 2 e Sn(s) Ni2t(aq) + 2 e\" Ni(s) Co2t(aq) Co(s) Cdlt(aq) 2 e Cd(s) Crt(aq) Cr2+(aq) Fe2t(aq) 2 e Fe(s) Crt(aq) 3 e Cr(s) Zn2t(aq) + 2 e Zn(s) 2 HzO() + 2 e Hz(g) + 2 OH (aq)-0.1260.14-0.25-0.280.403-0.41-0.440.740.763-0.83Mn2+(aq) + 2 eMn(s)-1.18(aq) +3 e Mg?t(aq) + 2 eAl(s)-1.66Mg(s)2.372 714\nPb2t(aq) + 2 e Pb(s) Sn?t(aq) + 2 e Sn(s) Ni2t(aq) + 2 e\" Ni(s) Co2t(aq) Co(s) Cdlt(aq) 2 e Cd(s) Crt(aq) Cr2+(aq) Fe2t(aq) 2 e Fe(s) Crt(aq) 3 e Cr(s) Zn2t(aq) + 2 e Zn(s) 2 HzO() + 2 e Hz(g) + 2 OH (aq) -0.126 0.14 -0.25 -0.28 0.403 -0.41 -0.44 0.74 0.763 -0.83 Mn2+(aq) + 2 e Mn(s) -1.18 (aq)...\n##### CelniFountromukbtEOT nuletbeanentto-Jotn Cenmal Thtdem Eanlti osfa ctnp wunadstoltx 0' ; noM/ N017ess [041mk4 0Eo Mnatetuzc. Udettng Eepuaen ramalrhulo Ente Uul on Ernathlleyroral @ n8 tatcbL28 dte untetyin mpaston bcltt Crtollra Theotm stabra [nt {n Ginnn AnnJoatb W70lueint Ei= Eann Enuta Tioruf n rnt u not '0l7?s0xtvo Cenett chaka Ita [ founeed 0 %ano Dotchaneda nd n DaEnater Bucora artvon 0N; Adu - Lmoi lteMus Ddc;\" Ealntenanee ruuculan enemn 0 upamncArah Rontteeetta Jd\ncelni Fount romuk btEOT nulet bean entto- Jotn Cenmal Thtdem Eanlti osfa ctnp wunadstoltx 0' ; noM/ N017ess [041mk4 0Eo Mnatetuzc. Udettng Eepuaen ramalrhulo Ente Uul on Ernathlleyroral @ n8 tatcbL28 dte untetyin mpaston # bcltt Crtollra Theotm stabra [nt {n Ginnn AnnJoatb W70lueint Ei= Eann...\n##### Induction refers to when 3. How much Cuso, SHO would you need to weigh out if...\nInduction refers to when 3. How much Cuso, SHO would you need to weigh out if you wanted a sample that contains 5.00 mol of H atoms? (Make sure your response contains appropriate units and sig. digits and the logic and equa tions are shown clearly.) Check your solution (NOT just the final answe...\n##### At 19 weeks pregnant, Royce Young and his wife, Keri, found out that their unborn daughter...\nAt 19 weeks pregnant, Royce Young and his wife, Keri, found out that their unborn daughter had a rare birth defect called anencephaly, a condition in which the baby will be born with an underdeveloped brain and an incomplete skull. Their options were either to terminate the pregnancy or to...\njust the last journal and part b The following inventory transactions apply to Green Company for Year 2: Jan. 1 Apr. 1 Aug. 1 Dec. 1 Purchased Sold Purchased Sold 260 unitse $9 130 units @$ 18 440 units @ $10 550 units @$ 19 The beginning inventory consisted of 195 units at \\$10 per unit. All..." ]	[ null, "https://img.homeworklib.com/questions/55d337f0-7155-11ea-a0f2-f19d5fdc1e6f.png", null, "https://img.homeworklib.com/questions/5643dd40-7155-11ea-8bd3-cbbe81a69b5b.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88225687,"math_prob":0.93195975,"size":3633,"snap":"2023-14-2023-23","text_gpt3_token_len":1246,"char_repetition_ratio":0.19399284,"word_repetition_ratio":0.039215688,"special_character_ratio":0.4153592,"punctuation_ratio":0.21583514,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95585614,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-30T02:24:37Z\",\"WARC-Record-ID\":\"<urn:uuid:f75e6a8c-5e73-4ba9-a077-963bce721dec>\",\"Content-Length\":\"112222\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cbb03fb1-4df3-4f08-9004-d0f12daf855e>\",\"WARC-Concurrent-To\":\"<urn:uuid:2d38efae-9179-455c-a2db-200bdc9c92ab>\",\"WARC-IP-Address\":\"172.67.132.66\",\"WARC-Target-URI\":\"https://solvedlib.com/homework-chapter-10-homework-save-5-of-8-0,403461\",\"WARC-Payload-Digest\":\"sha1:QHZ3YWNXYLTY5T6EW332F7LJQYKAP23F\",\"WARC-Block-Digest\":\"sha1:A2D3R5MTC4STPEX2U6EXF7OBXXGBLO5J\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296949093.14_warc_CC-MAIN-20230330004340-20230330034340-00311.warc.gz\"}"}
https://www.memrise.com/course/700001/learn-mathematics/270/	[ "Level 269 Level 271\nLevel 270\n\n## Ignore words\n\nCheck the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.\n\nIgnore?\ncoordinate plane\nA plan formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis.\ndirect variation\nA situation when one value increases as the other vaule increases or as one decreases the other decreases. y = kx k≠0\nordered pair\nA pair of numbers that can be used to locate a point on a coordinate plane.\norigin\nThe centre point of a number line (ground floor of a hotel, freezing point on a thermometer)\nFour regions into which a coordinate plane is divided by the x-axis and the y-axis\nunit rate\nA rate with the denominator of 1.\nx axis\nThe horizontal axis on a coordinate graph, for the varaible that controls the other (an axis ia a line on a graph)\ny axis\nhas the dependent variable, the vertical line on a graph\nx coordinate\nIn an ordered pair, the value that is always written first.\ny coordinate\nIn an ordered pair, the value that is always written second.\ny=mx+b\nmultiply-multiply\ny=kx^n\ny=ab^x, b^x=1 or when x=0\na^ma^n\na^n+m\n(a^m)/(a^n)\na^m-n\ny=kx\nDirect Variation\nStandard From\nAx + By=C\npoint slope form\nwhere m is the slope and (x1, y1) is a point on the line\nExample of distributive property\n5(3 + 1) = 5 × 3 + 5 × 1\nconstant of variation\nk; the coefficient of x\nvaries directly\nis proportional to\nconstant of variation\nthe ratio between two variables that are proportional\nm = k h\nmoney earned (m) is directly proportional to hours worked (h)\nrate\na ratio that compares two quantities with different units of measure\nratio\nA comparison of two quantities, also know as fancy word for fraction.\npercent\n/ division\nRational Number\nAny number that can be expressed as a ratio of two integers. Example; 6 can be expressed as 6/1, and 0.5 as 1/2.\nVariation" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8653863,"math_prob":0.994011,"size":2017,"snap":"2019-51-2020-05","text_gpt3_token_len":527,"char_repetition_ratio":0.104321904,"word_repetition_ratio":0.039325844,"special_character_ratio":0.23351513,"punctuation_ratio":0.0631068,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99948937,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-09T23:08:53Z\",\"WARC-Record-ID\":\"<urn:uuid:9f6dcb90-1d20-4842-9643-495a99e6ef0c>\",\"Content-Length\":\"155357\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a3481c4d-1a62-470f-82a8-6fd9213dd4a7>\",\"WARC-Concurrent-To\":\"<urn:uuid:2943efe1-565b-4652-ac08-7ffdead5a964>\",\"WARC-IP-Address\":\"3.222.195.117\",\"WARC-Target-URI\":\"https://www.memrise.com/course/700001/learn-mathematics/270/\",\"WARC-Payload-Digest\":\"sha1:TFROUJVI7RW37JWITE5XTMXJX2XG3PTQ\",\"WARC-Block-Digest\":\"sha1:FTTMXYXIEZUAECODCYPGCFEDYDNFBDYP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540525598.55_warc_CC-MAIN-20191209225803-20191210013803-00332.warc.gz\"}"}
http://scientifictutor.org/1528/chem-college-pressure-and-the-equilibrium-constant-kp/	[ "## Chem – College: Pressure and the Equilibrium Constant (Kp)\n\nWhat is the equilibrium constant Kp and how does it relate to pressure?\n\nYou can also talk about a chemical equation and its equilibrium in the form of pressure. Most books and teachers will call this equilibrium constant Kp. It works the same as any other equilibrium constant. All the same rules apply as in the equilibrium equations we have been solving for so far. The only difference is you can use the values of pressure (usually in atm, torr, mmHg, or Pa). For the examples I give I will use the units of atm. Because Kp does not directly involve concentration the Kp equation for the equilibrium constant is slightly different. You don’t use brackets in the equation so the equation looks like the one below.\n\nFor the chemical equation: N2(g) + 3 H2(g) <—-> 2 NH3(g)\n\n Kp = ( NH3 )2 ( N2 ) ( H2 )3\n\nVIDEO Solving the Equilibrium Equation (Kp) Demonstrated Example 1: What is the equilibrium constant of the equation below when the pressure at equilibrium of C4 is 1atm, O2 is 4atm, and CO2 is 5atm?\n\nC4(s) + 4 O2(g) <—-> 4 CO2(g)\n\nWhat is the equilibrium equation look like with chemicals?\n\n Kp = ( CO2 )4 ( O2 )4\n\nC4 is not shown above because it is a solid. Replace the chemicals with their corresponding pressure (numbers).\n\n Kp = ( 5atm )4 ( 4atm )4\n\nCalculate in steps. First the exponents.\n\n Kp = ( 625atm4 ) ( 256atm4 )\n\nThen divide top and bottom\n\n Kp = 2.44 1\n\nPRACTICE PROBLEMS: Solve the problems below for the Kp or different pressures.\n\nWhat is the Kp of the equation below when the pressure at equilibrium of N2O3 is 20atm, N2 is 5atm, and O2 is 9atm?\n\n2 N2O3(g) <——> 2 N2(g) + 3 O2(g)\n\nWhat is the equilibrium constant of the equation below when the pressure at equilibrium of Ba(OH)2 is 0.1atm, HCl is 0.2 atm, and BaCl2 is 0.4atm?\n\nBa(OH)2(aq) + 2 HCl(aq) <—-> 2 H2O(l) + BaCl2(aq)\n\nWhat is the pressure of O2 in the equation below when the pressure at equilibrium of H2O is 0.7atm, H2 is 40atm, and Kp is 65atm?\n\n2 H2O(g) <—-> 2 H2(g) + O2(g)\n\nAnswer: pressure of O2 = 0.02 atm\n\nWhat is the pressure of NH3 in the equation below when the pressure at equilibrium of OF2 is 0.5 atm, N2F4 is 1.3atm, O2 is 2.5atm, H2 is 0.8atm, and the Kp is 2.7 * 102atm?\n\n2 OF2(g) + 2 NH3(g) <—> N2F4(g) + O2(g) + 3 H2(g)\n\nAnswer: pressure of NH3 = 0.157 atm", null, "", null, "" ]	[ null, "https://www.paypalobjects.com/en_US/i/scr/pixel.gif", null, "http://scientifictutor.org/wp-content/uploads/2016/09/Patreon-e1473193051600.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8409438,"math_prob":0.99961084,"size":2323,"snap":"2023-40-2023-50","text_gpt3_token_len":778,"char_repetition_ratio":0.20008625,"word_repetition_ratio":0.09750567,"special_character_ratio":0.32802412,"punctuation_ratio":0.11133201,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998252,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-24T06:28:40Z\",\"WARC-Record-ID\":\"<urn:uuid:19432317-f33c-4a18-b681-c215588331b8>\",\"Content-Length\":\"29486\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c66b238e-f5c7-4634-8172-9da130d6af2e>\",\"WARC-Concurrent-To\":\"<urn:uuid:838c2fe3-1faf-4acc-884f-b7cb8b676610>\",\"WARC-IP-Address\":\"162.144.109.137\",\"WARC-Target-URI\":\"http://scientifictutor.org/1528/chem-college-pressure-and-the-equilibrium-constant-kp/\",\"WARC-Payload-Digest\":\"sha1:TZVPYJIHI2QW3JPAZ5KWDYC5IJRYOGCG\",\"WARC-Block-Digest\":\"sha1:MVU4HJICIA6WJCJYUWODYWIHBYIX6DSS\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506623.27_warc_CC-MAIN-20230924055210-20230924085210-00474.warc.gz\"}"}
https://adam.scherlis.com/2023/01/01/fun-math-facts-about-2023/	[ "# Fun math facts about 2023\n\n2023=7×172\n\nMaybe that’s not fun enough? Try this:\n\n2023=211−52\n\nOr better yet:\n\n20233=(31176029+245568392)/(384321573)\n\nWe can scientifically quantify how fun a math fact is, so we can rest assured that this is the funnest fact about 2023 ever discovered.\n\nBut if it’s not to your liking:\n\n2023=(21034−1)/41\n\n2023=(5511+24)/17\n\n2023=(3647+27)/17\n\n2023=(24792−36)/72=(2279/7)2−(33/7)2\n\nHappy New Year!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5956002,"math_prob":0.74857056,"size":390,"snap":"2022-40-2023-06","text_gpt3_token_len":140,"char_repetition_ratio":0.12176166,"word_repetition_ratio":0.0,"special_character_ratio":0.53846157,"punctuation_ratio":0.08139535,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99707276,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-01T16:50:00Z\",\"WARC-Record-ID\":\"<urn:uuid:0aa69edf-5a72-4f16-8015-ff6272e8db16>\",\"Content-Length\":\"88167\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f3b322fb-625f-4a8e-929a-ccf59b02b5ea>\",\"WARC-Concurrent-To\":\"<urn:uuid:237ab9cd-6945-4fad-ba98-0c2b779d5043>\",\"WARC-IP-Address\":\"192.0.78.13\",\"WARC-Target-URI\":\"https://adam.scherlis.com/2023/01/01/fun-math-facts-about-2023/\",\"WARC-Payload-Digest\":\"sha1:XHKD2MVEKE75XWVEEFHMGEYTJBERJFNY\",\"WARC-Block-Digest\":\"sha1:YLEQY6M7XT5HBFCIDLWAONZA62ATXTJB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499946.80_warc_CC-MAIN-20230201144459-20230201174459-00055.warc.gz\"}"}
http://mathskills4kids.com/number-patterns-worksheets-pdf-grade-4	[ "# Number Patterns Worksheets Pdf Grade 4 - Shapes and Patterns Worksheets for Grade 4 PDF\n\nNumber patterns worksheets pdf grade 4 has been created to enhance kid’s understanding of mathematical relationships. Nonetheless, with our shapes and patterns worksheets for grade 4 pdf, your kids will gain mastery of sequencing, leading to extraordinary number sense skills, logic structure in algebra, and establishing order in life.\n\nAs it is essential to introduce kids to a variety of repeating patterns, so too is understanding of pattern rule grade 4 of vital importance.\n\n##", null, "4th GRADE MATH PRINTABLES\n\nPattern rules are an excellent strategy to strengthen kid’s skills on the four basic math operations. This is because these rules use at least one or more mathematical operations to describe the relationship between consecutive numbers in the pattern.\n\n### Simple strategies to instant mastering patterns and sequences concept\n\nProvided here are simple strategies to instant mastering patterns and sequences concept. These strategies involve concentration, intuition and pattern rule.\n\nFollowing pattern rule grade 4, every activity in shapes and patterns worksheets for grade 4 pdf first of all requires kids to have a full concentration and thus perceive whether numbers are getting larger or smaller as the sequence continues.\n\nSecondly, you will now put your four basic math operations (add, subtract, multiply, divide) skills at work given that;\n\n-You add or multiply when you notice that numbers gets larger as the sequence continues.\n\n-You subtract or divide when you notice that numbers gets smaller as the sequence continues.\n\n•" ]	[ null, "http://mathskills4kids.com/content/images/five-stars.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88749576,"math_prob":0.8601062,"size":2168,"snap":"2021-43-2021-49","text_gpt3_token_len":422,"char_repetition_ratio":0.1409427,"word_repetition_ratio":0.0862069,"special_character_ratio":0.19372694,"punctuation_ratio":0.10236221,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97099316,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-19T20:48:02Z\",\"WARC-Record-ID\":\"<urn:uuid:5343db8f-b7cb-424d-90cf-930a32055b35>\",\"Content-Length\":\"50933\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:522ee863-6fde-4779-8ff5-9699ef628064>\",\"WARC-Concurrent-To\":\"<urn:uuid:6b46036c-4a8f-44fa-b542-271925f30901>\",\"WARC-IP-Address\":\"66.85.133.203\",\"WARC-Target-URI\":\"http://mathskills4kids.com/number-patterns-worksheets-pdf-grade-4\",\"WARC-Payload-Digest\":\"sha1:OBIDW3TBGQPFXGXEDPF7SYAIL27GJV6B\",\"WARC-Block-Digest\":\"sha1:FQEUQEDML2FHZZQ2HJIKMT7ABX7XU742\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585281.35_warc_CC-MAIN-20211019202148-20211019232148-00247.warc.gz\"}"}
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-4-section-4-4-trigonometric-functions-of-any-angle-exercise-set-page-575/81	[ "## Precalculus (6th Edition) Blitzer\n\nPublished by Pearson\n\n# Chapter 4 - Section 4.4 - Trigonometric Functions of Any Angle - Exercise Set - Page 575: 81\n\n#### Answer\n\nThe exact value of the expression is $\\frac{\\sqrt{2}}{2}$.\n\n#### Work Step by Step\n\n$\\cos \\frac{23\\pi }{4}$ lies in quadrant IV. Subtract $4\\pi$ from $\\frac{23\\pi }{4}$ to find the positive co-terminal angles less than $2\\pi$. \\begin{align} & \\theta =\\frac{23\\pi }{4}-4\\pi \\\\ & =\\frac{23\\pi -16\\pi }{4} \\\\ & =\\frac{7\\pi }{4} \\end{align} The positive acute angle formed by the terminal side of $\\theta$ and the x-axis is the reference angle ${\\theta }'$. Since $\\frac{7\\pi }{4}$ angle lies in quadrant IV, subtract $\\frac{7\\pi }{4}$ from $2\\pi$ to find the reference angle. \\begin{align} & {\\theta }'=2\\pi -\\frac{7\\pi }{4} \\\\ & =\\frac{8\\pi -7\\pi }{4} \\\\ & =\\frac{\\pi }{4} \\end{align} Hence, $\\cos \\frac{\\pi }{4}=\\frac{\\sqrt{2}}{2}$ In quadrant I all the trigonometric function are positive. In quadrant II sine and cosecant are positive and all other trigonometric functions are negative. In quadrant III tangent and cotangent are positive and all other trigonometric functions are negative. In quadrant IV cosine and secant are positive and all other trigonometric functions are negative. Here, the cosine is positive in quadrant IV. Therefore, $\\cos \\frac{23\\pi }{4}=\\cos \\frac{\\pi }{4}$ Substitute $\\frac{\\sqrt{2}}{2}$ for $\\cos \\frac{\\pi }{4}$. $\\cos \\frac{23\\pi }{4}=\\frac{\\sqrt{2}}{2}$ The exact value of the expression is $\\frac{\\sqrt{2}}{2}$.\n\nAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.66031075,"math_prob":0.99946064,"size":1357,"snap":"2021-21-2021-25","text_gpt3_token_len":451,"char_repetition_ratio":0.16999261,"word_repetition_ratio":0.140625,"special_character_ratio":0.36182755,"punctuation_ratio":0.06225681,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99998987,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-20T21:51:43Z\",\"WARC-Record-ID\":\"<urn:uuid:4b403d69-114e-4196-a82f-8a1c4d62e513>\",\"Content-Length\":\"104382\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8cc589a2-c98f-4eb5-9894-14369df7f693>\",\"WARC-Concurrent-To\":\"<urn:uuid:5de4942e-6cdc-4fe7-bfbd-b0c28a301111>\",\"WARC-IP-Address\":\"54.158.15.170\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-4-section-4-4-trigonometric-functions-of-any-angle-exercise-set-page-575/81\",\"WARC-Payload-Digest\":\"sha1:AXDYJIH54PQKAJLHICPGCJFTHRKXDYFE\",\"WARC-Block-Digest\":\"sha1:CWS7SX7C6QUMHPD25LSFT2NDXOSOP3XP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488257796.77_warc_CC-MAIN-20210620205203-20210620235203-00071.warc.gz\"}"}
https://answers.everydaycalculation.com/multiply-fractions/8-24-times-3-63	[ "Solutions by everydaycalculation.com\n\n## Multiply 8/24 with 3/63\n\nThis multiplication involving fractions can also be rephrased as \"What is 8/24 of 3/63?\"\n\n8/24 × 3/63 is 1/63.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 8/24 × 3/63 = 8 × 3/24 × 63 = 24/1512\n3. After reducing the fraction, the answer is 1/63\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":0.83409655,"math_prob":0.98635817,"size":398,"snap":"2020-34-2020-40","text_gpt3_token_len":148,"char_repetition_ratio":0.15989847,"word_repetition_ratio":0.0,"special_character_ratio":0.42713568,"punctuation_ratio":0.06666667,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98375845,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-23T00:47:50Z\",\"WARC-Record-ID\":\"<urn:uuid:25359a7e-4b44-4455-a8a3-b024d0d34836>\",\"Content-Length\":\"7109\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:da0e47b8-465f-4dff-9dfc-c759df367776>\",\"WARC-Concurrent-To\":\"<urn:uuid:28c52c3d-affb-40b9-a27f-cf46a3f7684b>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/multiply-fractions/8-24-times-3-63\",\"WARC-Payload-Digest\":\"sha1:VEFH5CJWLLKNP7YLGWRPF5NEBKTLC7QZ\",\"WARC-Block-Digest\":\"sha1:ZDDQOPHEHZ3C6LBVYJUN6VYFMUGHJ6AF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400208095.31_warc_CC-MAIN-20200922224013-20200923014013-00330.warc.gz\"}"}
https://percentages.io/what-is-73-percent-of-8120	[ "What is % of ?\n5927.6\n\n# How to solve this problem\n\n## A step by step guide\n\nThe purpose of solving this problem is to determine what 73% of 8120 is. One common real life problem where a solution like this may be helpful include calculating how much tip to leave at a restaurant. Solving this problem requires two simple math operations that you can perform on any calculator. The first step is a division and the second step is a multiplication. Here's a cool tip though, you can actually reverse the order of these operations and the result will be the same! Here are the steps:\n\nStep 1: Divide 8120 by 100\nIn this case, the number that we are \"comparing\" to 100 is 8120, so we must first normalize the number by dividing it by 100. The operation we have to solve is this: $$\\frac{8120}{ 100 } = 8120 \\div {{ 100 }} = 81.2$$\n\nStep 2: Multiply 81.2 by 73 to get the solution\nNow that we have our normalized number, 81.2, we just have to multiply it by 73 to get our final answer. The forumla for this is obviously quite simple: $$81.2 \\times 73 = 5927.6$$\n\nThat's all there is to it! Note that you can replace these values with new ones from any similar problem.\n\nSimilar problems" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92962855,"math_prob":0.9953004,"size":1133,"snap":"2020-10-2020-16","text_gpt3_token_len":293,"char_repetition_ratio":0.10717449,"word_repetition_ratio":0.0,"special_character_ratio":0.29037952,"punctuation_ratio":0.10084034,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9990214,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-23T09:08:44Z\",\"WARC-Record-ID\":\"<urn:uuid:a9e184f0-c922-446f-88f7-7e0d9538e50d>\",\"Content-Length\":\"33742\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:db77aaee-ab41-4a08-8ee1-e1e66a575062>\",\"WARC-Concurrent-To\":\"<urn:uuid:a475bef8-3212-456e-a4e6-a203acaa7e90>\",\"WARC-IP-Address\":\"34.239.215.123\",\"WARC-Target-URI\":\"https://percentages.io/what-is-73-percent-of-8120\",\"WARC-Payload-Digest\":\"sha1:AZ5FSTYWHSK4HIHQN3AOZCZCFDJDQGQT\",\"WARC-Block-Digest\":\"sha1:22HN2GXME6U6POFNBJVMPHROR7YH5UQ4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145747.6_warc_CC-MAIN-20200223062700-20200223092700-00450.warc.gz\"}"}
https://www.civillead.com/unit-weight-of-building-materials/	[ "# Unit Weight of Building Materials Used In Construction\n\n## What is Unit Weight?\n\nUnit weight or specific weight of any material is its weight per unit volume that means in a unit volume, how much weight of the material can be placed.\n\nVolume is measured in litres or cubic meters, and weight is expressed in kg or kilo Newton. Hence it is expressed in KN/m3 in the SI unit and KG/ m3 in the MKS unit system, and g/cc in the CGS unit system.\n\nUnit or Specific Weight = Weight / Volume = W / V\n\n## What is Density?\n\nThe density of any substance/material is its mass per unit volume, and it is expressed in KG/ m3 or lb/m3. The symbol Rho (ρ) represents it.\n\nDensity describes the level of compactness of a substance. If the material has more density, that means it is more compact.\n\nDensity = Mass / Volume\n\nρ = M/V\n\n## What is the difference Between Unit or Specific Weight and Density?\n\nUnit weight of any substance is its weight per unit volume, while the density of any material is its mass per unit volume. Both terms can be used interchangeably.\n\nTo understand the difference between unit weight and the density first, we need to understand the difference between weight and mass.\n\nAny substance or material on this planet or anywhere has some mass, and it can’t be zero, and it is measured in kg. M denotes it.\n\nM = w/g\n\nWhile weight is a force due to gravity acceleration and it is measured in newton. If there is no gravity acceleration, it may be zero. It is denoted by W.\n\nW = m × g\n\nWhere g = acceleration due to gravity\n\nI hope now you understood the difference between these two terms.\n\n## Why is Unit Weight Important?\n\nThe unit weight is essential for weight calculation purposes. With the help of Unit Weight, we can calculate the weight of any material.\n\nIt also helps to determine the structure’s weight, which is designed to carry the specific load so that it remains intact and within limits.\n\nUnit weight of any material also helps to calculate the quantity of material required for particular space.\n\nThe density of any material also decides whether it will sink or float on water. Suppose the substance density is less than water’s density.\n\nIn that case, it will float, and if the substance density is more than the water’s density, it will sink into the water.\n\n## Unit Weight of MaterialsUsed In Construction\n\nHere we are providing the unit weight of different building materials in alphabetical order for your convenience.\n\nConversion:\n\n1 kN/m3 = 101.9716 kg/m3 say = 100 kg/m3 (round off)\n\n1 kg/m3 = 0.0624 lb/ft3" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6601522,"math_prob":0.9887729,"size":7248,"snap":"2023-40-2023-50","text_gpt3_token_len":3217,"char_repetition_ratio":0.09221425,"word_repetition_ratio":0.0102476515,"special_character_ratio":0.5332506,"punctuation_ratio":0.15615962,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.993346,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-02T19:26:30Z\",\"WARC-Record-ID\":\"<urn:uuid:e5f8996a-4fdd-4c78-a92f-f0c7ace1f539>\",\"Content-Length\":\"153124\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e539d52a-5668-4659-858f-ac5b3dbc81a7>\",\"WARC-Concurrent-To\":\"<urn:uuid:01b9df48-c441-44fb-b755-9e29799529b1>\",\"WARC-IP-Address\":\"172.67.212.93\",\"WARC-Target-URI\":\"https://www.civillead.com/unit-weight-of-building-materials/\",\"WARC-Payload-Digest\":\"sha1:SAL5BU7DCHMUZSM2K4X5BMFYG6UUUQT2\",\"WARC-Block-Digest\":\"sha1:CXMSEGC2KQ5VAXBGJ7DZKV4GVVTJ2JB6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100448.65_warc_CC-MAIN-20231202172159-20231202202159-00474.warc.gz\"}"}
https://sciencenotes.org/calculating-molarity-example-problem/	[ "# Calculating Molarity Example Problem 1", null, "Molarity is a measure of the concentration of a solute in a solution. This molarity example problem shows the steps needed to calculate the molarity of a solution given the amount of solute and the desired volume of solution.\n\nProblem\n\nCalculate the molarity of a solution created by pouring 7.62 grams of MgCl2 into enough water to create 400 mL of solution.\n\nSolution\n\nThe formula to calculate molarity is", null, "In this case, the solute is 7.62 grams of MgCl2. The formula needs the number of moles.\n\nUsing a periodic table, the molecular mass of MgCl2 is 95.21 grams/mol. Find the number of moles in 7.62 grams in MgCl2.", null, "moles MgCl2 = 0.08 moles\n\nMolarity also needs to have the volume in liters, not milliliters.\n\nThe final volume of our solution is 400 mL, which is 0.4 L.\n\nPlug this information into the formula", null, "M = 0.2 moles/L or 0.2 M" ]	[ null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8697274,"math_prob":0.99721074,"size":888,"snap":"2019-51-2020-05","text_gpt3_token_len":241,"char_repetition_ratio":0.16515838,"word_repetition_ratio":0.012738854,"special_character_ratio":0.25112614,"punctuation_ratio":0.119170986,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99981517,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-06T04:17:16Z\",\"WARC-Record-ID\":\"<urn:uuid:e5a3a29b-9248-47ca-ac7c-980f662157fa>\",\"Content-Length\":\"50761\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b7a941c4-431e-431b-93f2-ef6f47f30cb7>\",\"WARC-Concurrent-To\":\"<urn:uuid:1daea908-0eb7-49e3-81e8-7fb0713e46ae>\",\"WARC-IP-Address\":\"146.66.100.151\",\"WARC-Target-URI\":\"https://sciencenotes.org/calculating-molarity-example-problem/\",\"WARC-Payload-Digest\":\"sha1:UKOXSBL4KPYUB2U7CHBUDAROSHE5RYU2\",\"WARC-Block-Digest\":\"sha1:UT4XYUTMKQTOYPAMRBB2OZCO6C34QBZP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540484477.5_warc_CC-MAIN-20191206023204-20191206051204-00423.warc.gz\"}"}
https://dsp.stackexchange.com/questions/48037/is-it-possible-to-replace-an-integrator-system-with-an-equivalent-differentiator	[ "# Is it possible to replace an integrator system with an equivalent differentiator?\n\nI have a system whose input-output relation is as follows\n\n$$y(t)=x(t)+\\int_{-\\infty }^{t} x(\\tau) \\,\\mathrm d \\tau$$\n\nCan I create an equivalent system by using differentiators rather than integrators?\n\nI think something like taking derivative of both sides of the equation but improper integral makes it hard. Is there any nice way to convert this system? Thanks in advance.\n\n• How can a differentiator be \"equivalent\" to an integrator? To me it's unclear what you're trying to do. – Matt L. Mar 23 '18 at 8:31\n• Integration is the opposite of differentiation, so that will not be possible. If the integral bothers you, the function can be rewritten as $$y(t)=x(t) + x(t)*\\epsilon (-t)$$ – Max Mar 23 '18 at 8:57\n• yes, you can typically create equivalent block diagram in terms of just differentiators or just integrators. In circuit theory a gyrator en.m.wikipedia.org/wiki/Gyrator can do this. An inductor can be made to behave like a capacitor. – user28715 Mar 23 '18 at 9:42\n• @Stanley Pawlukiewicz Thanks for brief explanation and source. – Tokugava Mar 23 '18 at 9:57\n• Do you want to convert the integral equation into a differential equation? Or do you want a block diagram that uses differentiators rather than integrators? – Rodrigo de Azevedo Mar 23 '18 at 12:02\n\nTypically you can devise equivalent block diagrams in terms of just integrators or just differentiators.\n\nA simple example is on page 2-15 of\n\nhttps://web.stanford.edu/~boyd/ee102/systems.pdf\n\nwhich should look remarkably familiar. You should be cautioned that mathematical equivalence doesn't mean that there aren't reasons where one form would be prefered over the other. OP Amp integrators have better noise characteristics. You also have to band limit an analog differentiator to make it physically realizable.\n\nAnother issue is that they will not in general have the same complexity.\n\nWhen modeling ordinary differential equations systems, $$\\mathbf{M}(t) \\frac{d \\mathbf{y}(t)}{dt}= \\mathbf{g}(t,\\mathbf{y})$$ where $\\mathbf{M}(t)$ (mass matrix) is invertible is often more sparse for physical systems than $$\\frac{d \\mathbf{y}(t)}{dt}= \\mathbf{h}(t,\\mathbf{y})$$ which is a more general way of writing the common state space representation.\n\nOne can write : $$\\frac{d \\mathbf{y}(t)}{dt}= \\mathbf{M}^{-1}(t)\\mathbf{g}(t,\\mathbf{y})$$ but if $\\mathbf{M}(t)$ is sparse, $\\mathbf{M}^{-1}(t)$ probably isn't ,which makes a big difference when the dimension of $\\mathbf{y}$ is large.\n\nThe Matlab Control systems toolbox also includes state variable equations of the form\n\n$$\\mathbf{E} \\frac{d \\mathbf{y}}{dt}= \\mathbf{A}\\mathbf{y}+ \\mathbf{B}\\mathbf{u}$$" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.81913316,"math_prob":0.99757445,"size":1354,"snap":"2020-34-2020-40","text_gpt3_token_len":388,"char_repetition_ratio":0.15555556,"word_repetition_ratio":0.0,"special_character_ratio":0.26366323,"punctuation_ratio":0.07786885,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997993,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-12T06:23:08Z\",\"WARC-Record-ID\":\"<urn:uuid:eceb025e-24ea-4837-af08-0bd6556c3c02>\",\"Content-Length\":\"151166\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:87f1a996-8bc2-4f0c-a167-dbdd71674e45>\",\"WARC-Concurrent-To\":\"<urn:uuid:fa765397-11ad-4e1d-91b9-6a21dd6f0fde>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://dsp.stackexchange.com/questions/48037/is-it-possible-to-replace-an-integrator-system-with-an-equivalent-differentiator\",\"WARC-Payload-Digest\":\"sha1:5OB4VA4XA4LNPUFP23CVIGJCKU7HVVJK\",\"WARC-Block-Digest\":\"sha1:DPED7HG2F4UWNA2VMUCLLLYZKFWRKOC4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738878.11_warc_CC-MAIN-20200812053726-20200812083726-00261.warc.gz\"}"}
https://www.jobilize.com/course/section/box-counting-dimension-decision-trees-by-openstax?qcr=www.quizover.com	[ "# 0.11 Decision trees (Page 5/5)\n\n Page 5 / 5\n\nThe dyadic decision trees studied here are different than classical tree rules, such as CART orC4.5. Those techniques select a tree according to\n\n$\\stackrel{^}{k}=arg\\underset{k\\ge 1}{min}\\left\\{{\\stackrel{^}{R}}_{n},\\left({\\stackrel{^}{f}}_{n}^{\\left(k\\right)}\\right),+,\\alpha ,k\\right\\},$\n\nfor some $\\alpha >0$ whereas ours was roughly\n\n$\\stackrel{^}{k}=arg\\underset{k\\ge 1}{min}\\left\\{{\\stackrel{^}{R}}_{n},\\left({\\stackrel{^}{f}}_{n}^{\\left(k\\right)}\\right),+,\\alpha ,\\sqrt{k}\\right\\},$\n\nfor $\\alpha \\approx \\sqrt{\\frac{3log2}{2n}}$ . The square root penalty is essential for the risk bound. No such bound exists for CARTor C4.5. Moreover, recent experimental work has shown that the square root penalty often performs better in practice. Finally,recent results show that a slightly tighter bounding procedure for the estimation error can be used to show thatdyadic decision trees (with a slightly different pruning procedure) achieve a rate of\n\n$E\\left[R\\left({\\stackrel{^}{f}}_{n}^{T}\\right)\\right]-{R}^{}\\phantom{\\rule{4pt}{0ex}}=\\phantom{\\rule{4pt}{0ex}}O\\left({n}^{-1/2}\\right),\\phantom{\\rule{4pt}{0ex}}\\phantom{\\rule{4.pt}{0ex}}\\text{as}\\phantom{\\rule{4.pt}{0ex}}n\\to \\infty ,$\n\nwhich turns out to be the minimax optimal rate (i.e., under the boundary assumptions above, no method can achieve a faster rate of convergence tothe Bayes error).\n\n## Box counting dimension\n\nThe notion of dimension of a sets arises in many aspects of mathematics, and it is particularly relevant to the study offractals (that besides some important applications make really cool t-shirts). The dimension somehow indicates how we shouldmeasure the contents of a set (length, area, volume, etc...). The box-counting dimension is a simple definition of the dimension ofa set. The main idea is to cover the set with boxes with sidelength $r$ . Let $N\\left(r\\right)$ denote the smallest number of such boxes, then the box counting dimension is defined as\n\n$\\underset{r\\to 0}{lim}\\frac{logN\\left(r\\right)}{-logr}.$\n\nAlthough the boxes considered above do not need to be aligned on a rectangulargrid (and can in fact overlap) we can usually consider them over a grid and obtain an upper bound on the box-counting dimension. Toillustrate the main ideas let's consider a simple example, and connect it to the classification scenario considered before.\n\nLet $f:\\left[0,1\\right]\\to \\left[0,1\\right]$ be a Lipschitz function, with Lipschitz constant $L$ ( i.e., $\|f\\left(a\\right)-f\\left(b\\right)\|\\le L\|a-b\|,\\phantom{\\rule{4pt}{0ex}}\\forall a,b\\in \\left[0,1\\right]$ ). Define the set\n\n$A=\\left\\{x=\\left({x}_{1},{x}_{2}\\right):{x}_{2}=f\\left({x}_{1}\\right)\\right\\},$\n\nthat is, the set $A$ is the graphic of function $f$ .\n\nConsider a partition with ${k}^{2}$ squared boxes (just like the ones we used in the histograms), the points in set $A$ intersect at most ${C}^{\\text{'}}k$ boxes, with ${C}^{\\text{'}}=\\left(1+⌈L⌉\\right)$ (and also the number of intersected boxes is greater than $k$ ). The sidelength of the boxes is $1/k$ therefore the box-counting dimension of $A$ satisfies\n\n$\\begin{array}{ccc}\\hfill {dim}_{B}\\left(A\\right)& \\le & \\underset{1/k\\to 0}{lim}\\frac{log{C}^{\\text{'}}k}{-log\\left(1/k\\right)}\\hfill \\\\ & =& \\underset{k\\to \\infty }{lim}\\frac{log{C}^{\\text{'}}+log\\left(k\\right)}{log\\left(k\\right)}\\hfill \\\\ & =& 1.\\hfill \\end{array}$\n\nThe result above will hold for any “normal” set $A\\subseteq {\\left[0,1\\right]}^{2}$ that does not occupy any area. For most sets the box-counting dimension is always going to be an integer, butfor some “weird” sets (called fractal sets) it is not an integer. For example, the Koch curvehas box-counting dimension $log\\left(4\\right)/log\\left(3\\right)=1.26186...$ . This means that it is not quite as small as a 1-dimensional curve, but not as big as a2-dimensional set (hence occupies no area).\n\nTo connect these concepts to our classification scenario consider a simple example. Let $\\eta \\left(x\\right)=P\\left(Y=1\|X=x\\right)$ and assume $\\eta \\left(x\\right)$ has the form\n\n$\\eta \\left(x\\right)=\\frac{1}{2}+{x}_{2}-f\\left({x}_{1}\\right),\\phantom{\\rule{1.em}{0ex}}\\forall x\\equiv \\left({x}_{1},{x}_{2}\\right)\\in \\mathcal{X},$\n\nwhere $f:\\left[0,1\\right]\\to \\left[0,1\\right]$ is Lipschitz with Lipschitz constant $L$ . The Bayes classifier is then given by\n\n${f}^{}\\left(x\\right)={\\mathbf{1}}_{\\left\\{\\eta \\left(x\\right)\\ge 1/2\\right\\}}\\equiv {\\mathbf{1}}_{\\left\\{{x}_{2}\\ge f\\left({x}_{1}\\right)\\right\\}}.$\n\nThis is depicted in [link] . Note that this is a special, restricted class of problems. That is, we areconsidering the subset of all classification problems such that the joint distribution ${P}_{XY}$ satisfies $P\\left(Y=1\|X=x\\right)=1/2+{x}_{2}-f\\left({x}_{1}\\right)$ for some function $f$ that is Lipschitz. The Bayes decision boundary is therefore given by\n\n$A=\\left\\{x=\\left({x}_{1},{x}_{2}\\right):{x}_{2}=f\\left({x}_{1}\\right)\\right\\}.$\n\nHas we observed before this set has box-counting dimension 1.\n\nwhat is the stm\nHow we are making nano material?\nwhat is a peer\nWhat is meant by 'nano scale'?\nWhat is STMs full form?\nLITNING\nscanning tunneling microscope\nSahil\nhow nano science is used for hydrophobicity\nSantosh\nDo u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq\nRafiq\nwhat is differents between GO and RGO?\nMahi\nwhat is Nano technology ?\nwrite examples of Nano molecule?\nBob\nThe nanotechnology is as new science, to scale nanometric\nbrayan\nnanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale\nDamian\nIs there any normative that regulates the use of silver nanoparticles?\nwhat king of growth are you checking .?\nRenato\nWhat fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?\nwhy we need to study biomolecules, molecular biology in nanotechnology?\n?\nKyle\nyes I'm doing my masters in nanotechnology, we are being studying all these domains as well..\nwhy?\nwhat school?\nKyle\nbiomolecules are e building blocks of every organics and inorganic materials.\nJoe\nanyone know any internet site where one can find nanotechnology papers?\nresearch.net\nkanaga\nsciencedirect big data base\nErnesto\nIntroduction about quantum dots in nanotechnology\nwhat does nano mean?\nnano basically means 10^(-9). nanometer is a unit to measure length.\nBharti\ndo you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?\nabsolutely yes\nDaniel\nhow to know photocatalytic properties of tio2 nanoparticles...what to do now\nit is a goid question and i want to know the answer as well\nMaciej\nAbigail\nfor teaching engĺish at school how nano technology help us\nAnassong\nHow can I make nanorobot?\nLily\nDo somebody tell me a best nano engineering book for beginners?\nthere is no specific books for beginners but there is book called principle of nanotechnology\nNANO\nhow can I make nanorobot?\nLily\nwhat is fullerene does it is used to make bukky balls\nare you nano engineer ?\ns.\nfullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.\nTarell\nwhat is the actual application of fullerenes nowadays?\nDamian\nThat is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.\nTarell\nGot questions? Join the online conversation and get instant answers!", null, "", null, "By", null, "", null, "By Rhodes", null, "By Danielrosenberger", null, "", null, "By", null, "", null, "By", null, "By" ]	[ null, "https://www.jobilize.com/quiz/thumb/thermal-fluid-systems-mcq-quiz-by-dr-steve-gibbs.png;jsessionid=eSIeEk_Z9imkvJKnS0UY3piA66jRVZ6fpSjnwEBb.condor3363", null, "https://www.jobilize.com/quiz/thumb/biology-ch-01-the-study-of-life-mcq-quiz-openstax-college.png;jsessionid=eSIeEk_Z9imkvJKnS0UY3piA66jRVZ6fpSjnwEBb.condor3363", null, "https://farm9.staticflickr.com/8640/16656923381_6bf805ffed_t.jpg", null, "https://www.jobilize.com/quiz/thumb/mmt-review-flashcards.png;jsessionid=eSIeEk_Z9imkvJKnS0UY3piA66jRVZ6fpSjnwEBb.condor3363", null, "https://www.jobilize.com/quiz/thumb/2011-dynamics-crm-quiz-by-danielrosenberger.png;jsessionid=eSIeEk_Z9imkvJKnS0UY3piA66jRVZ6fpSjnwEBb.condor3363", null, "https://farm9.staticflickr.com/8845/18258330488_4fd54b5895_t.jpg", null, "https://www.jobilize.com/quiz/thumb/microeconomics-01-what-is-economics-ch-01-flashcards-by-openstax.png;jsessionid=eSIeEk_Z9imkvJKnS0UY3piA66jRVZ6fpSjnwEBb.condor3363", null, "https://www.jobilize.com/quiz/thumb/cultural-anthropology-definition-by-prof-richley-crapo-utah-usu.png;jsessionid=eSIeEk_Z9imkvJKnS0UY3piA66jRVZ6fpSjnwEBb.condor3363", null, "https://www.jobilize.com/quiz/thumb/sociology-01-an-introduction-to-sociology-mcq-quiz-openstax.png;jsessionid=eSIeEk_Z9imkvJKnS0UY3piA66jRVZ6fpSjnwEBb.condor3363", null, "https://www.jobilize.com/quiz/thumb/human-body-anatomy-physiology-essay-quiz.png;jsessionid=eSIeEk_Z9imkvJKnS0UY3piA66jRVZ6fpSjnwEBb.condor3363", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90621656,"math_prob":0.99426067,"size":3180,"snap":"2019-51-2020-05","text_gpt3_token_len":679,"char_repetition_ratio":0.119962215,"word_repetition_ratio":0.011320755,"special_character_ratio":0.2062893,"punctuation_ratio":0.09671848,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99811167,"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,1,null,1,null,null,null,1,null,1,null,null,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-18T07:12:54Z\",\"WARC-Record-ID\":\"<urn:uuid:fa1613f0-124f-4e9e-9b98-ef4ee804a066>\",\"Content-Length\":\"137672\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:93446d84-6faf-4603-a041-bd9135e11fdf>\",\"WARC-Concurrent-To\":\"<urn:uuid:f7ec2611-2893-4b83-85f1-75ec3e20fe94>\",\"WARC-IP-Address\":\"207.38.87.179\",\"WARC-Target-URI\":\"https://www.jobilize.com/course/section/box-counting-dimension-decision-trees-by-openstax?qcr=www.quizover.com\",\"WARC-Payload-Digest\":\"sha1:57K2IVMEHFKFD5IRJGQZIZKMLPGQWYQD\",\"WARC-Block-Digest\":\"sha1:WFG6TLQYCFZVLIZPXFTNBBDRJTUR6MCF\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250592261.1_warc_CC-MAIN-20200118052321-20200118080321-00366.warc.gz\"}"}
https://gcc.gnu.org/legacy-ml/gcc/2007-07/msg00107.html	[ "This is the mail archive of the gcc@gcc.gnu.org mailing list for the GCC project.\n\nIndex Nav: Message Nav: [Date Index] [Subject Index] [Author Index] [Thread Index] [Date Prev] [Date Next] [Thread Prev] [Thread Next] [Raw text]\n\n# Re: About the is_gimple_min_invariant predicate\n\n```> Passes ought to distinguish GIMPLE values from GIMPLE invariants\n> according to context. As this test case shows, a GIMPLE invariant is\n> not always the right value to replace as it cannot be used as a valid\n> ARRAY_REF index.\n\nOK, but the replacement is not made by FRE itself, but by fold:\n\n/* Simplify the binary expression RHS, and return the result if\nsimplified. /\n\nstatic tree\nsimplify_binary_expression (tree rhs)\n{\n[...]\nresult = fold_binary (TREE_CODE (rhs), TREE_TYPE (rhs), op0, op1);\n\n/ Make sure result is not a complex expression consiting\nof operators of operators (IE (a + b) + (a + c))\nOtherwise, we will end up with unbounded expressions if\nfold does anything at all. */\nif (result)\n{\nif (is_gimple_min_invariant (result))\nreturn result;\nelse if (SSA_VAR_P (result))\nreturn result;\nelse if (EXPR_P (result))\n[...]\n\nWe have\n\nTREE_CODE (rhs) = POINTER_PLUS_EXPR\nop0 = &p__name_buffer with TREE_INVARIANT\nop1 = MAX_EXPR <D.738_31, 0>\n\nAt this point, op0 is_gimple_val (and valid GIMPLE) but op1 is not. The\nproblem is that, after the call to fold_binary, we have\n\nresult = &p__name_buffer[(<unnamed-signed:32>) MAX_EXPR <D.738_31, 0> + 1]\n\nand this is_gimple_min_invariant hence accepted by simplify_binary_expression.\nMoreover, is_gimple_min_invariant => is_gimple_val so any subsequent attempt\nto gimplify will fail.\n\n> My proposal is that we add a predicate is_gimple_const() and\n> is_gimple_invariant() such that is_gimple_invariant() is implemented as:\n>\n> bool\n> is_gimple_invariant (tree expr)\n> {\n> if (is_gimple_const (expr))\n> return true;\n> else\n> return TREE_INVARIANT (expr);\n> }\n>\n> And is_gimple_const() is the current is_gimple_min_invariant() without\n> the ARRAY_REF case.\n\nDo you mean \"without the ADDR_EXPR case\" or...?\n\n> So my proposal is that PRE/FRE and the value propagators need to make\n> sure that they propagate is_gimple_invariant() except inside ARRAY_REF\n> indexes.\n\n> Also, we need to update the GIMPLE grammar so that ARRAY_REF and\n> ARRAY_RANGE_REF take the appropriate values:\n>\n> \tinner-compref: ...\n>\n> \t\t\t\| ARRAY_REF\n>\n> \t\t\t\top0 -> inner-compref\n> \t\t\t\top1 -> index-val\n> \t\t\t\top2 -> val\n> \t\t\t\top3 -> val\n>\n> \tindex-val: ID \| CONST\n>\n> \tval: index-val \| invariant\n>\n> \tinvariant: rhs with TREE_INVARIANT set\n\nI don't see why you're special-casing ARRAY_REF (and ARRAY_RANGE_REF). As\nRichard pointed out, there are other rules that would need to be changed.\n\n--\nEric Botcazou\n\n```\n\nIndex Nav: Message Nav: [Date Index] [Subject Index] [Author Index] [Thread Index] [Date Prev] [Date Next] [Thread Prev] [Thread Next]" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7187859,"math_prob":0.9261879,"size":2545,"snap":"2020-34-2020-40","text_gpt3_token_len":702,"char_repetition_ratio":0.13892168,"word_repetition_ratio":0.004962779,"special_character_ratio":0.28369352,"punctuation_ratio":0.14423077,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95128864,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-26T19:14:50Z\",\"WARC-Record-ID\":\"<urn:uuid:22df0f57-3345-4fc8-80d6-eac2e7a3f2b6>\",\"Content-Length\":\"7317\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:255cbe3e-0771-45e5-9aa1-9630aacf4257>\",\"WARC-Concurrent-To\":\"<urn:uuid:ad003207-2533-40e5-bde7-00ccc1754ddd>\",\"WARC-IP-Address\":\"8.43.85.97\",\"WARC-Target-URI\":\"https://gcc.gnu.org/legacy-ml/gcc/2007-07/msg00107.html\",\"WARC-Payload-Digest\":\"sha1:BBF3F2CXHUIYWWFCSQDOWOXPHFLPWX4D\",\"WARC-Block-Digest\":\"sha1:IBLSYHQAD4FRBASVNL2J4YOYNWFQSJQF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400244353.70_warc_CC-MAIN-20200926165308-20200926195308-00748.warc.gz\"}"}
https://www.xelplus.com/if-function-with-wildcard-partial-text-match/	[ "# (IF with Wildcards)\n\nHow can we look for an approximate match using wildcards with Excel’s IF Function?\n\n`=IF(YouTu* THEN…)`\n\nCan you use wildcards in the logical test portion of the IF Function?\n\nIt seems like this would be an easy “Yes”, but sadly, it’s not.\n\nWildcards work well with functions like SUMIFS, AVERAGEIFS, and COUNTIFS; sadly, they don’t work with IF functions.\n\nWhy don’t they work with IF functions? Let’s explore the reason why and see if we can come up with a work-around.\n\nNOTE: If you are interested in learning about using wildcards with the SUMIFS function, check out the link below to the post on “EXCEL SUM based on Partial Text Match”.\n\n`Sum Values based on Partial Text Match`", null, "# Getting IF to Work with Wildcards\n\nIn the dataset below, we want to write a formula in column B that will search the text in column A. Our formula will search the column A text for the text sequence “AT” and if found display “AT” in column B.", null, "It doesn’t matter where the letters “AT” occur in the column A text, we need to see “AT” in the adjacent cell of column B. If the letters “AT” do not occur in the column A text, the formula in column B should display nothing.\n\n# Searching for Text with the IF Function\n\nLet’s begin by selecting cell B5 and entering the following IF formula.\n\n`=IF(A5=”AT”,”AT”,””)`", null, "Notice the formula returns nothing, even though the text in cell A5 contains the letter sequence “AT”.\n\nThe reason it fails is that Excel doesn’t work well when using wildcards directly after an equals sign in a formula.", null, "Any function that uses an equals sign in a logical test does not like to use wildcards in this manner.\n\nBut what about the SUMIFS function?”, I hear you saying.\n\nIf you examine a SUMIFS function, the wildcards don’t come directly after the equals sign; they instead come after an argument. As an example:\n\n`=SUMIFS(\\$C\\$4:\\$C\\$18,\\$A\\$4:\\$A\\$18,”AT”)`\n\nThe wildcard usage does not appear directly after an equals sign.\n\n# SEARCH Function to the Rescue\n\nThe first thing we need to understand is the syntax of the SEARCH function. The syntax is as follows:\n\nSEARCH(find_text, within_text, [start_num])\n\n• find_text – is a required argument that defines the text you are searching for.\n• within_text – is a required argument that defines the text in which you want to search for the value defined in the find_text\n• Start_num – is an option argument that defines the character number/position in the within_text argument you wish to start searching. If omitted, the default start character position is 1 (the first character on the left of the text.)\n\nTo see if the search function works properly on its own, lets perform a simple test with the following formula.\n\n`=SEARCH(“AT”,A5)`", null, "We are returned a character position which the letters “AT” were discovered by the SEARCH function. The first SEARCH found the letters “AT” beginning in the 1st character position of the text. The next discovery was in the 5th character position, and the last discovery was in the 4th character position.\n\nThe “#VALUE!” responses are the SEARCH function’s way of letting us know that the letters “AT” were not found in the search text.\n\nWe can use this new information to determine if the text “AT” exists in the companion text strings. If we see any number as a response, we know “AT” exists in the text string. If we receive an error response, we know the text “AT” does not exist in the text string.\n\nNOTE: The SEARCH function is NOT case-sensitive. A search for the letters “AT” would find “AT”, “At”, “aT”, and “at”. If you wish to search for text and discriminate between different cases (case-sensitive), use the FIND function. The FIND function works the same as SEARCH, but with the added behavior of case-sensitivity.\n\n# Turning Numbers into Decisions\n\nAn interesting function in Excel is the ISNUMBER function. The purpose of the ISNUMBER function is to return “True” if something is a number and “False” if something is not a number. The syntax is as follows:\n\nISNUMBER(value)\n\n• value – is a required argument that defines the data you are examining. The value can refer to a cell, a formula, or a name that refers to a cell, formula, or value.\n\nLet’s add the ISNUMBER function to the logic of our previous SEARCH function.\n\n`=ISNUMBER(SEARCH(“AT”,A5))`", null, "Any cell that contained a numeric response is now reading “True” and any cell that contained an error is now reading “False”.\n\nWe are now able to use the ISNUMBER/SEARCH functions as our wildcard statement in the original IF function.\n\n`=IF(ISNUMBER(SEARCH(“AT”,A5)),”AT”,””)`", null, "This is a great way to perform logical tests in functions that do not allow for wildcards.\n\n# Let’s see another scenario\n\nSuppose we want to search for two different sets of text (“AT” or “DE”) and return the word “Europe” if either of these text strings are discovered in the searched text. We will combine the original formula with an OR function to search for multiple text strings.\n\n`=IF(OR(ISNUMBER(SEARCH(“AT”,A5)),ISNUMBER(SEARCH(“DE”,A5))),”Europe”,””)`", null, "" ]	[ null, "https://www.xelplus.com/wp-content/uploads/2019/06/IF-with-Wildcards-2881b9.png", null, "https://www.xelplus.com/wp-content/uploads/2019/06/IF-Wildcards-01.png", null, "https://www.xelplus.com/wp-content/uploads/2019/06/IF-Wildcards-02.png", null, "https://www.xelplus.com/wp-content/uploads/2019/06/IF-Wildcards-03.png", null, "https://www.xelplus.com/wp-content/uploads/2019/06/IF-Wildcards-04.png", null, "https://www.xelplus.com/wp-content/uploads/2019/06/IF-Wildcards-05.png", null, "https://www.xelplus.com/wp-content/uploads/2019/06/IF-Wildcards-06.png", null, "https://www.xelplus.com/wp-content/uploads/2019/06/IF-Wildcards-07.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8784616,"math_prob":0.81471527,"size":5097,"snap":"2020-24-2020-29","text_gpt3_token_len":1192,"char_repetition_ratio":0.14372668,"word_repetition_ratio":0.025581395,"special_character_ratio":0.22817343,"punctuation_ratio":0.09741551,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9754476,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-29T05:05:45Z\",\"WARC-Record-ID\":\"<urn:uuid:ce9c9a9a-9ea7-4053-91a0-299ee34eb145>\",\"Content-Length\":\"79639\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:54e8795c-4ed8-4aa8-81a7-54e3485775da>\",\"WARC-Concurrent-To\":\"<urn:uuid:bf15c890-f0cd-40d9-bd30-6f48a2e2e250>\",\"WARC-IP-Address\":\"35.214.238.235\",\"WARC-Target-URI\":\"https://www.xelplus.com/if-function-with-wildcard-partial-text-match/\",\"WARC-Payload-Digest\":\"sha1:2OKWU35ARC753BOWM4ZRESZ7GFRS6BNY\",\"WARC-Block-Digest\":\"sha1:44SSSEXRVH5RJS2EAD5TTQRKSGY532TN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347401260.16_warc_CC-MAIN-20200529023731-20200529053731-00131.warc.gz\"}"}
https://web2gotech.com/tf-tensorflow-operations/	[ "# TF – TensorFlow Operations\n\n• Subtract\n• Multiply\n• Divide\n• Square\n• Reshape\n\nYou can add two tensors using tensorA.add(tensorB):\n\n### Example\n\nconst tensorA = tf.tensor([[1, 2], [3, 4], [5, 6]]);\nconst tensorB = tf.tensor([[1,-1], [2,-2], [3,-3]]);\n\nconst tensorNew = tensorA.add(tensorB);\n\n// Result: [ [2, 1], [5, 2], [8, 3] ]\n\nTry it Yourself »\n\n## Tensor Subtraction\n\nYou can subtract two tensors using tensorA.sub(tensorB):\n\n### Example\n\nconst tensorA = tf.tensor([[1, 2], [3, 4], [5, 6]]);\nconst tensorB = tf.tensor([[1,-1], [2,-2], [3,-3]]);\n\n// Tensor Subtraction\nconst tensorNew = tensorA.sub(tensorB);\n\n// Result: [ [0, 3], [1, 6], [2, 9] ]\n\n## Tensor Multiplication\n\nYou can multiply two tensors using tensorA.mul(tensorB):\n\n### Example\n\nconst tensorA = tf.tensor([1, 2, 3, 4]);\nconst tensorB = tf.tensor([4, 4, 2, 2]);\n\n// Tensor Multiplication\nconst tensorNew = tensorA.mul(tensorB);\n\n// Result: [ 4, 8, 6, 8 ]\n\nTry it Yourself »\n\n## Tensor Division\n\nYou can divide two tensors using tensorA.div(tensorB):\n\n### Example\n\nconst tensorA = tf.tensor([[1, 2], [3, 4], [5, 6]]);\nconst tensorB = tf.tensor([[1,-1], [2,-2], [3,-3]]);\n\n// Tensor Division\nconst tensorNew = tensorA.div(tensorB);\n\n// Result: [ 2, 2, 3, 4 ]\n\nTry it Yourself »\n\n## Tensor Square\n\nYou can square a tensor using tensor.square():\n\n### Example\n\nconst tensorA = tf.tensor([1, 2, 3, 4]);\n\n// Tensor Square\nconst tensorNew = tensorA.square();\n\n// Result [ 1, 4, 9, 16 ]\n\nTry it Yourself »\n\n## Tensor Reshape\n\nThe number of elements in a tensor is the product of the sizes in the shape.\n\nSince there can be different shapes with the same size, it is often useful to reshape a tensor to other shapes with the same size.\n\nYou can reshape a tensor using tensor.reshape():\n\n### Example\n\nconst tensorA = tf.tensor([[1, 2], [3, 4]]);\nconst tensorB = tensorA.reshape([4, 1]);\n\n// Result: [ , , , ]\n\nTry it Yourself » (courtesy by W3Schools.com)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.528353,"math_prob":0.978371,"size":1803,"snap":"2022-40-2023-06","text_gpt3_token_len":578,"char_repetition_ratio":0.24235687,"word_repetition_ratio":0.18794326,"special_character_ratio":0.37770382,"punctuation_ratio":0.28850856,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9992071,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-06T05:07:46Z\",\"WARC-Record-ID\":\"<urn:uuid:6d5764b3-7777-4301-b273-c924e75aee4c>\",\"Content-Length\":\"77511\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fdbe2935-aa46-4d6a-b1a7-a26f5ad9d11a>\",\"WARC-Concurrent-To\":\"<urn:uuid:13b09bef-99b4-47c9-b2f3-55c8d3f46a50>\",\"WARC-IP-Address\":\"192.0.78.24\",\"WARC-Target-URI\":\"https://web2gotech.com/tf-tensorflow-operations/\",\"WARC-Payload-Digest\":\"sha1:UTCNKB4WRSEV5BZCWXEKAPBQAGWI2HXX\",\"WARC-Block-Digest\":\"sha1:NGZSYA5VG4726A2JPBV3L4VNY5USXNEL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337723.23_warc_CC-MAIN-20221006025949-20221006055949-00360.warc.gz\"}"}
https://community.jmp.com/t5/JMP-Add-Ins/Genomic-Bayesian-Methods-Add-in-for-JMP-Genomics/ta-p/186399	[ "Choose Language Hide Translation Bar\n\n## Genomic Bayesian Methods Add-in for JMP® Genomics\n\nThe Genomic Bayesian Methods Add-in is a wrapper around the Bayesian Generalized linear Regression (BGLR; de los Campos and Rodriguez 2014, Genetics 198:483-495). Genetic marker effects can be estimated using Bayes A, Bayes B, Bayes C, Bayesian LASSO, or Bayesian Ridge Regression. The methods in this Add-In are fully integrated with the Cross Validation Model Comparison tool in JMP Genomics, allowing the comparison of accuracy of many distinct models. Additionally, the marker effects of the fitted models are saved in a score file that can be subsequently loaded in the Cross Evaluation and Progeny Selection breeding tools in JMP Genomics to predict breeding values of individuals, evaluate crosses, and simulate progenies in multiple generations of breeding.\n\nFigure bellow shows the Bayes B method fitted to a barley data set. Notice the correlation between predicted and observed trait values is 0.8777.", null, "Figure bellow shows the average of correlation between predicted and observed trait values obtained by 3-fold cross validation ran for 6 iterations. Therefore, the correlation shown in the plot is the average taken over 18 runs for each tested model. While the average correlation for Bayes B is 0.5357 in the cross validation runs, the correlation for Bayes B in the entire data set without cross validation is 0.8777 (shown in the first figure). This example shows the importance of comparing models through cross validation to get more realistic measure of predictive accuracy.", null, "Article Labels\nArticle Tags\nContributors" ]	[ null, "https://kvoqx44227.i.lithium.com/t5/image/serverpage/image-id/16165iA98C20DB3E8B8434/image-size/large", null, "https://kvoqx44227.i.lithium.com/t5/image/serverpage/image-id/16221iEE98B0564C9B86EA/image-size/large", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88087523,"math_prob":0.8646431,"size":1492,"snap":"2019-51-2020-05","text_gpt3_token_len":301,"char_repetition_ratio":0.13104838,"word_repetition_ratio":0.026200874,"special_character_ratio":0.1997319,"punctuation_ratio":0.09737828,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97734857,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-28T00:46:38Z\",\"WARC-Record-ID\":\"<urn:uuid:aa4da634-5316-4e8b-b377-6c53aa353dab>\",\"Content-Length\":\"625375\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2b718fdc-6a69-4eb2-a5e3-1595b8d06b02>\",\"WARC-Concurrent-To\":\"<urn:uuid:bcb7425a-d919-4541-ba4b-aa9308e7498d>\",\"WARC-IP-Address\":\"208.74.205.23\",\"WARC-Target-URI\":\"https://community.jmp.com/t5/JMP-Add-Ins/Genomic-Bayesian-Methods-Add-in-for-JMP-Genomics/ta-p/186399\",\"WARC-Payload-Digest\":\"sha1:G2SVO32AXPXALWBLJ3SEXYP7RRTOEU7W\",\"WARC-Block-Digest\":\"sha1:GJ75B226IV2APEMMVGVK7NCHCSYT54LG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251737572.61_warc_CC-MAIN-20200127235617-20200128025617-00081.warc.gz\"}"}
https://feet-to-meters.appspot.com/77.1-feet-to-meters.html	[ "Feet To Meters\n\n# 77.1 ft to m77.1 Foot to Meters\n\nft\n=\nm\n\n## How to convert 77.1 foot to meters?\n\n 77.1 ft * 0.3048 m = 23.50008 m 1 ft\nA common question is How many foot in 77.1 meter? And the answer is 252.952755905 ft in 77.1 m. Likewise the question how many meter in 77.1 foot has the answer of 23.50008 m in 77.1 ft.\n\n## How much are 77.1 feet in meters?\n\n77.1 feet equal 23.50008 meters (77.1ft = 23.50008m). Converting 77.1 ft to m is easy. Simply use our calculator above, or apply the formula to change the length 77.1 ft to m.\n\n## Convert 77.1 ft to common lengths\n\nUnitUnit of length\nNanometer23500080000.0 nm\nMicrometer23500080.0 µm\nMillimeter23500.08 mm\nCentimeter2350.008 cm\nInch925.2 in\nFoot77.1 ft\nYard25.7 yd\nMeter23.50008 m\nKilometer0.02350008 km\nMile0.0146022727 mi\nNautical mile0.0126890281 nmi\n\n## What is 77.1 feet in m?\n\nTo convert 77.1 ft to m multiply the length in feet by 0.3048. The 77.1 ft in m formula is [m] = 77.1 * 0.3048. Thus, for 77.1 feet in meter we get 23.50008 m.\n\n## 77.1 Foot Conversion Table", null, "## Alternative spelling\n\n77.1 ft to Meters, 77.1 ft to Meter, 77.1 Foot in m, 77.1 Feet in Meter, 77.1 Foot to Meters, 77.1 Foot to Meter, 77.1 Feet in Meters," ]	[ null, "https://feet-to-meters.appspot.com/image/77.1.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.84619415,"math_prob":0.860161,"size":629,"snap":"2022-40-2023-06","text_gpt3_token_len":227,"char_repetition_ratio":0.2064,"word_repetition_ratio":0.0,"special_character_ratio":0.4308426,"punctuation_ratio":0.2173913,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98163086,"pos_list":[0,1,2],"im_url_duplicate_count":[null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-01T10:40:52Z\",\"WARC-Record-ID\":\"<urn:uuid:5116081b-903a-47f9-bee9-e536fd9631f2>\",\"Content-Length\":\"28153\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bc0b567b-48c6-4152-810e-86ebdafe2879>\",\"WARC-Concurrent-To\":\"<urn:uuid:521d4fdc-5101-434c-9cdf-4bf48529a822>\",\"WARC-IP-Address\":\"142.251.16.153\",\"WARC-Target-URI\":\"https://feet-to-meters.appspot.com/77.1-feet-to-meters.html\",\"WARC-Payload-Digest\":\"sha1:7ZLGOLUJZ6B6ZPEHR7SXXNMKT2V6TVT7\",\"WARC-Block-Digest\":\"sha1:7SJYMLJGTFDGTJDSLCO5MCAAEVAASK6A\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499919.70_warc_CC-MAIN-20230201081311-20230201111311-00860.warc.gz\"}"}
https://www.stata.com/statalist/archive/2011-09/msg01376.html	[ "", null, "Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.\n\n# st: Plot coefficients and confidence intervals for rolling regressions\n\n From Richard Herron To statalist@hsphsun2.harvard.edu Subject st: Plot coefficients and confidence intervals for rolling regressions Date Fri, 30 Sep 2011 17:52:13 -0400\n\n```I found that I can plot fitted values with confidence intervals from\n-regress- with -lfitci-. Is there a similar functionality that I can\ncombine with -rolling- regressions (i.e., -rolling: regress-) to do\nsimilar plots of regression coefficients and confidence intervals?\n\n* ----- begin code -----\n* plot of fitted values and confidence intervals\nsysuse auto, clear\ntwoway lfitci mpg weight\n\n* but can I plot confidence intervals from -rolling: regress- ? My\nmanual solution seems hackish.\nclear\nset obs 200\ngenerate t = _n\ngenerate y = 1\nreplace y = 0.5y[_n - 1] + rnormal() if t > 1\ntsset t\nrolling _b _se, window(10) recursive clear keep(t): regress y l.y\n\n generate plot \"manually\"\ntsset date\ngenerate lower = _stat_1 - 1.96_stat_3\ngenerate upper = _stat_1 + 1.96_stat_3\ntsline _stat_1 lower upper\n* ----- end code -----\n\nIs there a more Stata way to do this? Thanks!\n\n For searches and help try:\n* http://www.stata.com/help.cgi?search\n* http://www.stata.com/support/statalist/faq\n* http://www.ats.ucla.edu/stat/stata/\n```" ]	[ null, "https://s7.addthis.com/static/btn/lg-share-en.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.62478137,"math_prob":0.4560088,"size":1468,"snap":"2022-27-2022-33","text_gpt3_token_len":419,"char_repetition_ratio":0.13114753,"word_repetition_ratio":0.046728972,"special_character_ratio":0.28405994,"punctuation_ratio":0.16549295,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.986591,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-27T02:48:59Z\",\"WARC-Record-ID\":\"<urn:uuid:3dc46ecd-e007-4aef-b74b-abc282a439b2>\",\"Content-Length\":\"8011\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b8446f88-0291-4cf4-9a78-55b2287b92a3>\",\"WARC-Concurrent-To\":\"<urn:uuid:49ea0257-be59-4ea4-9356-bb92158e551e>\",\"WARC-IP-Address\":\"66.76.6.5\",\"WARC-Target-URI\":\"https://www.stata.com/statalist/archive/2011-09/msg01376.html\",\"WARC-Payload-Digest\":\"sha1:UMTKSW4GVM4Z4UX7BDHFK5XEVFXLJFZ3\",\"WARC-Block-Digest\":\"sha1:EPDZ4UZZ2SSOJKB4JFNS37P4C2XCYP5B\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103324665.17_warc_CC-MAIN-20220627012807-20220627042807-00715.warc.gz\"}"}
https://pzwiki.wdka.nl/mediadesign/User:Jules/distuser	[ "# User:Jules/distuser\n\nI've used the IP address of the user to get their coordinates.\nThen, I convert the coordinates into spherical coordinates.\nAnd I multiply by 6373 to convert into kilometers.\nIt is also possible to multiply by 3961 to convert in Miles but I am in favour of the metric system.\n\n```\n#!/usr/bin/python\nimport cgitb; cgitb.enable()\nimport cgi\nimport pygeoip\nimport math\n\n#db\ni = cgi.FieldStorage()\ngi = pygeoip.GeoIP('path/to/db/GeoLiteCity.dat')\nuser = i.getvalue(\"ip\",\"74.125.140.101\")\n\n#recuperation infos utilisateur\nLatuser = infos.get('latitude')\nLonguser = infos.get('longitude')\n\n#My server's coordinates\nLatserver = 34.0202\nLongserver = -118.3928\n\ndef distance(Latuser, Longuser, Latserver, Longserver):\n# Let's pretend that the Earth's shape is spherical\n# Convert latitude and longitude to\n# phi = 90 - latitude\n# theta = longitude\n\n# Compute spherical distance from spherical coordinates.\n# For two locations in spherical coordinates\ncos = (math.sin(phi1)math.sin(phi2)math.cos(theta1 - theta2) +\nmath.cos(phi1)math.cos(phi2))\narc = math.acos( cos )\n\n# Multiply arc by the radius of the earth in km\narc = arc6373\narc = round(arc, 2)\narc = str(arc)\n\nprint \"Content-type:text/html\"\nprint\nprint \"<h1> Your request has been sent \" + arc + \" km away and back</h1>\"\n\ndistance(Latuser, Longuser, Latserver, Longserver)\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6544482,"math_prob":0.79653686,"size":1638,"snap":"2022-05-2022-21","text_gpt3_token_len":452,"char_repetition_ratio":0.12913096,"word_repetition_ratio":0.069565214,"special_character_ratio":0.2832723,"punctuation_ratio":0.147651,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9960369,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-24T08:20:08Z\",\"WARC-Record-ID\":\"<urn:uuid:b7ac297e-937c-495b-9689-5d5b75a1eb3d>\",\"Content-Length\":\"22138\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3a83ca1f-45ae-42ce-9d36-2ad26588820d>\",\"WARC-Concurrent-To\":\"<urn:uuid:130d8668-3451-4106-9a1f-352f672be025>\",\"WARC-IP-Address\":\"83.96.162.96\",\"WARC-Target-URI\":\"https://pzwiki.wdka.nl/mediadesign/User:Jules/distuser\",\"WARC-Payload-Digest\":\"sha1:D6YJRKVC2QRC3OHGQJKQPULESIZDS4BE\",\"WARC-Block-Digest\":\"sha1:7OJJZROKM3YDLY3ECFZYLVMESSGI4UL2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662570051.62_warc_CC-MAIN-20220524075341-20220524105341-00681.warc.gz\"}"}
https://dsp.stackexchange.com/questions/21621/what-kind-of-filter-is-that-is-it-iir	[ "# What kind of filter is that? Is it IIR?\n\nI am trying to answer the following question:\n\nIs the system described by equation:\n\n$$y[n]=0.5y[n-1]+x[n]-0.5x[n-1]$$\n\nan IIR filter? My answer is yes.\n\nThank you\n\n• there is a class of FIR filters called \"Truncated IIR\" (TIIR) filters. you can google that and you will find stuff from Julius Smith and Avery Wang. another example of TIIR filters is the Moving Sum or Moving Average filter or CIC filter (all pretty much different names for the same thing). what makes this recursive filter an FIR is pole-zero cancellation. as implemented, there are internal poles and if they were unstable, the filter could blow up inside, but you wouldn't see it in the output until there numerical limits were exceeded. – robert bristow-johnson Feb 19 '15 at 22:12\n• what are the numerical limits? – Black Yasmin Feb 20 '15 at 11:12\n• depends on the numerical type (float or fixed) and the word width. this stuff can be looked up. (say, for IEEE-754 floats. for fixed, it depends on how many bits, $n_I$, are left of the binary point; roughly $\\pm 2^{n_I - 1}$. – robert bristow-johnson Feb 20 '15 at 17:20\n• thank you again sirs for all help! it helps a lot I am glad I found this web site – Black Yasmin Feb 22 '15 at 17:49\n• @AnthonyParks: You say: \"why are people making this complicated..this is is clearly an IIR because first term of the filter has a feedback portion.\"? I say: \"why people don't bother to understand the basic concepts of DSP\"? IIR filter always implies the recursive form, but FIR doesn't necessary mean that the filter is non-recursive. That is the only correct answer and you are confusing the concepts here. If that was the exam question, you would fail by saying it is an IIR. Oppenheim explains this topic in his book on DSP. – jojek May 30 '15 at 21:57\n\nThis is the FIR filter, although it looks like an IIR. If you calculate the coefficients you get finite impulse response:\n\n$h=$\n\nThis happens due to zero-pole cancellation:\n\n$Y(z)-0.5Y(z)z^{-1}=X(z)-0.5X(z)z^{-1}$\n\n$H(z)=\\dfrac{Y(z)}{X(z)}=\\dfrac{1-0.5z^{-1}}{1-0.5z^{-1}}=1$\n\nYes, it can be tricky. Seeing $y[n-k]$ coefficients in LCCDE (Linear Constant Coefficients Difference Equation) doesn't necessarily mean it's an IIR filter. It might be just a recursive FIR filter.\n\n• thanks for the recognition! I was fooled to say IIR, without ever looking carefully at the coefficients... I deleted my answer. – Fat32 Feb 18 '15 at 22:30\n• Still, if you implement the equations as originally stated, it will not behave exactly as H(z) = 1 because of finite word length effects (despite the pole-zero cancellation being exact in this case). – Oscar Feb 19 '15 at 9:23\n• That is true @Oscar, but these are numerical issues which have nothing to do with filter being F/IIR. – jojek Feb 19 '15 at 9:27\n• @jojek: you are of course completely correct. However, using recursive FIR filters cause quite a bit of problems if you are unaware of these things (which many, even \"high-quality\" researchers, are). Hence, my comment. Ideally there should be a discussion of algorithm vs transfer function as well. – Oscar Feb 19 '15 at 9:31\n• jojek i am reading your answer from this question you answerd but i cannot comment. dsp.stackexchange.com/questions/17605/… can i use diffrent window? – Black Yasmin Feb 20 '15 at 11:18\n\nJojek's answer is of course correct. I would just like to add some more information because much too often have I seen the terms \"IIR\" and \"recursive\" confused. The following implications always hold:\n\n\\begin{align}\\text{IIR}& \\Longrightarrow\\text{recursive}\\\\ \\text{non-recursive}&\\Longrightarrow\\text{FIR}\\end{align}\n\ni.e. every IIR filter (i.e. a discrete-time filter having an infinitely long impulse response) must be implemented recursively (unless you have infinite memory available), and every non-recursive LTI system has a finite impulse response (again, unless you have infinite memory).\n\nHowever, the reverse is generally not true. A recursive filter can have a finite impulse response, as is the case for the example in the question. Another famous example is a moving average filter. This a non-recursive implementation of a moving average (necessarily FIR):\n\n$$y[n]=\\frac{1}{N}\\sum_{k=n-N+1}^nx[k]$$\n\nAnd this is a recursive implementation of the same filter (also FIR): $$y[n]=y[n-1]+\\frac{1}{N}(x[n]-x[n-N])$$\n\n• Concise and accurate as always, +1 ;) Thank you for bringing up the MA case. – jojek Feb 18 '15 at 22:48\n• @jojek: yeah, I think it's a classic that everybody should know. – Matt L. Feb 18 '15 at 22:49\n• And while I was primarily thinking of round-off noise in the comment to jojek's answer, for MA, overflow will be a potential issue which needs to be carefully considered. Easily solved by two's complement arithmetic and enough word length though. – Oscar Feb 19 '15 at 9:26\n• @Oscar: Well, after doing very simple analysis with double floating point precision I got an error of 8.881784197001252e-16. This is after processing the equivalent of 1 year of audio at sampling frequency 44.1kHz. Input data is a Gaussian noise with normalized distribution. Here is the code to reproduce the result !click! (it might take a 3 days to run). Providing this is correct, then I believe there is nothing to worry about. – jojek Mar 2 '15 at 9:25\n• @jojek: Three things. 1) I was referring to the moving average filter of the answer, not the one in the original question. 2) Yes, that is OK for audio (but not exact, so no reason to put \"no\" in bold), but I prefer my safety critical signal processing to work independent of the input signal having synthetic properties. 3) The interesting thing is that the filter you simulated with will not have the problems I described (as the pole is inside the unit circle, not on it), but will always have round-off errors independent of representation (which can be avoided in the moving average case). – Oscar Mar 3 '15 at 10:52" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8801872,"math_prob":0.7497044,"size":2027,"snap":"2020-34-2020-40","text_gpt3_token_len":558,"char_repetition_ratio":0.112703905,"word_repetition_ratio":0.13818182,"special_character_ratio":0.27035028,"punctuation_ratio":0.105515584,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99087435,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T18:35:07Z\",\"WARC-Record-ID\":\"<urn:uuid:011e0d3d-01c8-4639-a900-601ff3569469>\",\"Content-Length\":\"179447\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d3a0806d-238a-45b9-8441-183fa582b8b8>\",\"WARC-Concurrent-To\":\"<urn:uuid:52e623b9-1103-47c3-be30-771553c11ece>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://dsp.stackexchange.com/questions/21621/what-kind-of-filter-is-that-is-it-iir\",\"WARC-Payload-Digest\":\"sha1:HQGPHIXPYGOT7PE56TFTN3FIMMNQ6ECM\",\"WARC-Block-Digest\":\"sha1:TUZS2UFPH4ZIZALRDT6MQL4YHSDMPVBB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400198287.23_warc_CC-MAIN-20200920161009-20200920191009-00536.warc.gz\"}"}
https://www.physicsforums.com/threads/how-is-momentum-measured.82208/	[ "# How is Momentum Measured?\n\nNicky\nWhat kind of experimental apparatus provides the purest measurement of a low-energy particle's momentum? By \"pure\" momentum measurement, I mean allowing for the maximum achievable uncertainty in position, and therefore the most accurate possible reading of momentum as per the uncertainty principle.\n\n## Answers and Replies\n\nHomework Helper\nGold Member\nMomentum is usually measured by R=pc/qB (in Gaussian units).\nThe measurement is of the radius of the path of a moving particle of charge q i a magnetic field B..\n\nNicky\nMeir Achuz said:\nMomentum is usually measured by R=pc/qB (in Gaussian units).\nThe measurement is of the radius of the path of a moving particle of charge q i a magnetic field B..\n\nI am trying to imagine how one would display interference effects analogous to the double-slit experiment, except that the roles of position and momentum are reversed. With the usual double-slit setup, the beam components passing through the two slits interfere, resulting in some spots on the detection screen that receive less total particle flux. So in the alternative experiment, I guess interference would be manifest as certain path radii showing stronger particle flux than others.\n\nHow to produce the two interfering beams is less clear. Maybe a single beam could be split into two, somehow doppler shift one of the two beams, then recombine the two beams to form a superposition of momentum states. Has anything like this been attempted?\n\nStaff Emeritus\nGold Member\nNicky said:\nWhat kind of experimental apparatus provides the purest measurement of a low-energy particle's momentum? By \"pure\" momentum measurement, I mean allowing for the maximum achievable uncertainty in position, and therefore the most accurate possible reading of momentum as per the uncertainty principle.\n\nXtal diffraction ! At least, that's how it is done with slow neutrons: a monochromator is nothing else but a pure monocrystal (for instance, of silicium) and by selecting an outgoing angle you impose a Bragg condition and hence a pure momentum.\nThe bigger and the purer the Xtal is, the better your momentum selection (and of course the worse your position, because it is limited to the entire Xtal).\n\ncheers,\nPatrick.\n\nStaff Emeritus\nNicky said:\nWhat kind of experimental apparatus provides the purest measurement of a low-energy particle's momentum? By \"pure\" momentum measurement, I mean allowing for the maximum achievable uncertainty in position, and therefore the most accurate possible reading of momentum as per the uncertainty principle.\n\nHow about a hemispherical electron analyzer?\n\nMy avatar is actually a 2D plot of E vs. k of electrons coming out of a material from a photoemission process and into a Scienta SES200 electron analyzer. And we all know that \"k\" is equivalent to the momentum, in this case, the momentum of the electron and the crystal. (\"crystal momentum\") So the horizontal axis is really the momentum of the electrons. And these ARE low energy electrons, with energy in the range of ~0 to about 10 eV.\n\nThis is now a common technique in angle-resolved photoemission spectroscopy (ARPES), so most papers using this technique will have references to it.\n\nZz." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.82747495,"math_prob":0.83338463,"size":321,"snap":"2022-40-2023-06","text_gpt3_token_len":67,"char_repetition_ratio":0.12302839,"word_repetition_ratio":0.0,"special_character_ratio":0.20560747,"punctuation_ratio":0.078431375,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95105064,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-26T21:38:55Z\",\"WARC-Record-ID\":\"<urn:uuid:9e76026a-e98b-4af2-9312-e3c2fdf6d328>\",\"Content-Length\":\"70556\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:91bc5494-8c27-4b83-a7bc-a0a6f84bbcc3>\",\"WARC-Concurrent-To\":\"<urn:uuid:ccb6c1f2-1e0b-48e1-8ffd-b45b8d2efff9>\",\"WARC-IP-Address\":\"104.26.14.132\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/how-is-momentum-measured.82208/\",\"WARC-Payload-Digest\":\"sha1:LKUFUMWVCKBMSXNFVB35R6GQS4L5CQE4\",\"WARC-Block-Digest\":\"sha1:PFMFM5WJRWNS3LMQWAFL3Y4UCPRTPHSC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030334942.88_warc_CC-MAIN-20220926211042-20220927001042-00056.warc.gz\"}"}
http://sgmgqhay.gq/fytyc/7-feet-in-cm-typi.php	[ "# What is 7 Feet 7 Inches in Centimeters?", null, "However, it is practical unit of length for many everyday measurements.", null, "", null, "", null, "", null, "", null, "", null, "", null, "A corresponding unit of area is the square centimetre. A corresponding unit of volume is the cubic centimetre. The centimetre is a now a non-standard factor, in that factors of 10 3 are often preferred. However, it is practical unit of length for many everyday measurements. A centimetre is approximately the width of the fingernail of an adult person.\n\nThere are twelve inches in one foot and three feet in one yard. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types.\n\nExamples include mm, inch, kg, US fluid ounce, 6'3\", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more! You can do the reverse unit conversion from ft to cm , or enter any two units below: Enter two units to convert From: Centimeter A centimetre American spelling centimeter, symbol cm is a unit of length that is equal to one hundreth of a metre, the current SI base unit of length. The answer is 0. We assume you are converting between foot and centimetre.\n\nYou can view more details on each measurement unit: Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between feet and centimetres. Type in your own numbers in the form to convert the units! You can do the reverse unit conversion from cm to feet , or enter any two units below:. There are twelve inches in one foot and three feet in one yard.\n\nA centimetre American spelling centimeter, symbol cm is a unit of length that is equal to one hundreth of a metre, the current SI base unit of length. A centimetre is part of a metric system. It is the base unit in the centimetre-gram-second system of units. A corresponding unit of area is the square centimetre.\n\nHow many feet in 1 cm? The answer is We assume you are converting between foot and centimetre. You can view more details on each measurement unit: feet or cm The SI base unit for length is the metre. 1 metre is equal to feet, or cm. Note that rounding errors may occur, so always check the results. Other feet in cm conversion on this website include: 4′ 11″ in cm – 4 Feet 11 Inches in cm; 5 1/2′ in cm – 5 1/2 Feet in cm; 27′ 2″ in cm – 27 Feet 2 Inches in cm; 7 ft 7 in cm. Now you already know the height 7′ 7″ in cm. 7′ 7″ to cm is centimeters. Here you can convert cm in . 1 metre is equal to cm, or ft. Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between centimetres and feet." ]	[ null, "http://worldgiants.narod.ru/foto/stadnik29.jpg", null, "https://s-media-cache-ak0.pinimg.com/236x/85/6e/9c/856e9cb43c4c6f43f3a1e9e62d7ae679.jpg", null, "https://s-media-cache-ak0.pinimg.com/736x/23/61/b3/2361b37e6e46a0040c333fe89613b7cd.jpg", null, "https://www.vratim.com/uploads/4/9/8/7/49871791/3865867_orig.png", null, "https://qph.fs.quoracdn.net/main-qimg-7c82f625a910c2e4c1fe8057156d949e", null, "https://i.ytimg.com/vi/RzNMbl98B4k/maxresdefault.jpg", null, "http://www4.pcmag.com/media/images/278446-male-7cm.jpg", null, "https://s-media-cache-ak0.pinimg.com/736x/bb/97/fc/bb97fc372d29681283c567493e4df4cf.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9060505,"math_prob":0.97400886,"size":2690,"snap":"2019-26-2019-30","text_gpt3_token_len":669,"char_repetition_ratio":0.14631422,"word_repetition_ratio":0.3446215,"special_character_ratio":0.23791821,"punctuation_ratio":0.13379073,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9797685,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,2,null,1,null,1,null,3,null,1,null,2,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-17T02:16:55Z\",\"WARC-Record-ID\":\"<urn:uuid:3165a146-0945-4c84-b498-21f524d6aca8>\",\"Content-Length\":\"9165\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9befa476-1933-493b-bcfa-c34a6b36f778>\",\"WARC-Concurrent-To\":\"<urn:uuid:f74b0d64-b809-4dba-a2c7-088dd28515d1>\",\"WARC-IP-Address\":\"104.18.34.136\",\"WARC-Target-URI\":\"http://sgmgqhay.gq/fytyc/7-feet-in-cm-typi.php\",\"WARC-Payload-Digest\":\"sha1:OEAZ7ROBSRB6LGN6VZOTD5RG67PX7JJI\",\"WARC-Block-Digest\":\"sha1:D4QQKK3L6ZEPZOPSPLYX3KLEP5SFJLGV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195525009.36_warc_CC-MAIN-20190717021428-20190717043428-00179.warc.gz\"}"}
http://www.thefreedictionary.com/response+variable	[ "response variable\n\nAlso found in: Wikipedia.\n\nresponse variable\n\nn\n1. (Mathematics) statistics a more modern term for dependent variable2\n2. (Psychology) statistics a more modern term for dependent variable2\nReferences in periodicals archive ?\nCT is a nonparametric statistical method used for the determination of the relationship between a response variable and the other variables that may be related to the response variable.\nAn alternative in this situation is the partial correlation coefficient, which allows the study of the degree of association between two traits, given the existence of a third trait or of a set of traits with the potential to influence the main response variable (CRUZ et al.\nIn this study, the weld strength as response variable was maximized by using FFD with the optimal level of the process parameters which has been obtained with the combination of individual parameters.\nCompared to the others, the statistical models allow optimizing process parameters in short computational times and more than one response variable simultaneously.\nLinear regression assumes that the unknown relation between the factor and the response variable is a linear relation Y = a + bx, where b is the coefficient of x.\n2012), we first computed the individual linear regression model between each log-transformed response variable (IDW and GSI) and mean individual body size for each combination of levels of both factors.\nThe items were combined to create the indirect response variable for \"pay late\" behavior.\nHowever, since this value represents an individual fit, such result did not interfere with the estimation process, because the optimal fit identified the fit of the controllable factors and that minimizes the variability of the response variable, regardless of whether the model is significant or not.\nQuantile Regression is a method for estimating the relationship between a response variable and a set of explanatory variables for the whole conditional probability distribution of the response variable.\nFor these models it is common to consider the response variable following a normal distribution (when it is the best choice to model the biological characteristic), since this approach is theoretically consolidated from the formulation, adjustment methods and diagnostic analysis (residual analysis and influence), as observed in Diggle, Heagerty, Liang, and Zeger (2002), Fitzmaurice, Laird, and Ware (2004), Nobre and Singer (2007), Nobre and Singer (2011) with availability of use in applications such as R and SAS as verified in Pinheiro and Bates (2000) and Littel, Stroup, Wolfinger, and Schabenberger (2006).\nSite: Follow: Share:\nOpen / Close" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9142128,"math_prob":0.9508031,"size":2601,"snap":"2019-26-2019-30","text_gpt3_token_len":506,"char_repetition_ratio":0.16827108,"word_repetition_ratio":0.015151516,"special_character_ratio":0.18762015,"punctuation_ratio":0.08275862,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98678434,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-18T16:39:08Z\",\"WARC-Record-ID\":\"<urn:uuid:e350de48-422a-4554-a5e0-39a3a272929d>\",\"Content-Length\":\"46701\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:46dba52e-966f-401a-8254-15bec3fc69af>\",\"WARC-Concurrent-To\":\"<urn:uuid:c0ff4b70-8387-4196-87f7-695008c947f3>\",\"WARC-IP-Address\":\"209.160.67.6\",\"WARC-Target-URI\":\"http://www.thefreedictionary.com/response+variable\",\"WARC-Payload-Digest\":\"sha1:U52CLU5WOIJJWBIGTYACIFBNR7OORYBX\",\"WARC-Block-Digest\":\"sha1:5UNCJ7CDQSVYTWT77NKARP33623KCEYX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627998755.95_warc_CC-MAIN-20190618143417-20190618165417-00549.warc.gz\"}"}
http://www.mathreference.com/la-det,perm.html	[ "# Determinants, Permutation Definition\n\n## Permutation Definition\n\nReview the formula for a 3×3 determinant, as given in the previous section. It isn't recursive; it is a simple sum of products. Call this formula det2(M). We showed that this formula was the same as det1(M), at least for 3×3 matrices.\n\nNotice that each tterm, each product of 3 matrix elements, represents each row once and each column once. We don't go straight down or straight across, we multiply along diagonal lines. For the 3×3 case, there are 6 ways to do this, hence 6 terms in the formula. Choose any entry from the first row and mark that column as \"used\". Then choose an enttry from the second row, avoiding the used column. Mark that column used, and in the third row, there is only one entry available. That's 3×2×1 or 6 combinations.\n\nIf you write down the numbers of the columns, in the order they are \"used\" by the rows, you'll find a permutation on the numbers 1 through n. Each product is associated with one of these permutations. The product is negated when the permutation is odd. At least that's how it looks in the 3×3 case.\n\nIf we derive a formula for the determinant of a 4×4 matrix, it will have 24 terms, each term a product of 4 entries according to a permutation on 4 columns. Half the terms are negated, according to the parity of the permutations. A 5×5 matrix gives a formula with 120 terms, and so on. This quickly becomes impractical, but let's prove it anyways.\n\nLet det2(M) be the sum of all permutation products, where a product is negated when its associated permutation is odd. This definition agrees with det1 for n = 1, 2, and 3. Proceed by induction on n.\n\nGiven an n×n matrix, delete the first row and jth column, and write the subdeterminant as a sum of permutation products. For each permutation, add 1 to each column number that is j or larger. We are pushing them over to make room for column j. Write this permutation as a series of swaps. (Remember that swaps, like transpositions, are odd.) The number of swaps gives the parity. Now place j in position, just after the first j-1 numbers. Each swap is still a swap, and still odd. Some of them pass through j, but that's ok. The result is the same permutation, with the same parity, but if has j in position j. However, j is suppose to be first in line. After all, det1 says to multiply the subdeterminant by the entry in row 1 column j, so j comes first. A series of j-1 transpositions moves j to the head of the line. Have we changed the parity of the permutation by putting j in front? Only if an odd number of transpositions are needed to move j from its home in position j to the front in position 1. This happens only when j is even. When j is 4, swap it with 3 2 and 1 to move it to the front, giving 3 transpositions. In the same way, det1(M) tells us to negate the product precisely when j is even. The two formulas agree." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9341303,"math_prob":0.9767472,"size":2590,"snap":"2022-40-2023-06","text_gpt3_token_len":639,"char_repetition_ratio":0.1434648,"word_repetition_ratio":0.0,"special_character_ratio":0.24169885,"punctuation_ratio":0.12434326,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9975831,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-27T04:43:51Z\",\"WARC-Record-ID\":\"<urn:uuid:e8bc2d1a-35b0-4c12-9057-1419a86cd3b5>\",\"Content-Length\":\"4200\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3bd71eeb-4f0e-4638-b5c8-baffa9983f46>\",\"WARC-Concurrent-To\":\"<urn:uuid:3be047b5-323b-429e-ab1b-16e5690118d8>\",\"WARC-IP-Address\":\"216.252.162.35\",\"WARC-Target-URI\":\"http://www.mathreference.com/la-det,perm.html\",\"WARC-Payload-Digest\":\"sha1:XUVJI2CDOODXB4M2KFFQZIM2FAO2DT3H\",\"WARC-Block-Digest\":\"sha1:TZ3LDWONXPNN3DL4IPAR6IXNHNKOR2TK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764494936.89_warc_CC-MAIN-20230127033656-20230127063656-00505.warc.gz\"}"}
http://mizar.org/version/current/html/proofs/glib_009/122	[ "let G1 be _Graph; :: thesis: for G2 being Subgraph of G1\nfor E2 being RepEdgeSelection of G2 ex E1 being RepEdgeSelection of G1 st E2 = E1 /\\ ()\n\nlet G2 be Subgraph of G1; :: thesis: for E2 being RepEdgeSelection of G2 ex E1 being RepEdgeSelection of G1 st E2 = E1 /\\ ()\nlet E2 be RepEdgeSelection of G2; :: thesis: ex E1 being RepEdgeSelection of G1 st E2 = E1 /\\ ()\nset A = { { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } where v1, v2 is Vertex of G1 : ( ex e0 being object st e0 Joins v1,v2,G1 & ( for e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 ) )\n}\n;\ndefpred S1[ object , object ] means ex S being non empty set st\n( \\$1 = S & \\$2 = the Element of S );\nA1: for x, y1, y2 being object st x in { { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } where v1, v2 is Vertex of G1 : ( ex e0 being object st e0 Joins v1,v2,G1 & ( for e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 ) )\n}\n& S1[x,y1] & S1[x,y2] holds\ny1 = y2 ;\nA2: for x being object st x in { { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } where v1, v2 is Vertex of G1 : ( ex e0 being object st e0 Joins v1,v2,G1 & ( for e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 ) )\n}\nholds\nex y being object st S1[x,y]\nproof\nlet x be object ; :: thesis: ( x in { { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } where v1, v2 is Vertex of G1 : ( ex e0 being object st e0 Joins v1,v2,G1 & ( for e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 ) )\n}\nimplies ex y being object st S1[x,y] )\n\nassume x in { { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } where v1, v2 is Vertex of G1 : ( ex e0 being object st e0 Joins v1,v2,G1 & ( for e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 ) )\n}\n; :: thesis: ex y being object st S1[x,y]\nthen consider v1, v2 being Vertex of G1 such that\nA3: x = { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } and\nA4: ex e0 being object st e0 Joins v1,v2,G1 and\nfor e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 ;\nreconsider B = x as set by A3;\nconsider e0 being object such that\nA5: e0 Joins v1,v2,G1 by A4;\nreconsider e0 = e0 as Element of the_Edges_of G1 by ;\ne0 in B by A3, A5;\nthen reconsider B = B as non empty set ;\ntake the Element of B ; :: thesis: S1[x, the Element of B]\ntake B ; :: thesis: ( x = B & the Element of B = the Element of B )\nthus ( x = B & the Element of B = the Element of B ) ; :: thesis: verum\nend;\nconsider f being Function such that\nA6: ( dom f = { { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } where v1, v2 is Vertex of G1 : ( ex e0 being object st e0 Joins v1,v2,G1 & ( for e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 ) )\n}\n& ( for x being object st x in { { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } where v1, v2 is Vertex of G1 : ( ex e0 being object st e0 Joins v1,v2,G1 & ( for e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 ) )\n}\nholds\nS1[x,f . x] ) ) from for e being object st e in rng f holds\ne in the_Edges_of G1\nproof\nlet e be object ; :: thesis: ( e in rng f implies e in the_Edges_of G1 )\nassume e in rng f ; :: thesis:\nthen consider C being object such that\nA7: ( C in dom f & f . C = e ) by FUNCT_1:def 3;\nconsider C0 being non empty set such that\nA8: ( C = C0 & f . C = the Element of C0 ) by A6, A7;\nconsider v1, v2 being Vertex of G1 such that\nA9: C = { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } and\nex e0 being object st e0 Joins v1,v2,G1 and\nfor e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 by A6, A7;\ne in C0 by A7, A8;\nthen consider e2 being Element of the_Edges_of G1 such that\nA10: ( e = e2 & e2 Joins v1,v2,G1 ) by A8, A9;\nthus e in the_Edges_of G1 by ; :: thesis: verum\nend;\nthen A11: rng f c= the_Edges_of G1 by TARSKI:def 3;\nthe_Edges_of G2 c= the_Edges_of G1 ;\nthen E2 c= the_Edges_of G1 by XBOOLE_1:1;\nthen reconsider E1 = E2 \\/ (rng f) as Subset of () by ;\nfor v, w, e0 being object st e0 Joins v,w,G1 holds\nex e being object st\n( e Joins v,w,G1 & e in E1 & ( for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e ) )\nproof\nlet v, w, e0 be object ; :: thesis: ( e0 Joins v,w,G1 implies ex e being object st\n( e Joins v,w,G1 & e in E1 & ( for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e ) ) )\n\nA12: ( v is set & w is set ) by TARSKI:1;\nassume A13: e0 Joins v,w,G1 ; :: thesis: ex e being object st\n( e Joins v,w,G1 & e in E1 & ( for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e ) )\n\nper cases ( ex e1 being object st\n( e1 Joins v,w,G1 & e1 in E2 ) or for e1 being object st e1 Joins v,w,G1 holds\nnot e1 in E2 )\n;\nsuppose ex e1 being object st\n( e1 Joins v,w,G1 & e1 in E2 ) ; :: thesis: ex e being object st\n( e Joins v,w,G1 & e in E1 & ( for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e ) )\n\nthen consider e1 being object such that\nA14: ( e1 Joins v,w,G1 & e1 in E2 ) ;\ne1 Joins v,w,G2 by ;\nthen consider e being object such that\nA15: ( e Joins v,w,G2 & e in E2 ) and\nA16: for e8 being object st e8 Joins v,w,G2 & e8 in E2 holds\ne8 = e by Def5;\ntake e ; :: thesis: ( e Joins v,w,G1 & e in E1 & ( for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e ) )\n\nthus A17: e Joins v,w,G1 by ; :: thesis: ( e in E1 & ( for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e ) )\n\nthus e in E1 by ; :: thesis: for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e\n\nlet e9 be object ; :: thesis: ( e9 Joins v,w,G1 & e9 in E1 implies e9 = e )\nassume A18: ( e9 Joins v,w,G1 & e9 in E1 ) ; :: thesis: e9 = e\nnot e9 in rng f\nproof\nassume e9 in rng f ; :: thesis: contradiction\nthen consider C being object such that\nA19: ( C in dom f & f . C = e9 ) by FUNCT_1:def 3;\nconsider v1, v2 being Vertex of G1 such that\nA20: C = { k where k is Element of the_Edges_of G1 : k Joins v1,v2,G1 } and\nex k0 being object st k0 Joins v1,v2,G1 and\nA21: for k0 being object st k0 Joins v1,v2,G1 holds\nnot k0 in E2 by ;\nconsider C0 being non empty set such that\nA22: ( C = C0 & f . C = the Element of C0 ) by ;\ne9 in C0 by ;\nthen consider k being Element of the_Edges_of G1 such that\nA23: ( e9 = k & k Joins v1,v2,G1 ) by ;\n( ( v1 = v & v2 = w ) or ( v1 = w & v2 = v ) ) by ;\nhence contradiction by A15, A17, A21, GLIB_000:14; :: thesis: verum\nend;\nthen A24: e9 in E2 by ;\nthen e9 Joins v,w,G2 by ;\nhence e9 = e by ; :: thesis: verum\nend;\nsuppose A25: for e1 being object st e1 Joins v,w,G1 holds\nnot e1 in E2 ; :: thesis: ex e being object st\n( e Joins v,w,G1 & e in E1 & ( for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e ) )\n\nA26: ( v is Vertex of G1 & w is Vertex of G1 ) by ;\nset B = { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } ;\nA27: { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } in { { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } where v1, v2 is Vertex of G1 : ( ex e0 being object st e0 Joins v1,v2,G1 & ( for e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 ) )\n}\nby ;\nthen consider B0 being non empty set such that\nA28: ( { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } = B0 & f . { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } = the Element of B0 ) by A6;\nf . { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } in { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } by A28;\nthen consider e being Element of the_Edges_of G1 such that\nA29: ( f . { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } = e & e Joins v,w,G1 ) ;\ntake e ; :: thesis: ( e Joins v,w,G1 & e in E1 & ( for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e ) )\n\nthus e Joins v,w,G1 by A29; :: thesis: ( e in E1 & ( for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e ) )\n\ne in rng f by ;\nhence e in E1 by XBOOLE_0:def 3; :: thesis: for e9 being object st e9 Joins v,w,G1 & e9 in E1 holds\ne9 = e\n\nlet e9 be object ; :: thesis: ( e9 Joins v,w,G1 & e9 in E1 implies e9 = e )\nassume A30: ( e9 Joins v,w,G1 & e9 in E1 ) ; :: thesis: e9 = e\nthen not e9 in E2 by A25;\nthen e9 in rng f by ;\nthen consider C being object such that\nA31: ( C in dom f & f . C = e9 ) by FUNCT_1:def 3;\nconsider v1, v2 being Vertex of G1 such that\nA32: C = { k where k is Element of the_Edges_of G1 : k Joins v1,v2,G1 } and\nex k0 being object st k0 Joins v1,v2,G1 and\nfor k0 being object st k0 Joins v1,v2,G1 holds\nnot k0 in E2 by ;\nconsider C0 being non empty set such that\nA33: ( C = C0 & f . C = the Element of C0 ) by ;\nf . C in C0 by A33;\nthen consider k being Element of the_Edges_of G1 such that\nA34: ( f . C = k & k Joins v1,v2,G1 ) by ;\nfor x being object holds\n( x in { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } iff x in C0 )\nproof\nlet x be object ; :: thesis: ( x in { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } iff x in C0 )\nA35: ( ( v1 = v & v2 = w ) or ( v1 = w & v2 = v ) ) by ;\nhereby :: thesis: ( x in C0 implies x in { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } )\nassume x in { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } ; :: thesis: x in C0\nthen consider k being Element of the_Edges_of G1 such that\nA36: ( x = k & k Joins v,w,G1 ) ;\nk Joins v1,v2,G1 by ;\nhence x in C0 by ; :: thesis: verum\nend;\nassume x in C0 ; :: thesis: x in { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 }\nthen consider k being Element of the_Edges_of G1 such that\nA37: ( x = k & k Joins v1,v2,G1 ) by ;\nk Joins v,w,G1 by ;\nhence x in { e where e is Element of the_Edges_of G1 : e Joins v,w,G1 } by A37; :: thesis: verum\nend;\nhence e9 = e by ; :: thesis: verum\nend;\nend;\nend;\nthen reconsider E1 = E1 as RepEdgeSelection of G1 by Def5;\ntake E1 ; :: thesis: E2 = E1 /\\ ()\nfor x being object holds\n( x in E2 iff ( x in E1 & x in the_Edges_of G2 ) )\nproof\nlet x be object ; :: thesis: ( x in E2 iff ( x in E1 & x in the_Edges_of G2 ) )\nthus ( x in E2 implies ( x in E1 & x in the_Edges_of G2 ) ) by ; :: thesis: ( x in E1 & x in the_Edges_of G2 implies x in E2 )\nassume A38: ( x in E1 & x in the_Edges_of G2 ) ; :: thesis: x in E2\nnot x in rng f\nproof\nassume x in rng f ; :: thesis: contradiction\nthen consider C being object such that\nA39: ( C in dom f & f . C = x ) by FUNCT_1:def 3;\nconsider v1, v2 being Vertex of G1 such that\nA40: C = { e where e is Element of the_Edges_of G1 : e Joins v1,v2,G1 } and\nex e0 being object st e0 Joins v1,v2,G1 and\nA41: for e0 being object st e0 Joins v1,v2,G1 holds\nnot e0 in E2 by ;\nconsider C0 being non empty set such that\nA42: ( C = C0 & f . C = the Element of C0 ) by ;\nf . C in C0 by A42;\nthen consider e being Element of the_Edges_of G1 such that\nA43: ( f . C = e & e Joins v1,v2,G1 ) by ;\nx Joins v1,v2,G2 by ;\nthen consider e1 being object such that\nA44: ( e1 Joins v1,v2,G2 & e1 in E2 ) and\nfor e9 being object st e9 Joins v1,v2,G2 & e9 in E2 holds\ne9 = e1 by Def5;\nthus contradiction by A41, A44, GLIB_000:72; :: thesis: verum\nend;\nhence x in E2 by ; :: thesis: verum\nend;\nhence E2 = E1 /\\ () by XBOOLE_0:def 4; :: thesis: verum" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5664261,"math_prob":0.99571055,"size":11245,"snap":"2023-40-2023-50","text_gpt3_token_len":4836,"char_repetition_ratio":0.23787919,"word_repetition_ratio":0.56820625,"special_character_ratio":0.43112496,"punctuation_ratio":0.17967951,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99638397,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-26T22:44:51Z\",\"WARC-Record-ID\":\"<urn:uuid:4ef66df7-4972-4686-bb9f-b26fa49af978>\",\"Content-Length\":\"120094\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a30433ab-450c-4d52-8201-228e3f824a1b>\",\"WARC-Concurrent-To\":\"<urn:uuid:30086395-04db-40b8-8dfa-feae52d0a00d>\",\"WARC-IP-Address\":\"193.219.28.149\",\"WARC-Target-URI\":\"http://mizar.org/version/current/html/proofs/glib_009/122\",\"WARC-Payload-Digest\":\"sha1:MEK3U3YZQ3CROCJOBN4KUTDXQNILYKRN\",\"WARC-Block-Digest\":\"sha1:WQHMKE7U3O74QHY3D7KV24FKIBAU3DYS\",\"WARC-Identified-Payload-Type\":\"application/xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510225.44_warc_CC-MAIN-20230926211344-20230927001344-00818.warc.gz\"}"}
https://blog.csdn.net/natual177/article/details/104669892	[ "# [python][excel][xlsl]操作\n\n# -- coding: utf-8 --\n\nfilename = 'test.xlsx'\n\nsheetnames = wb.get_sheet_names()\n\nws = wb.get_sheet_by_name(sheetnames)\n\nfirst_column = ws['A']\n\nprint(\"len(first_column)\",len(first_column))\n\ncount = 0\n\nstart = False\n\nend = False\n\nfor x in range(len(first_column)):\n\nif first_column[x].value != None:\n\nif start == True:\n\nend = True\n\nstart = True\n\nx = x + 1\n\npos = 'B' + str(x)\n\ncount = 1\n\nelse:\n\ncount = count + 1\n\nif start == True and end == True:\n\nws[pos] = count\n\nwb.save(filename)\n\n01-11", null, "1923", null, "08-18\n06-29", null, "12万+\n04-12", null, "3万+\n04-30", null, "1万+\n01-02", null, "2万+\n08-19", null, "10万+\n03-18", null, "6051\n03-04", null, "5659\n10-18", null, "3767" ]	[ null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/commentFlag@2x.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6204508,"math_prob":0.7767369,"size":541,"snap":"2020-45-2020-50","text_gpt3_token_len":161,"char_repetition_ratio":0.16201118,"word_repetition_ratio":0.0,"special_character_ratio":0.3401109,"punctuation_ratio":0.14130434,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98681986,"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,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\":\"2020-10-23T02:42:27Z\",\"WARC-Record-ID\":\"<urn:uuid:f967f877-445e-4e57-8e0e-1e780013406c>\",\"Content-Length\":\"130653\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fb360a42-c39f-4cd1-9273-32748df653d1>\",\"WARC-Concurrent-To\":\"<urn:uuid:179cc132-3672-4145-bd3e-5c8854f71b55>\",\"WARC-IP-Address\":\"101.200.35.175\",\"WARC-Target-URI\":\"https://blog.csdn.net/natual177/article/details/104669892\",\"WARC-Payload-Digest\":\"sha1:DLL4YINPP2ZWKZCBZCGOTQO7ZGPPYTDM\",\"WARC-Block-Digest\":\"sha1:WWIUE364HXX2AP3B7CUDZBVOXDEHZYTW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107880519.12_warc_CC-MAIN-20201023014545-20201023044545-00608.warc.gz\"}"}
https://ecce216.com/blog/how-do-you-prove-the-correctness-of-an-algorithm/	[ "# How do you prove the correctness of an algorithm?\n\n## How do you prove the correctness of an algorithm?\n\nThe only way to prove the correctness of an algorithm over all possible inputs is by reasoning formally or mathematically about it. One form of reasoning is a “proof by induction”, a technique that’s also used by mathematicians to prove properties of numerical sequences.\n\n### How do you prove the correctness of an algorithm explain using an example?\n\nOne way to prove the correctness of the algorithm is to check the condition before (precondition) and after (postcondition) the execution of each step. The algorithm is correct only if the precondition is true then postcondition must be true. Consider the problem of finding the factorial of a number n.\n\n#### How do you prove algorithms correctness by induction?\n\nThe proof consists of three steps: first prove that insert is correct, then prove that isort’ is correct, and finally prove that isort is correct. Each step relies on the result from the previous step. The first two steps require proofs by induction (because the functions in question are recursive).\n\nHow do you prove the correctness of the greedy algorithm?\n\nOne of the simplest methods for showing that a greedy algorithm is correct is to use a “greedy stays ahead” argument. This style of proof works by showing that, according to some measure, the greedy algorithm always is at least as far ahead as the optimal solution during each iteration of the algorithm.\n\nHow can you prove the correctness of an algorithm using loop invariant?\n\nTermination: When the for-loop terminates i=(n−1)+1=n. Now the loop invariant gives: The variable answer contains the sum of all numbers in subarray A[0:n]=A. This is exactly the value that the algorithm should output, and which it then outputs. Therefore the algorithm is correct.\n\n## Are greedy algorithms always correct?\n\nApplications. Greedy algorithms typically (but not always) fail to find the globally optimal solution because they usually do not operate exhaustively on all the data. They can make commitments to certain choices too early, preventing them from finding the best overall solution later.\n\n### Which type of algorithm is harder to prove the correctness?\n\nGreedy algorithms\nGreedy algorithms are easy to design, but hard to prove correct • Usually, a counterexample is the best way to do this • Interval scheduling provided an example where it was easy to come up with a simple greedy algorithm. – However, we were able to show the algorithm non-optimal by using a counterexample.\n\n#### How can you prove correctness of dynamic programming algorithm?\n\nYou can view DP as a way to speed up recursion, and the easiest way to prove a recursive algorithm correct is nearly always by induction: Show that it’s correct on some small base case(s), and then show that, assuming it is correct for a problem of size n, it is also correct for a problem of size n+1.\n\nHow can you prove that greedy algorithm is optimal?\n\nIs an essential tool for proving the statement that proves an algorithm’s correctness?\n\nMathematical induction (MI) is an essential tool for proving the statement that proves an algorithm’s correctness.\n\n## What is the difference between Kruskal and Prim algorithm?\n\nLike Kruskal’s algorithm, Prim’s algorithm is also a Greedy algorithm. It starts with an empty spanning tree. The idea is to maintain two sets of vertices….Difference between Prim’s and Kruskal’s algorithm for MST.\n\nPrim’s Algorithm Kruskal’s Algorithm\nPrim’s algorithm runs faster in dense graphs. Kruskal’s algorithm runs faster in sparse graphs.\n\n### What is the difference between Kruskal and Bellman-Ford algorithm?\n\nDijkstra’s algorithm is very similar to Prim’s algorithm for minimum spanning tree….What are the differences between Bellman Ford’s and Dijkstra’s algorithms?\n\nBellman Ford’s Algorithm Dijkstra’s Algorithm\nIt can easily be implemented in a distributed way. It can not be implemented easily in a distributed way.\nPosted in Blog" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.911111,"math_prob":0.98292345,"size":3913,"snap":"2023-40-2023-50","text_gpt3_token_len":796,"char_repetition_ratio":0.18828344,"word_repetition_ratio":0.0752,"special_character_ratio":0.19320215,"punctuation_ratio":0.08737864,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99658084,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-09T20:47:53Z\",\"WARC-Record-ID\":\"<urn:uuid:d5460f23-ae82-4b89-8ebe-16952925de47>\",\"Content-Length\":\"60072\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:995a01e6-95db-4db4-90d6-c7af3b711142>\",\"WARC-Concurrent-To\":\"<urn:uuid:baea9b7e-28cc-4197-8325-a6978c86f81d>\",\"WARC-IP-Address\":\"104.21.85.71\",\"WARC-Target-URI\":\"https://ecce216.com/blog/how-do-you-prove-the-correctness-of-an-algorithm/\",\"WARC-Payload-Digest\":\"sha1:FUKHIC7WM4OO32D4CWDCPYYJ7UAJSXL2\",\"WARC-Block-Digest\":\"sha1:E732W3C5SATLATRHRB5PT5BXJI5GV4FV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100972.58_warc_CC-MAIN-20231209202131-20231209232131-00342.warc.gz\"}"}
https://www.scirp.org/journal/paperinformation.aspx?paperid=79296	[ "On the Emergence, Development and Prospect of Financial Mathematics\nXiaogang Yang\n\nAbstract\n\nSince its emergence in 1980s, financial mathematics has developed into an interdisciplinary subject with independent theoretical system. On the one hand, financial mathematics has become the key technology that can be seen everywhere in finance. On the other hand, the development of Finance provides an important platform for the application of mathematics. The purpose of this paper is to analyze and summarize the emergence and development of financial mathematics, and to analyze the future of financial mathematics.\n\nKeywords\n\nShare and Cite:\n\nYang, X. (2017) On the Emergence, Development and Prospect of Financial Mathematics. Modern Economy, 8, 1129-1134. doi: 10.4236/me.2017.89078.\n\n1. The Emergence of Financial Mathematics\n\nFinancial mathematics was an interdisciplinary subject of mathematics and finance in the 1980s. It is the study of financial market risk assets, and its purpose is to use effective mathematical tools to reveal the essential features of finance, so as to achieve the optimal strategy for a potential risk of contingent claim pricing and risk averse. Its history can be traced back to 1900, the French mathematician Basch Lee E’s doctoral dissertation, “speculative theory”. In this paper, for the first time using Brown Bachelier motion to describe the stock price changes, this was the finance development, especially lays a theoretical foundation for the modern option pricing theory. However, his work has not received much attention from the financial mathematics community. Until 1952, Markowitz’s doctoral dissertation “portfolio selection” proposed mean-variance model, the establishment of portfolio theory, and a mathematical theory of finance. Based on Markowitz work, 1973 Black and Scholes got famous option pricing formula, and won the 1997 Nobel prize in economics study. It provides a satisfactory answer to an important practical problem, namely, to seek fair prices for European call options. The latter two discoveries promoted the development of mathematical research to finance, and gradually formed a new cross subject, financial mathematics .\n\nFinancial mathematics is a frontier subject of mathematics and finance that has developed rapidly on the basis of the two Wall Street revolution. The core of the study is to study the optimal portfolio selection theory and asset pricing theory in the uncertain stochastic environment. Arbitrage, optimization and equilibrium are the basic economic ideas and three basic concepts of financial mathematics. Internationally, this subject has been developed for more than 50 years. Especially in recent years, many experts in the field of financial mathematics have been able to prove, simulate and perfect it in the efforts of many experts and scholars. The rapid development of financial mathematics has led to the rapid innovation of financial products in modern financial markets, making the scope and level of financial transactions more abundant and diverse. This new discipline also has close relationship with China’s financial reform and development, and its development prospects in China are limitless.\n\n2. The Development of Financial Mathematics\n\nAs early as in 1990, French mathematician Bacheri described the stock as Brown’s movement in his doctoral thesis “speculative theory”. This is also the first rigorous mathematical description of the Brown movement. This theory lays the foundation for the future development of financial mathematics, especially the establishment of option theory. But this work has not attracted the attention of the financial mathematics for a long time. The name of the subject of financial mathematics didn’t appear until the late 1980s. It is the portfolio theory mark position (H. Kowitz 1990 Nobel prize in Economics) option pricing theory and Scholes-Merton (M. Scholes-R. Merton. 1997 won the Nobel Prize in Economics), the direct result of the two revolution of Wall Street. International calls it mathematical finance .\n\nFinancial mathematics originated in the early twentieth Century by French mathematician Basch Lee E in his doctoral thesis, the principle of speculation, depicting Brown’s movements in stock prices. Although 1905 Einstein also did the study, but this new approach was not able to attract more people’s attention, until 1950, Seoul by SA Liao statistician Savage finally found the great significance of this practice, and began to do comprehensive research on financial mathematics, financial mathematics which finally ushered in the development of the heyday modern finance which officially opened the curtain.\n\nModern financial mathematics grew up in the context of the two Wall Street revolution. The achievements of the first revolution are embodied in the study of the theory of static portfolio theory. In 1952 Marco Chavez presented portfolio mean variance model based on the theory of the investment risk and return the quantitative characterization, which pioneered the use of mathematical methods to study the financial problems of precedent. His model, however, calculates the covariance of the prices of each risky asset, which is very large. The second Wall Street revolution evolved from a static decision to a dynamic one. In 1970 the collapse of the Bretton Woods Agreement, the floating exchange rate instead of a fixed exchange rate, many financial derivatives such as options, futures are randomly generated, the introduction of these financial derivatives are mainly for financial risk management, and to make scientific and effective risk on the tube on the need for scientific pricing of derivatives. Brown makes a motion model of Bachelier twins: the birth of financial engineering option pricing mathematics stochastic process with continuous time and continuous time. The introduction of mathematical tools is mainly for financial risk management, and to make scientific and effective risk on the tube on the need for scientific pricing of derivatives. Shortly thereafter, Merton used another rigorous mathematical approach to derive the pricing formula and to extend it. The option pricing formula has brought unprecedented convenience to financial traders and bankers in the transaction of financial derivatives, and the rapid development of options trading has quickly become the main content of the world financial market. The theory of Black, Hughes and Morton has become a milestone in modern financial economics, and is still an important source of modern financial theory .\n\n3. The Future of Financial Mathematics\n\nWith the further development and perfection of financial market, people find complete information of all the previous research on the financial model assumed that investors can get the market, but investors can only depict the observed system state price process itself, the drift coefficient of Brown motion and dynamic assets can not be observed, that investors can only get some market information. Therefore, many scholars have systematically studied the investment and consumption problems based on incomplete information using various mathematical methods, and have made some progress.\n\nThe introduction of saddle theory is the latest research achievement of modern financial theory. In 1977, Harrison (Harrison J. M.) and Corey Poos (Kreps S. R.) proposed the martingale method of option pricing theory, they use martingale measure concept in martingale theory characterizing no arbitrage and incomplete markets, and use the equivalent martingale measure on option pricing and hedging or hedge. Saddle method advocated by Karatza. S and Shreve, directly to the saddle theory into modern financial theory, the pricing problem of using the concept of equivalent martingale measure of derivative securities, the result can not only reveal the operation of the financial market, but also can provide a set of effective algorithms, pricing and risk management of complex problem solving financial derivative products.\n\nAnother function of the saddle theory in the study of financial theory is that it can solve the problem of the pricing of derivative securities when the financial market is incomplete, so that the modern financial theory has made a breakthrough progress”. At present, the derivative securities pricing theory based on saddle method is dominant in modern financial theory, but it is still a blank in our country.\n\n3.2. Intelligent Optimization\n\nThe intelligent optimization method (genetic algorithm, simulated annealing algorithm, artificial neural network and wavelet analysis) and combine traditional methods, applied to the risk control and investment decision problem is another has more broad research areas, provides a wide range of research topics for us. The international research on this aspect has made preliminary achievements, and there are a large number of scholars in China devoted to this research. Due to the development of this field is relatively late, there are many problems have not been solved yet, but we still believe that the financial experts, mathematicians and artificial intelligence experts to work together in this emerging field of study will be able to achieve a breakthrough.\n\n3.3. Differential Game Theory\n\nThe application of differential game method to the option pricing problem and the investment decision problem is another important aspect of the development of modern financial theory, and some achievements have been made. When the financial market does not satisfy the steady-state assumption or abnormal fluctuations in stock prices, often do not obey the geometry Brown motion, then using the method of random dynamic model of securities investment decision problems both in theory, or in fact there is deviation from. Using the differential game method to study the financial decision problem can relax the hypothesis. The uncertainty disturbance is assumed to be a hostile one, and the optimal investment strategy with strong robustness can be obtained by optimizing the worst case. In addition, the Behrman equation for differential games is a first-order partial differential equation, which is much simpler than the two order partial differential equations for stochastic control problems. Therefore, the application of differential game method to the study of financial problems has broad application prospects.\n\n3.4. Stochastic Optimal Control Theory\n\nAn important application field of financial theory is to solve the stochastic problem of continuous time, and the important means to solve this problem is stochastic optimal control theory. Stochastic optimal control was developed in the late 1960s and early 70s. Mathematicians applied the Behrman optimization principle and developed new mathematical research fields using measurement theory and functional analysis. 1971 Merton (Merton) using continuous time methods and discuss the consumption portfolio problem, Brock (Brock) and Millman (Mirman) used in the discrete time case method to solve the problem of uncertain optimal economic growth. So far, the stochastic optimal control method has been applied to most financial fields and has broad prospects for development.\n\n3.5. Optimal Stopping Time Theory\n\nThe theory of optimal stopping time is a very practical field in the system of probability theory. In recent years, many financial mathematicians combine this theory with modern portfolio theory, and have achieved good results. However, the research literature in this field is still not much, and the field is still in its infancy. Based on the optimal stopping theory, Moton A and Pliska S R studied the investment decision problem with fixed transaction costs, and gave a simplified algorithm for the investment decision making problem with two risk securities. In China, the research on this aspect is still rare. It is believed that the application of the optimal stopping theory to the study of investment decision problems and risk minimization problems will lead to greater progress.\n\n3.6. The Market Price Fluctuations\n\nThe so-called price volatility, usually refers to the future price deviation from the expected value of the possibility. In financial economics, volatility is measured by standard deviations of returns, not by standard deviations of prices. For example, in the “B S model” and most of its generalizations, it is unreasonable to assume that the volatility of stock prices is constant. In order to more accurately describe the stock price change rules, must consider the following factors: the stock price volatility of stock price volatility and dependence; other random variables depend on the stock price may jump suddenly. Stochastic volatility models can reflect some of these factors, and are now highly valued. Such models assume that volatility obeys a stochastic process, such as geometric Brown motion.\n\n3.7. The Term Structure of Interest Rates\n\nIn the B-S model, interest rates are given constants. In fact, the changes in interest rates are quite complex. The laws of interest rates vary in different properties and maturities, which is the term structure of interest rates. It can usually be expressed in the form of yield curves. The term structure of interest rate includes three theories: market expectation theory, market segmentation theory and investment preference theory, and liquidity preference theory. These theories explain the irregular changes in interest rates from different angles. In recent years, interest rate risk has become increasingly prominent, interest rate options and other interest rate derivative securities have been developed rapidly, and the mathematical model of the term structure of interest rates has been put forward.\n\n3.8. Emergency Issues\n\nUnexpected events can not be ignored in the financial field, such as the financial crisis in Southeast Asia in 1997, which has caused great losses to some countries. The prediction theory based on the traditional stationary random process is not applicable at all. Traditional theories may explain how the market took place in 95% of the time. However, if people admit that emergencies occur in the remaining 5% of the time, then the picture described by the traditional theory does not reflect the actual situation. Now we apply chaos theory and fractal theory to explain how the stock price soared and plummeted. The early warning of financial emergencies is often difficult because it involves many factors, quantification and alarm sensitivity, which is also an important field of financial mathematics research.\n\n3.9. American Option Problem\n\nMost of the options traded in the market are American options. The problem of Pricing American options is much more difficult than that of European options. Because American options can be executed at any time before maturity, this involves the optimal execution time of the expiration rights. In general, the optimal execution time of options is a very complicated problem and has not been well solved so far. If the method of partial differential equation is used to discuss the pricing of American options, the problem of the corresponding partial differential equation will become a “free boundary” problem, which is difficult to deal with mathematically. In general, no accurate analytical pricing formula of American option, and can only use numerical solution or approximate analytic solution, therefore, it has important practical significance of numerical methods for American options pricing development .\n\n4. Epilogue\n\nFinancial mathematics is a new frontier subject which studies the law of financial operation by means of mathematical theories and methods. The core problem is portfolio selection and asset pricing theory under uncertain multiple periods. Arbitrage, optimality and equilibrium are three main concepts. The latest research results of financial mathematics are stochastic optimal control theory, saddle theory, differential game theory, optimal stopping time theory and intelligent optimization. The current problems and prospects of financial mathematics are mainly about American option, Asian option, interest rate structure, market price fluctuation and unexpected events.\n\nConflicts of Interest\n\nThe authors declare no conflicts of interest.\n\n Zhang, Y. (2010) The Application of Economic Mathematics. Journal of Liaoning Teachers College (NATURAL SCIENCE EDITION), 19, 68-70. Xue, J.J. and Qiao, L.F. (2011) Current Situation and Development of Financial Mathematics. Journal of Daqing Normal University, 31, 80-83. Sun, Z.Q. and Liu, X.H. (2010) An Overview of Financial Mathematics and Its Prospect. Journal of Chongqing Academy of Arts and Sciences (NATURAL SCIENCE EDITION), 29, 24. Guo, C. (2011) A Review of Recent Advances in Financial Mathematics. 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https://calculator.name/multiplying-fractions/24over2/14over8	[ "# 24/2 times 14/8 as a fraction\n\nWhat is 24/2 times 14/8 as a fraction? 24/2 times 14/8 is equal to 21\n\nHere we will show you how to multiply 24/2 times 14/8 written in maths equation as 24/2 * 14/8, or 24/2 × 14/8, answer in fraction and decimal form with step by step detailed solution.\n\n• 21\n\nTo multiply 24/2 times 14/8, follow these steps:\n\nTo multiply fractions, simply multiply the top numbers together (numerators) and then multiply the bottom numbers together (denominators).\n\n= 24 * 14/2 * 8 = 336/16\n\nSimplify\n\n= 336/16 = 21\n\nMore Examples" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8420771,"math_prob":0.9978907,"size":489,"snap":"2023-14-2023-23","text_gpt3_token_len":156,"char_repetition_ratio":0.17319588,"word_repetition_ratio":0.0,"special_character_ratio":0.3640082,"punctuation_ratio":0.07692308,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9992586,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-23T18:28:21Z\",\"WARC-Record-ID\":\"<urn:uuid:a449ad48-0060-461d-a336-cd378f553e79>\",\"Content-Length\":\"130369\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6f06fe7a-f70f-4945-bda4-aae246b81302>\",\"WARC-Concurrent-To\":\"<urn:uuid:95d9d18d-93e2-451e-81c6-66dc9dfff9ea>\",\"WARC-IP-Address\":\"68.178.146.134\",\"WARC-Target-URI\":\"https://calculator.name/multiplying-fractions/24over2/14over8\",\"WARC-Payload-Digest\":\"sha1:PD2EQK57QLCZNVAJMMGLOYWZF76QRLQ4\",\"WARC-Block-Digest\":\"sha1:SBLE7YK3JS4DAQB5HL4KPZB6RVIF5BS3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296945182.12_warc_CC-MAIN-20230323163125-20230323193125-00729.warc.gz\"}"}
http://www.mrithescienceguy.com/2015/11/math-10c-week-12-math-10-qujiz-function.html	[ "## Monday, November 23, 2015\n\n### Math 10C: Week 12 - Math 10 Quiz, Function Notation & Intercepts\n\n This week we are: Working on our understanding of function notation and intercepts I will: express functions as an equation I will: determine values for functions using the equation I will: define values as intercepts on function graphs I can: calculate values for function equations I can: differentiate between known values such as f(3) vs f(x)=3 I can: label and define both x and y intercepts\n\nMonday\n\n1. Today we will be having a quiz on functions/relations and range/domain\n2. If done on time, we will start Tuesdays Lesson Early\n\nTuesday\n\n1. We will go over Function notation and equations in the the from of slope-intercept\n2. Have students work on handouts for function notation.\n\nWednesday\n\n1. Formative assessment 4.3 on Function notation\n2. Go over x-y intercepts on a graph\n3. Have students work in workbook and handouts for intercpts\n\nThursday\n1. Formative assessment 4.4 on X-Y intercpets\n2. Handout Review Assignment\n3. Students can work on review assignment.\n\nFriday\n\n1. We will look at kahoot as a review for the test on monday.\n2. When done, students can work on review assignment." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8963126,"math_prob":0.91602904,"size":1453,"snap":"2021-43-2021-49","text_gpt3_token_len":342,"char_repetition_ratio":0.13043478,"word_repetition_ratio":0.008097166,"special_character_ratio":0.22023399,"punctuation_ratio":0.10996564,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9775073,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-18T16:56:19Z\",\"WARC-Record-ID\":\"<urn:uuid:7e1eef92-1b84-4811-858a-1db2431131f0>\",\"Content-Length\":\"137859\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:884ba671-ead2-469c-a92d-33d7977093e5>\",\"WARC-Concurrent-To\":\"<urn:uuid:291fd16d-5230-4628-86a6-ec299fdcdeb1>\",\"WARC-IP-Address\":\"172.217.15.115\",\"WARC-Target-URI\":\"http://www.mrithescienceguy.com/2015/11/math-10c-week-12-math-10-qujiz-function.html\",\"WARC-Payload-Digest\":\"sha1:XFD3RD3DKDKOD3S6U5DLW3HMZKKFNQ3V\",\"WARC-Block-Digest\":\"sha1:NCZ3BKHJZZNWGJTT36WDXR633OEN6R7O\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585204.68_warc_CC-MAIN-20211018155442-20211018185442-00243.warc.gz\"}"}
https://pandascore.co/blog/cs-go-round-modeling	[ "", null, "Sep 16, 2022\n\nCS:GO Round Modeling\n\n### Background\n\nPandascore is the world’s AI-powered hub of esports data, whose odds feed is the main product serving the esports betting industry.\n\nWe use artificial intelligence to process and model more than 300 data points per second to empower our dedicated esports traders with the most up to date information in real-time.\n\nFirst-person shooter Counter-Strike: Global Offensive (CS:GO) is one of the big 3 esports titles for Western audiences, along with MOBAs League of Legends and Dota 2. When it comes to esports betting, CS:GO is far and away the most popular for punters. The biggest tournaments in the world regularly draw in betting turnover in the tens of millions of euros.\n\nMapping and modeling professional Counter-Strike as accurately as possible is essential to providing the best statistics and odds available on the market.\n\n### CS:GO Rules\n\nCounter-Strike has been an esports staple for over 20 years, with established tournaments featuring teams from every corner of the globe competing year-round and a growing Players’ Association to boot. The game itself boasts almost 35 million players and roughly 53m hours watched on Twitch every month.\n\nTo break the game down in simple terms:\n\n• 2 teams of 5 players face each other in a 30 round matchup\n• Each round is 1 minute and 55 seconds, with either team having specific win conditions\n• For the T-side, they can win a round by either eliminating every member of the opposing team OR by planting a bomb in a designated zone, which will detonate after 40 seconds\n• For the CT-side, they can win a round by eliminating all members of the T-side, or defusing the bomb after it has been planted\n• After playing 15 rounds, the two teams will switch sides from T-side to CT-side and vice versa\n• The first side to win 16 rounds wins the match\n\nThere is also overtime to account for:\n\n• A team must win by 2 rounds, otherwise the game will go into overtime after the 30 rounds are completed\n• In overtime, the two teams will need to win in a best-of-6 rounds format. If the teams are tied at the end of overtime, another round of overtime will start until there is a victor\n\nIn the competitive scene, teams will compete over multiple matches and maps in a best-of-3 or best-of-5 series. As you can imagine, there is a ton of data to process in any CS:GO esports match.\n\n### The problem\n\nWe need to have access to a lot of predictions (called markets in the betting industry) regarding CS:GO matches such as:\n\n• Who is going to win the match?\n• Who is going to have 10 rounds first?\n• What will be the round difference at the end of the match?\n• How many rounds will be played in the match?\n\nIt is not possible to have one model per prediction since it could potentially lead to contradictory predictions easily exploitable by bettors. We need to model the round dynamic of CS:GO all at once. This means that we need to have access to probabilities to reach any given intermediate and final round score.\n\nSince our model will run also during live for in-play betting, the model also needs to be able to infer predictions fast — typically a few dozens of milliseconds. This motivated us to try analytical-based solutions for inference instead of simulation-based ones.\n\n### The approach\n\nFor the model we are describing in this blog post, we are going to make the following assumption:\n\n• The probability for a team to win a round only depends on the outcome of the previous round\n\nAnyone knowing a bit about the game CS:GO could argue that this assumption is too naïve for the problem we are trying to solve. Indeed, it is commonly accepted that the best feature in CS:GO to predict the outcome of the coming round in live is the economy which has its own round dynamic. However, we found it interesting to check how a simple model like the one we are going to present would perform.\n\n### Binomial distribution with Markov states\n\nA 2 states Markov Chain Binomial (MB in this post) can be seen as an extension of a binomial distribution in which the probability for the nth trial to be a success or a failure depends on the outcome of the previous trial.\n\nLet’s walk through the equations while keeping in mind CS:GO.\n\nMore formally, we can define:\n\n• The probability for team A to win (j=1) or lose (j=0) the round m+1 round given they won (i=1) or lost (i=0) round m\n• Alongside a transition matrix P representation\n\nFollowing this paper, we can rewrite P\n\n• p being the probability of success of the first trial (first pistol round in CS:GO)\n• q = 1-p being the probability of failure of the first trial\n• delta can be interpreted as the first-order autocorrelation between 2 rounds\n\nThe details to go from the first matrix to the second one is well explained in the paper mentioned above.\n\nThe nth transition probability matrix is then equal to:\n\nOnly 2 parameters need to be estimated to fit such model to some data: p and delta.\n\nAgain following the paper, the likelihood of a sequence of trials parametrized by N1, N0 and Nij (i,j = 0\|1) following a MB model can be expressed as:\n\nN1 is a boolean equal to 1 if the first round was won by team A.\n\nN0 is a boolean equal to 1 if the first round was lost team A.\n\nNij denotes the total number of transitions from state i to state j within the sequence.\n\nLet’s change the notations from the paper for the application to CS:GO. We will call i the outcome of the first round, j the outcome of the last round, n the number of rounds, k the number of rounds won, l the number of pairs of successive round wins.\n\nWe then have the following equalities:\n\n• N1 + N01 is equal to the number of “individual successes”:\n• N0 + N10 is equal to the number of “individual failures”:\n• N11 is equal to the number of pairs of consecutive successes:\n• N00 is equal to the number of pairs consecutive failures:\n• N01 + N10 is the number of times the state (win, lose) has changed in the sequence:\n\nWe won’t take a detailed dive into the calculus that leads to the above equations, but you can easily check that they are correct on the specific example shown below!\n\nThe probability to observe a path with n rounds, k wins, l pairs of consecutive wins given that the first pistol round is i and the last round is j, under an MB model parametrized with p and delta can now be written as:\n\ni, j, n, k, l together define a sequence pattern, and we therefore consider all sequences that have the same structure equal in terms of probabilities. To compute the probability of having a given sequence pattern, we have to multiply the likelihood of a certain pattern to occur with the number of possible patterns, given by Ѱ.\n\nFollowing Lemma 2 of Rudolfer (1990) “A Markov chain model of extrabinomial variation”.\n\nThe picture above shows one counting example of the sequence patterns of a MB model.\n\nWe can then write the probability for team A to reach k rounds in n rounds, with l pairs of consecutive rounds given than the outcome of the first round is i and the last is j:\n\nTo get the probability of team A to win, we just need to marginalise over n, l and i. Indeed, if team A wins, they will win the last round so j = 1. However there is something we have not considered at all for now which is the half time.\n\nIndeed, in a CS:GO game, after round 15, both teams switch sides (T-side becomes CT-side and vice-versa) and the outcome of the 16th round (second pistol round) can be considered as independent from what happened before.\n\nThis brings us to model a CS:GO game as follows:\n\n• The first half (from round 1 to 15) should be modeled with a fixed-n Markov Binomial distribution (a fixed number of trials is run, in our case 15)\n• The second half (after round 15) should be modeled with a Negative Markov Binomial (some trials are run until there is a winner, 16 rounds if no overtime)\n\nFollowing what we have said in the previous section we have:\n\n• The probability to have k successes in n trials for a sequence modeled with a Markov Binomial distribution can be written as:\n• The probability to reach k successes and r failures, the last trial being a success\n\nWe are almost there!\n\nImagine you are watching a game of CS:GO and the score at the half of the game is 8–7. Then the probability for team A to win 16–14 at the end of the game (8 successes and 7 failures in the second half) is:\n\nWithout any assumption on the first half (prematch setup), we can still compute the probability for team A to win the game 16–14 by just marginalizing on all possible scores for the first half:\n\nFinally:\n\n• the probability for team A to win the game without overtime is:\n• the probability to go to overtime is:\n• the probability for team B to win the game without overtime is:\n\nAnd this is it! We manage to have a closed-form expression that models the round dynamic in CS:GO.\n\nN.B. It’s possible to model the overtimes with the same idea since they are just a sequence of 6 rounds maximum with a “first to 4” rule.\n\n### How to use such a model?\n\nFirst, the delta parameter can be found easily from the data we collect at PandaScore. The other parameter p (probability to win the pistol rounds) can be found using a machine learning model or with the help of humans.\n\nSecondly, it’s also possible to work the other way around. We can for instance have another model estimating the probability for team A to win the game, and then infer p using some optimisation algorithms.\n\n### Experiments\n\nWe have fixed delta to 0.35 which appeared to work well. Let’s take as example 2 scenarios.\n\n1. Team A has a 50% of chance to win the game and we deduce p from that\n\nThe first plot below shows the probability for every possible in-play round score to be reached. The anti-diagonals sum to 1 since they gather all possible scores for a given fixed number of rounds played. Since both teams have the same chance to win, the plot is symmetrical and the biggest probabilities stand near the diagonal.\n\nThe second plot below shows the probabilities on all end scores. Since both teams are equal, the highest probabilities are on scores ranging from 16–14 to 16–10.\n\n2. Team A has only 5% of chance to win the game and we deduce p from that\n\nThe plots below are the same as described above. But obviously the matrices are not symmetrical anymore!\n\n### Limitations\n\nObviously the assumption made with this model is too strong. While the model proposed has its advantages (fast to compute with analytic solutions, easy to interpret, good estimates of the round distribution), it has shown some limitations e.g.\n\n• Overestimation of close games for teams of similar strengths\n• Underestimation of stomps for teams of similar strengths\n• Fine grained dynamics are averaged\n\nThe plot above shows for teams of the same level, difference in % between empirical distribution (historical data) and our Markov Binomial model (Old model)\n\nMany aspects of CS:GO round dynamic were not taken into account in this attempt. To mention just a few of them:\n\n• Momentum\n• “Eco rounds”\n• Catchup mechanisms\n• Map\n• Pistol rounds\n\nThis led us to go for a more complex model for production which captures better these mechanisms.\n\n### Conclusion\n\nWhen we model some esports at PandaScore, we always try to evaluate simple solutions first and then iterate from this baseline. Markov Binomial models is not a common distribution — we did not know about it before working on CS:GO! — but has proven to be a good first approximation of the round dynamic of the game." ]	[ null, "https://px.ads.linkedin.com/collect/", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9426193,"math_prob":0.9576142,"size":11313,"snap":"2023-40-2023-50","text_gpt3_token_len":2538,"char_repetition_ratio":0.14183393,"word_repetition_ratio":0.052093476,"special_character_ratio":0.22133829,"punctuation_ratio":0.07890071,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98045915,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-28T07:21:27Z\",\"WARC-Record-ID\":\"<urn:uuid:c8192e34-5d2f-41d6-b2b7-ca7fc784738c>\",\"Content-Length\":\"41640\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a5bc73be-42ab-4470-8d8a-cbf3caa53be9>\",\"WARC-Concurrent-To\":\"<urn:uuid:88d944ed-c594-4ed0-b48c-c7ca5c43d7b2>\",\"WARC-IP-Address\":\"34.79.38.35\",\"WARC-Target-URI\":\"https://pandascore.co/blog/cs-go-round-modeling\",\"WARC-Payload-Digest\":\"sha1:2NNTMM7Y3P72LKA4BGC5DDEKX3ZGLSUT\",\"WARC-Block-Digest\":\"sha1:2PZH5LLX634GXMRWE2LLIAVYGMPA7Y4R\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510368.33_warc_CC-MAIN-20230928063033-20230928093033-00076.warc.gz\"}"}
https://idsoftwaredownload.com/binary/formula-options-in-excel/	[ "# Change formula recalculation, iteration, or precision in Excel", null, "## Formula options in excel\n\nmy input looks like this, in K i would like to see OJ6, when D is OJ and F is 6668. the first part of the nested commands works fine.\nD F K\nOJDS56 6668 OJ6\nSSDSC6 CX\n\n## IF Function with 3 Conditions - ExcelDemy \| Free Excel\n\n=if(and(A6=\"Y\",B6=\"N\",C6=\"N\"),\"AA\",if(and(A6=\"N\",B6=\"N\",C6=\"Y\"),\"BB\",if(and(A6=\"Y\",B6=\"N\",C6=\"Y\"),\"CC\",if(and(A6=\"N\",B6=\"Y\",C6=\"N\"),\"DD\",if(and(A6=\"Y\",B6=\"Y\",C6=\"N\"),\"EE\",if(and(A6=\"Y\",B6=\"Y\",C6=\"Y\"),\"FF\",if(and(A6=\"N\",B6=\"Y\",C6=\"Y\"),\"GG\",if(and(A6=\"N\",B6=\"N\",C6=\"N\"),\"HH\",\"\"))))))))\n\n### How to Use AutoFill in Excel? \| Top 5 Methods (with Examples)\n\nThere is a problem, though. Transpose is a one-time snapshot of the data. What if you have formulas in the horizontal data? Is there a way to transpose with a formula?\n\n#### IF AND in Excel: nested formula, multiple statements, and more\n\nTo recalculate all dependent formulas — except data tables — every time you make a change to a value, formula, or name, in the Calculation options section, under Workbook Calculation , click Automatic except for data tables.\n\nHave you ever seen a dollar sign in an Excel formula? When used in a formula, it isn't representing an American dollar instead, it makes sure that the exact column and row are held the same even if you copy the same formula in adjacent rows.\n\n8) Press CTRL-ENTER to get the formula to deliver the route needed, given the conditions in Cell B5 and C5 that the formula is using for evaluation. We see that if the patient has HIV/AIDS and the opportunistic infection Tuberculosis , this patient must first go to Ward One and then to the respiratory department of the hospital. The formula has, therefore, delivered the correct result.\n\nTo get started, highlight the group of cells you want to use conditional formatting on. Then, choose \"Conditional Formatting\" from the Home menu and select your logic from the dropdown. (You can also create your own rule if you want something different.) A window will pop up that prompts you to provide more information about your formatting rule. Select \"OK\" when you're done, and you should see your results automatically appear.\n\nDon’t waste time repeating the same formatting commands over and over again. Use the format painter to easily copy the formatting from one area of the worksheet to another. To do so, choose the cell you’d like to replicate, then select the format painter option (paintbrush icon) from the top toolbar.\n\nAs you play around with your data, you might find you're constantly needing to add more rows and columns. Sometimes, you may even need to add hundreds of rows. Doing this one-by-one would be super tedious. Luckily, there's always an easier way.\n\n=IF(D5=\"NEXT QUESTION\",\"\",IF(AND(B8=\"linux/Unix\",D5=\"Run the following network scan:\"),\"nmap -A \",\"6..755 \| % {echo ''.\\$_'' ping -n 6 -w 655 .\\$_} \| Select-String ttl\"))\n\nSometimes you may have a list of data that has no organization whatsoever. Maybe you exported a list of your marketing contacts or blog posts. Whatever the case may be, Excel’s sort feature will help you alphabetize any list.\n\nIn Excel for the web, a formula result is automatically recalculated when you change data in cells that are used in that formula. You can turn this automatic recalculation off and calculate formula results manually. Here's how to do it:\n\nWhen a formula performs calculations, Excel usually uses the values stored in cells referenced by the formula. For example, if two cells each contain the value and the cells are formatted to display values in currency format, the value \\$ is displayed in each cell. If you add the two cells together, the result is \\$ because Excel adds the stored values and , not the displayed values.\n\nTo make the formula more flexible, you can input the target customer name and amount in two separate cells and refer to those cells. Just remember to lock the cell references with \\$ sign (\\$G\\$6 and \\$G\\$7 in our case) so they won't change when you copy the formula to other rows:" ]	[ null, "http://www.asap-utilities.com/screenshots/tools/en_us/0041.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86548835,"math_prob":0.91728437,"size":4138,"snap":"2020-34-2020-40","text_gpt3_token_len":1018,"char_repetition_ratio":0.1301403,"word_repetition_ratio":0.05970149,"special_character_ratio":0.25495407,"punctuation_ratio":0.13325608,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99201363,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-24T02:07:54Z\",\"WARC-Record-ID\":\"<urn:uuid:b08a22a6-132d-4986-a750-2aaf2e1b0274>\",\"Content-Length\":\"21552\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b2b55b60-bff0-41e6-a225-67341a07a00a>\",\"WARC-Concurrent-To\":\"<urn:uuid:da90d17e-9df0-4fda-999d-fe2913753186>\",\"WARC-IP-Address\":\"104.27.137.85\",\"WARC-Target-URI\":\"https://idsoftwaredownload.com/binary/formula-options-in-excel/\",\"WARC-Payload-Digest\":\"sha1:AULL5S4A76L6SEOEVVPNTC5BSPBLIQWP\",\"WARC-Block-Digest\":\"sha1:TZQVLWBNHLHNJJQPEBIRZKMWD6GDLXHR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400213006.47_warc_CC-MAIN-20200924002749-20200924032749-00414.warc.gz\"}"}
https://stats.stackexchange.com/questions/89538/transformations-of-variables/89539	[ "Transformations of Variables\n\nSuppose that you are have a response variable $Y$ and explanatory variables $X_1$, $X_2$ and $X_3$. If we want to use a quadratic transformation for $X_1$, would we still include $X_1$? In other words, would we have:\n\n$$E[Y\|X] = \\beta_0+\\beta_{1}X_{1}^{2} + \\beta_{2}X_{2} + \\beta_{3}X_{3}$$ or $$E[Y\|X] = \\beta_0+\\beta_{1}X_{1} + \\beta_{2}X_{1}^{2} + \\beta_{3}X_{2}+\\beta_{4}X_{3}$$\n\nIf instead we did a logarithmic transformation, then would it just be:\n\n$$E[Y\|X] = \\beta_0+\\beta_{1} \\log(X_1) + \\beta_{2}X_{2} + \\beta_{3}X_{3}$$\n\n• NB the first model imposes a constraint that the minimum or maximum of $Y$ plotted against $X_1$ occurs at exactly $X_1=0$. You'll want to be sure that's sensible. It often isn't, & therefore the first model is ruled out a priori. Mar 11 '14 at 9:50\n\nEither model could work, and which to use depends on why you transformed. If you took the log because $Y$ is expected to be linearly related to $\\log X_1$ (e.g. response to log dose of medication), then you would probably just go with $\\log X_1$ and drop the untransformed term. On the other hand if you added a quadratic term because it looked like $Y$ was related to $X_1$ in a polynomial fashion (e.g. crop yield vs latitude) you would probably try keeping both $X_1$ and $X_1^2$ and then drop one (or both) if it turned out to not be significant." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8083258,"math_prob":0.99976975,"size":528,"snap":"2022-05-2022-21","text_gpt3_token_len":220,"char_repetition_ratio":0.1870229,"word_repetition_ratio":0.0,"special_character_ratio":0.46022728,"punctuation_ratio":0.071428575,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99993956,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-27T17:59:19Z\",\"WARC-Record-ID\":\"<urn:uuid:f6958ae2-820f-464f-819a-2bb203647a4f>\",\"Content-Length\":\"138957\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b44ca0d6-dc75-459f-838f-bb7457b1851d>\",\"WARC-Concurrent-To\":\"<urn:uuid:bbbec6e5-0bc3-4698-b92e-c009bee95e80>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://stats.stackexchange.com/questions/89538/transformations-of-variables/89539\",\"WARC-Payload-Digest\":\"sha1:PMO4SB6IHGTEH667TGD2W55CVPXJXKIZ\",\"WARC-Block-Digest\":\"sha1:3OHMR2DNWGCQ2IG7XG3IMKOIY245GR22\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320305277.88_warc_CC-MAIN-20220127163150-20220127193150-00679.warc.gz\"}"}
https://in.mathworks.com/help/map/ref/neworig.html	[ "# neworig\n\nOrient regular data grid to oblique aspect\n\n## Syntax\n\n```[Z,lat,lon] = neworig(Z0,R,origin) [Z,lat,lon] = neworig(Z0,R,origin,'forward') [Z,lat,lon] = neworig(Z0,R,origin,'inverse') ```\n\n## Description\n\n`[Z,lat,lon] = neworig(Z0,R,origin)` and ```[Z,lat,lon] = neworig(Z0,R,origin,'forward')``` will transform regular data grid `Z0` into an oblique aspect, while preserving the matrix storage format. In other words, the oblique map origin is not necessarily at (0,0) in the Greenwich coordinate frame. This allows operations to be performed on the matrix representing the oblique map. For example, azimuthal calculations for a point in a data grid become row and column operations if the data grid is transformed so that the north pole of the oblique map represents the desired point on the globe. Specify `R` as a `GeographicCellsReference` or `GeographicPostingsReference` object. The `RasterSize` property of `R` must be consistent with `size(Z)`.\n\n`[Z,lat,lon] = neworig(Z0,R,origin,'inverse')` transforms the regular data grid from the oblique frame to the Greenwich coordinate frame.\n\nThe `neworig` function transforms a regular data grid into a new matrix in an altered coordinate system. An analytical use of the new matrix can be realized in conjunction with the `newpole` function. If a selected point is made the north pole of the new system, then when a new matrix is created with `neworig`, each row of the new matrix is a constant distance from the selected point, and each column is a constant azimuth from that point.\n\n## Limitations\n\n`neworig` only supports data grids that cover the entire globe.\n\n## Examples\n\nLoad elevation raster data and a geographic cells reference object. Then, transform the map so that Sri Lanka is at the North Pole.\n\n```load topo60c origin = newpole(7,80); Z = neworig(topo60c,topo60cR,origin); axesm miller gridm on lat = linspace(-90,90,90); lon = linspace(-180,180,180); surfm(lat,lon,Z) demcmap(topo60c) tightmap```", null, "## Version History\n\nIntroduced before R2006a\n\nexpand all" ]	[ null, "https://in.mathworks.com/help/map/ref/neworigv2.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7562054,"math_prob":0.97992164,"size":3459,"snap":"2022-40-2023-06","text_gpt3_token_len":776,"char_repetition_ratio":0.17308249,"word_repetition_ratio":0.09034908,"special_character_ratio":0.1951431,"punctuation_ratio":0.1335505,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9596775,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-04T16:47:18Z\",\"WARC-Record-ID\":\"<urn:uuid:d4f0090a-4a73-44fe-ab4e-70a0ccc6d744>\",\"Content-Length\":\"77744\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1b84c73c-e918-49e6-992e-faea23cda6e9>\",\"WARC-Concurrent-To\":\"<urn:uuid:c3488724-8e5c-4a37-bb0f-a77ec5a21207>\",\"WARC-IP-Address\":\"23.218.145.211\",\"WARC-Target-URI\":\"https://in.mathworks.com/help/map/ref/neworig.html\",\"WARC-Payload-Digest\":\"sha1:GINJD2TQ7333L64DPHDEDT5FT7VUKLGY\",\"WARC-Block-Digest\":\"sha1:WJXCBGBQ33VQJAGEHGA7J6WJE6QLCMC2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337516.13_warc_CC-MAIN-20221004152839-20221004182839-00602.warc.gz\"}"}
https://quant.stackexchange.com/tags/mathematics/hot?filter=all	[ "# Tag Info\n\nA function $f : \\mathbb R^n\\backslash\\{0\\} →\\mathbb R$ is called (positive) homogeneous of degree $k$ if $$f(\\lambda \\mathbf x) = \\lambda^k f(\\mathbf x) \\,$$ for all $\\lambda > 0$. Here $k$ can be any complex number. The homogeneous functions are characterized by Euler's Homogeneous Function Theorem. Suppose that the function f : \\mathbb R^n \\... 13 I think he was jokingly suggesting to breed top PhD candidates in pure mathematics. I often heard complaints that a lot of PhDs in Mathematical disciplines lack a rigorous base in pure Mathematics. Obviously the hedge fund manager was not suggesting that the proof of the hypothesis will be in any way relevant to trading or financial pricing applications. On ... 12 Edit: Freddy's answer is good -- we wrote concurrently. He rightly points out that QF is a broad field, and that it is among other things a community. Here, I describe a practical, down-to-earth path for getting your feet wet in one key piece of it -- software and model development for derivatives analysis, starting with vanilla options. Your best bet ... 12 At the top of this list I still recommend you to seek employment in order to learn from others in QF space. Could you possible work in a quant team within an investment bank where you currently reside? Start to reach out to the quant finance community so you are connected once you decide to locate to where you can practice this discipline.reach out to alumni,... 12 I think there are a lot of different ways to specify this problem. For simplicity, consider independent Garch processes $$r_{1,t} \\sim N\\left(0,\\sigma_{1,t}^{2}\\right)$$ $$\\sigma_{1,t}^{2} = \\beta_{1,1}+\\beta_{1,2}\\varepsilon_{1,t-1}^{2}+\\beta_{1,3}\\sigma_{1,t-1}^{2}$$ and $$r_{2,t} \\sim N\\left(0,\\sigma_{2,t}^{2}\\right)$$ $$\\sigma_{2,t}^{2} = \\beta_{... 11 My understanding is because the Ito's integration definition keeps the martingale property. With Brownian motion W(t, \\omega) defined, to define stochastic integration in a Riemann–Stieltjes style:$$\\int_0^t f(t, \\omega) d W(t, \\omega) = \\lim_{\\\| \\Delta_n\\\| \\to 0 } \\sum_{i=1}^{n} f(\\tau_i,\\omega) \\left ( W(t_i, \\omega) - W(t_{i-1}, \\omega) \\right ) , ... 9 In fact Ito and Stratonovich calculus are both mathematically equivalent. In the following paper you can e.g. see that both derivations lead to the same result, i.e. the Black-Scholes equation: Black-Scholes option pricing within Ito and Stratonovich conventions by J. Perello, J. M. Porra, M. Montero and J. Masoliver From the abstract: Options financial ... 8 I'd say to read Prof. Shreve's well-known two-volume textbook Stochastic Calculus for Finance I and II. 8 As Sanjay said, you can apply Itô's Lemma to f(t,x)=x^2 and obtain \\begin{align} \\mathrm{d} S^2_t=\\left(2\\mu S_t^2+\\sigma^2S_t^2\\right)\\mathrm{d}t+\\left(2\\sigma S_t^2\\right)\\mathrm{d}W_t. \\end{align} Thus, (S_t^2) is again a geometric Brownian motion and hence, for each time point t log-normally distributed with drift 2\\mu+\\sigma^2 and volatility ... 7 People seem to think that using ML is going to circumvent the process of actually learning to trade, it doesn't. ML can be used to refine trading ideas, but it doesn't generate them, you need to use your brain for that. 7 I think one of the best (and very current) articles about how to break into QF (for any kind of background) is: \"On becoming a Quant\" by Mark Joshi For your special background in mathematics see this excerpt from section 9: The main challenge for a pure mathematician is to be able to get one’s hands dirty and learning to be more focussed on getting ... 7 The other answers are useful and sensible. I have worked full time in equity research for nearly two decades, so very much a \"qualitative\" rather than a quantitative approach. However, all the firms for which I have worked had quants and because of my casual interest in the area I've spent a lot of time talking to quant teams over the years, often over a ... 7 At the first glance, what you are asking for is a model admitting arbitrage, so there is a zero chance of losing money and positive chance of yielding profits. Well, many equilibrium models start with assuming arbitrage is not possible (otherwise it would be trivial wouldn't it). But, in my opinion, what you actually seek is the Efficient Markets Hypothesis.... 7 Let \\tau = T-t. Then \\begin{align} S_T = S_t e^{(\\mu - \\frac{1}{2}\\sigma^2) \\tau + \\sigma \\sqrt{\\tau}\\, Z}, \\end{align} where Z is a standard normal random variable, independent of \\mathcal{F}_t. Moreover, \\begin{align*} E\\left(S_T 1_{\\{S_T >K\\}}\\mid \\mathcal{F}_t \\right) &= E\\left(S_t e^{(\\mu - \\frac{1}{2}\\sigma^2) \\tau + \\sigma \\sqrt{\\tau}\\, ... 6 Just following Musiela Rutkowski (the link redirects to Amazon). The risk neutral measure is derived form imposing that the present value of a self financed portfolio (i.e.; no infusion or withdraw of money) is a martingale. A portfolio can be seen as a stochastic process where its value at time t is given by V_t = \\phi^0_tP_t + \\phi^1_tS_t\\ , $$... 5 No, a sum of two GARCH processes is generally not a GARCH process. (I am not even sure whether there exists a nontrivial special case where the opposite holds.) By GARCH I mean the classic definition of GARCH due to Bollerslev (1986), not an arbitrary variation like EGARCH, IGARCH, FIGARCH or whatever else. Let me provide an example. Take two ... 5 From this abstract: The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic ... 5 When you decide if the performance improvement is worth it you can add these to the downside ow using single precision: the result of your basic B-S pricer will eventually need to be multiplied with a notional and maybe a discount factor; For a sufficiently large notional you will see different results than the one calculated using double precision. Is that ... 5 A detailed description of the Hurst Exponent can be found here. A further (rather short search of Google) turned up this site claiming to provide an Excel Workbook with, among other things, Hurst Exponent estimation. 5 Sorry, but despite being used as a popular example in machine learning, no one has ever achieved a stock market prediction. It does not work for several reasons (check random walk by Fama and quite a bit of others, rational decision making fallacy, wrong assumptions ...), but the most compelling one is that if it would work, someone would be able to become ... 5 One possibility worth exploring is to use the support vector machine learning tool on the Metatrader 5 platform. Firstly, if you're not familiar with it, Metatrader 5 is a platform developed for users to implement algorithmic trading in forex and CFD markets (I'm not sure if the platform can be extended to stocks and other markets). It is typically used for ... 5 The general idea is to bootstrap the discount factors in the correct order, based on the data you have given. I'm going to make some assumptions that your bonds are paying annual coupons. The longest maturity is 2.5 years, meaning you need discount factors for 6M, 1.5Y and 2.5Y. The 6M deposit has a rate of 5%, this tells you that you should use the 5% rate ... 5 To price financial instruments such as options, bonds and stocks must be priced so as to be \"arbitrage free\". The concept of arbitrage can be made precise by one of the fundamental ideas of quantitative finance, the so called Arbitrage Theorem. Put differently the Arbitrage Theorem provides a very elegant and general method for pricing derivative ... 5 I think the main difference even in this little example is the gain-loss asymmetry which is a known stylized fact: When you look at the big bump both time series posses your artificial one is perfectly symmetric whereas the real one takes longer for going up and then crashes in a relatively shorter time frame. This is a known phenomenon in real financial ... 5 1) Gatheral expresses everything in forward terms: forward value of the spot and of the call. Consider an asset A. You need to hold A at time T but since you don't need it now you don't want to buy it now. Instead you enter a forward contract with someone that says that at time T you will pay the amount K and get the asset in exchange. What ... 5 All the topics you've mentioned are wonderful and shouldn't be eschewed by reading some finance-oriented review book. I recommend these instead. Linear algebra: Hoffman and Kunze and Halmos Set theory: Halmos Measure theory: Rudin and Tao 5 Swap Just to be clear, (3.4c) leads to (3.5a) when we assume lognormal R(\\tau). Lognormal R(\\tau) means we can write$$R(\\tau) = R_0 e^{-\\frac{1}{2}\\sigma^2 \\tau + \\sigma \\sqrt{\\tau} Z}$$with Z normal, and I'm assuming a zero mean -- which I think is required. Then for (3.4c) we have for the expectation value:$$ E\\left[(R(\\tau) - R_0)^2 \\right] = ... 5 Let define\\mathbb{Q}$and$\\mathbb{P}$two equivalent probabilities on a filtered space$(\\Omega,(\\mathcal{F}_t)_{t\\geq 0})$Let define$Z_T=\\frac{d\\mathbb{Q}}{d\\mathbb{P}}$restricted to$\\mathcal{F}_T$measurable events. It means that for$X_T$being$\\mathcal{F}_T\\$ measurable we have: $$\\mathbb{E}^{\\mathbb{Q}}[X_T] = \\mathbb{E}^{\\mathbb{P}}\\left[... 5 \\require{cancel}$$\\text{PnL} = -[P(t+\\delta t,S+\\delta S)-P(t,S)] + rP(t,S)\\delta t + \\Delta(\\delta S - rS \\delta t + q S\\delta t)$$Assuming a pure diffusion, at the order 1 as \\delta t \\to 0$$P(t+\\delta,S+\\delta S) = P(t,S) + \\frac{\\partial P}{\\partial t}\\delta t + \\frac{\\partial P}{\\partial S}\\delta S + \\frac{1}{2}\\frac{\\partial^2P}{\\partial S^2}(\\..." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89083606,"math_prob":0.98762524,"size":12903,"snap":"2020-24-2020-29","text_gpt3_token_len":3631,"char_repetition_ratio":0.12008683,"word_repetition_ratio":0.015781922,"special_character_ratio":0.29411766,"punctuation_ratio":0.12026295,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.997941,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-24T22:36:38Z\",\"WARC-Record-ID\":\"<urn:uuid:b861efb8-debc-44da-ae47-41bb99bbd588>\",\"Content-Length\":\"167646\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f307ad21-42a7-4536-8083-f2e85d1e9e7e>\",\"WARC-Concurrent-To\":\"<urn:uuid:f3c2bef0-c602-4da8-8fa5-3b46715a3cf5>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://quant.stackexchange.com/tags/mathematics/hot?filter=all\",\"WARC-Payload-Digest\":\"sha1:3Q4FMJXAKJZS5AHJQZZGKBFU7P7DWSXM\",\"WARC-Block-Digest\":\"sha1:ED7WR3ORVTTO325D23ADTIIDLBKHUKQT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347385193.5_warc_CC-MAIN-20200524210325-20200525000325-00193.warc.gz\"}"}