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In addition, knowledge of the GCSE curriculum is assumed.Paper 2: Mathematical Reasoning Paper 2 has 20 multiple-choice questions, with 75 minutes allowed to complete the paper. The second paper assesses a candidate’s ability to justify and interpret mathematical arguments and conjectures, and deal with elementary concepts from logic. It assumes knowledge of the Paper 1 specification and, in addition, requires students to have some knowledge of the structure of proof and basic logical concepts. Calculators or dictionaries are not allowed to be used in the test. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2402"} |
The old test was composed of two sections: a multiple-choice section consisting of 75 questions with five answer choices each, and a free-response section consisting of six essay prompts that required the authoring of chemical equations, solution of problems, and development of thoughtful essays in response to hypothetical scenarios. Section I, the multiple-choice portion, did allow the use of a calculator in 2023 exams, with additional reference material, other than a periodic table. Each question contained five answer choices or four. 90 minutes were allotted for the completion of Section I. Section I covered the breadth of the curriculum. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3013"} |
6755 teams participated Problem A Outstanding Winners Shanghai Jiaotong University, China Tsinghua University, China — INFORMS & Ben Fusaro Award Nanjing University, China Zhejiang University, China— SIAM Prize Recipient Beijing Normal University, China Tufts University, MA — MAA Prize Recipient DOWN THE COMPLETE PROBLEM (A) RESULTS Problem B Outstanding Winners Chongqing University, China University of International Business and Economics, China Southeast University, China Huazhong University of Science and Technology, China — Frank Giordano Award Southwest University for Nationalities, China — SIAM Prize Recipient College of Information Science and Engineering; Northeastern University, China NC School of Science and Mathematics, NC — INFORMS & MAA Prize RecipientDOWNLOAD THE COMPLETE PROBLEM (B) RESULTS | {"source": "wikipedia", "start_index": 0, "docstore_id": "4798"} |
The second round consists of several questions, in which all should be attempted. Total time allowed for the exam is 3 hours. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3563"} |
The competition consists of 15 questions of increasing difficulty, where each answer is an integer between 0 and 999 inclusive. Thus the competition effectively removes the element of chance afforded by a multiple-choice test while preserving the ease of automated grading; answers are entered onto an OMR sheet, similar to the way grid-in math questions are answered on the SAT. Leading zeros must be gridded in; for example, answers of 7 and 43 must be written and gridded in as 007 and 043, respectively. Concepts typically covered in the competition include topics in elementary algebra, geometry, trigonometry, as well as number theory, probability, and combinatorics. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4768"} |
Algebra began with computations similar to those of arithmetic, with letters standing for numbers. This allowed proofs of properties that are true no matter which numbers are involved. For example, in the quadratic equation a x 2 + b x + c = 0 , {\displaystyle ax^{2}+bx+c=0,} a , b , c {\displaystyle a,b,c} can be any numbers whatsoever (except that a {\displaystyle a} cannot be 0 {\displaystyle 0} ), and the quadratic formula can be used to quickly and easily find the values of the unknown quantity x {\displaystyle x} which satisfy the equation. That is to say, to find all the solutions of the equation. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3144"} |
The competition paper consists of twenty-five multiple-choice questions and five integer questions, which are ordered in increasing difficulty. Students record their personal details and mark their answers by pencil on a carbon-mark answer sheet, which is marked by computer in the Australian Maths Trust offices. Since 2016, an online option has been available to schools. | {"source": "wikipedia", "start_index": 0, "docstore_id": "143"} |
Every problem on the USAMTS is graded on a scale of 0 to 5, where a 0 is an answer that is highly flawed or incomplete and a 5 is a rigorous and well-written proof. As a result, possible scores over the three rounds range from 0 to 75. The solutions are graded every year by a volunteer group of university students and other people with professional mathematical experience. In addition to their scores, students receive detailed feedback on how they could improve their solutions. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2717"} |
Cubic function: Third degree polynomial. Quartic function: Fourth degree polynomial. Quintic function: Fifth degree polynomial. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4125"} |
Since c occurs in a term that does not involve x, it is called the constant term of the polynomial and can be thought of as the coefficient of x0. More generally, any polynomial term or expression of degree zero (no variable) is a constant. : 18 | {"source": "wikipedia", "start_index": 0, "docstore_id": "4844"} |
Carefully written justifications are required for each problem.Prior to academic year 2010–2011 the competition consisted of four rounds of five problems each, covering all non-calculus topics. Students were given approximately one month to solve the questions. Each question is scored out of five points; thus, a perfect score is 4 × 5 × 5 = 100 {\displaystyle 4\times 5\times 5=100} . | {"source": "wikipedia", "start_index": 0, "docstore_id": "2388"} |
This does not mean that it is claimed that they are true in some absolute sense. For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom, we can do quite well developing (the more general) group theory, and we can even take its negation as an axiom for the study of non-commutative groups. Thus, an axiom is an elementary basis for a formal logic system that together with the rules of inference define a deductive system. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1197"} |
The areas of study in Units 3 and 4 extend content from Mathematical Methods Units 3 and 4 to include rational and other quotient functions as well as other advanced mathematics topics such as logic and proof, complex numbers, vectors, differential equations, kinematics, and statistical inference. They also provide background for advanced studies in mathematics and other STEM fields. Study of Specialist Mathematics Units 3 and 4 assumes concurrent study or previous completion of Mathematical Methods. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3307"} |
Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients. Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line Linear function: First degree polynomial, graph is a straight line. Quadratic function: Second degree polynomial, graph is a parabola. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4178"} |
Assuming the centre of the slit is located at x = 0, the first equation above, for all values of y, is: Using Euler's formula, this can be simplified to: where sinc(p) = sin(p)/p. The sinc function is sometimes defined as sin(πp)/πp and this may cause confusion when looking at derivations in different texts. This can also be written as: where θ is the angle between z-axis and the line joining x to the origin and sin θ ≈ x/z when θ << 1. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3158"} |
Generally, proteins have four levels of structural complexity: quaternary (multiple polypeptides, or subunits), tertiary (the 3D folding of a polypeptide), secondary (alpha helices/beta sheets/random coils) and primary structure (linear amino acid sequences linked by peptide bonds). Ancient proteins are expected to lose their structural integrity over time, due to denaturation (protein unfolding) or other diagenetic processes.Ancient proteins also tend to be fragmented, damaged and altered. Proteins can be cleaved into small fragments over time, since hydrolysis (the addition of water) breaks peptide bonds (covalent bonds between two neighbouring alpha-amino acids). In terms of post-translational modifications (changes occur after RNA translation), ancient proteins are often characterised by extensive damage such as oxidation (methionine), hydroxylation (proline), deamidation (glutamine/asparagine), citrullination (arginine), phosphorylation (serine/threonine/tyrosine), N-terminus glutamate to pyroglutamate and the addition of advanced glycation products to lysine or arginine. | {"source": "wikipedia", "start_index": 0, "docstore_id": "439"} |
IUPAC also has a system for giving codes to identify amino acids and nucleotide bases. IUPAC needed a coding system that represented long sequences of amino acids. This would allow for these sequences to be compared to try to find homologies. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1497"} |
For every events, only answers are required. There are 4 questions in each Final Individual Event. The questions have to be solved by alternate contestants independently, and no discussions are allowed. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2636"} |
The maximum value of x x {\displaystyle {\sqrt{x}}} occurs at x = e {\displaystyle x=e} . Equivalently, for any value of the base b > 1, it is the case that the maximum value of x − 1 log b x {\displaystyle x^{-1}\log _{b}x} occurs at x = e {\displaystyle x=e} (Steiner's problem, discussed below). This is useful in the problem of a stick of length L that is broken into n equal parts. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4771"} |
Electromagnetism 538.9 Condensed matter physics. Solid state physics 539 Physical nature of matter 54 Chemistry. Crystallography. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3685"} |
A virtual-x and y value can be (3.5, 3.5) which means the center of the third tile. In the diagram on the left, this falls in the 3rd tile on the y in detail. When the virtual-x and y must add up to 4, the world x will also be 4. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3482"} |
A "QUICKPLAY" option was also available, where, to speed the game up, every question would be a wedge question. Up to six can play. The winner is the first one to earn all six wedges, land back in the center hub by exact count, and then give a correct answer. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4426"} |
Each time the eye moves, it adjusts to the new lighting level. If the degree of adaptation between visual tasks is too great, eye strain, fatigue and stress result. Similarly, a significant cause of eye strain for computer users is reflected light from poorly placed light fixtures on glass screens. Glare and brightness ratios provide guidelines for lighting schemes within libraries to minimise eye strain. Considering these ratios in balancing different light sources can be complicated considering a library's various uses, from computer-screen use and microfiche, to reading and browsing, but is important in creating a productive and safe library atmosphere for all patrons. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1537"} |
Estrogens, in females, are produced primarily by the ovaries, and during pregnancy, the placenta. Follicle-stimulating hormone (FSH) stimulates the ovarian production of estrogens by the granulosa cells of the ovarian follicles and corpora lutea. Some estrogens are also produced in smaller amounts by other tissues such as the liver, pancreas, bone, adrenal glands, skin, brain, adipose tissue, and the breasts. These secondary sources of estrogens are especially important in postmenopausal women. | {"source": "wikipedia", "start_index": 0, "docstore_id": "596"} |
Electrical engineers often need to know the power, P, dissipated by an electrical resistance, R. It is easy to do the calculation when there is a constant current, I, through the resistance. For a load of R ohms, power is given by: P = I 2 R . {\displaystyle P=I^{2}R.} However, if the current is a time-varying function, I(t), this formula must be extended to reflect the fact that the current (and thus the instantaneous power) is varying over time. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1688"} |
Electric and magnetic fields obey the properties of superposition. Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes. Further, as they are vector fields, all magnetic and electric field vectors add together according to vector addition. For example, in optics two or more coherent light waves may interact and by constructive or destructive interference yield a resultant irradiance deviating from the sum of the component irradiances of the individual light waves.The electromagnetic fields of light are not affected by traveling through static electric or magnetic fields in a linear medium such as a vacuum. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1417"} |
Further extensive numerical work, including use of negative numbers and surds. Estimation of π. Arithmetical terms, methods of multiplication, and squaring. Inverse rule of three, and rules of 3, 5, 7, 9, and 11. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1335"} |
Thus 3 + 52 = 28 and 3 × 52 = 75. These conventions exist to avoid notational ambiguity while allowing notation to remain brief. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used. | {"source": "wikipedia", "start_index": 0, "docstore_id": "539"} |
This phenomenon is known as asymptotic freedom. Forces which have a coupling constant greater than 1 are said to be "strongly coupled" while those with constants less than 1 are said to be "weakly coupled." == References == | {"source": "wikipedia", "start_index": 0, "docstore_id": "4769"} |
There are several semantic labelling types which utilises machine learning techniques. These techniques can be categorised following the work of Flach as follows: geometric (using lines and planes, such as Support-vector machine, Linear regression), probabilistic (e.g., Conditional random field), logical (e.g., Decision tree learning), and Non-ML techniques (e.g., balancing coverage and specificity). Note that the geometric, probabilistic, and logical machine learning models are not mutually exclusive. | {"source": "wikipedia", "start_index": 0, "docstore_id": "585"} |
Performing machine learning can involve creating a model, which is trained on some training data and then can process additional data to make predictions. Various types of models have been used and researched for machine learning systems. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1403"} |
PR1ME Mathematics teaching programme (PR1ME) is created for the primary or elementary grades and was first introduced in 2014 by Scholastic. It is adopted by schools in multiple countries such as Philippines, Australia, New Zealand and Mexico. PR1ME is a programme based on the Mathematics teaching and learning practices of Singapore, Hong Kong and Republic of Korea, which have consistently performed strongly in international mathematics studies such as the Trends in International Mathematics and Science Study (TIMSS) and Organisation for Economic Co-operation and Development's Programme for International Student Assessment (PISA). This programme was developed in collaboration with the Ministry of Education (MOE), Singapore and is adapted from the Primary Mathematics Project developed by MOE. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4724"} |
At the heart of this metabolic process is an electron transport system that is similar to that of chemoorganotrophs. The major difference between these two microorganisms is that chemolithotrophs directly provide electrons to the electron transport chain, while chemoorganotrophs must generate their own cellular reducing power by oxidizing reduced organic compounds. Chemolithotrophs bypass this by obtaining their reducing power directly from the inorganic substrate or by the reverse electron transport reaction. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3890"} |
The branched thiosulfate oxidation pathway, a mechanism in which water-insoluble globules of intermediate sulfur are formed during the oxidation of thiosulfate and sulfide. It is present in all the anoxygenic photolithotrophic green and purple sulfur bacteria, and the free-living as well as symbiotic strains of certain sulfur-chemolithotrophic bacteria.In any of these pathways, oxygen is the preferred electron acceptor, but in oxygen-limited environments nitrate, oxidized forms of iron and even organic matter are used instead.Cyanobacteria normally perform oxygenic photosynthesis using water as electron donor. However, in the presence of sulfide, oxygenic photosynthesis is inhibited, and some cyanobacteria can perform anoxygenic photosynthesis by oxidation of sulfide to thiosulfate − using Photosystem I with sulfite− as a possible intermediate sulfur compound. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4885"} |
However, isotope data suggests that microorganism influence dissolved inorganic nitrogen quantities and compositions and all pathways of the nitrogen cycle are likely to be found at hydrothermal vents. Biological nitrogen fixation is important to provide some of the biologically available nitrogen to the nitrogen cycle especially at unsedimented hydrothermal vents. Nitrogen fixation is done by many different microbes including methanogen in the orders Methanomicrobiales, Methanococcales, and Methanobacteriales. | {"source": "wikipedia", "start_index": 0, "docstore_id": "841"} |
The first life arose from abiotic chemical reactions. When this happened, how it happened, and even what planet it happened on are uncertain. However, life follows the rules of and arose from lifeless chemistry and physics. It is constrained by principles such as thermodynamics. | {"source": "wikipedia", "start_index": 0, "docstore_id": "198"} |
In the illuminated zone, benthic microphytes and macrophytes mediate biogeochemical fluxes through primary production, nutrient storage and sediment stabilization and act as a habitat and food source for a variety of animals, as shown in the diagram on the left above. Benthic animals contribute to biogeochemical transformations and fluxes between water and sediments both directly through their metabolism and indirectly by physically reworking the sediments and their porewaters and stimulating bacterial processes. Grazing on pelagic organic matter and biodeposition of feces and pseudofeces by suspension-feeding fauna increases organic matter sedimentation rates. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1439"} |
For example, the carboxylation of glutamate allows for better binding of calcium cations, and collagen contains hydroxyproline, generated by hydroxylation of proline. Another example is the formation of hypusine in the translation initiation factor EIF5A, through modification of a lysine residue. Such modifications can also determine the localization of the protein, e.g., the addition of long hydrophobic groups can cause a protein to bind to a phospholipid membrane.Some non-proteinogenic amino acids are not found in proteins. | {"source": "wikipedia", "start_index": 0, "docstore_id": "637"} |
Enzymes called peptidylarginine deiminases (PADs) hydrolyze the imine group of arginines and attach a keto group, so that there is one less positive charge on the amino acid residue. This process has been involved in the activation of gene expression by making the modified histones less tightly bound to DNA and thus making the chromatin more accessible. PADs can also produce the opposite effect by removing or inhibiting mono-methylation of arginine residues on histones and thus antagonizing the positive effect arginine methylation has on transcriptional activity. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4251"} |
Techniques are used to affect the amino acid sequence of the protein (site-directed mutagenesis), the folding and conformation of the protein, or the folding of a single tertiary protein within a quaternary protein matrix. Proteins that are the main focus of manipulation are typically enzymes. These are proteins that act as catalysts for biochemical reactions. By manipulating these catalysts, the reaction rates, products, and effects can be controlled. Enzymes and proteins are important to the biological field and research that there are specific divisions of engineering focusing only on proteins and enzymes. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4933"} |
Other disciplines essentially have morning and afternoon breadth exams.The Structural exam is 16 hours long and administered over two days, with two 4-hour sessions and a lunch break per day. Morning breadth sessions consist of 40 multiple-choice questions, while the afternoon depth sessions require essay responses. An examinee must earn a passing score on both days' exams in order to pass overall, but need not obtain those scores during the same administration of the exam. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2255"} |
The numerous reports of malformations in babies brought about the awareness of the side effects of the drug on pregnant women. The birth defects caused by the drug thalidomide can range from moderate malformation to more severe forms. Possible birth defects include phocomelia, dysmelia, amelia, bone hypoplasticity, and other congenital defects affecting the ear, heart, or internal organs. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4142"} |
Organoids are derived from three kinds of human or animal stem cells—embryonic pluripotent stem cells (ESCs), adult somatic stem cells (ASCs), and induced pluripotent stem cells (iPSCs). These organoids are grown in vitro and mimic the structure and function of different organs such as the brain, liver, lung, kidney, and intestine. Organoids have been developed to study infectious disease. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3665"} |
Like most computer algebra systems, Maxima supports a variety of ways of reorganizing symbolic algebraic expressions, such as polynomial factorization, polynomial greatest common divisor calculation, expansion, separation into real and imaginary parts, and transformation of trigonometric functions to exponential and vice versa. It has a variety of techniques for simplifying algebraic expressions involving trigonometric functions, roots, and exponential functions. It can calculate symbolic antiderivatives ("indefinite integrals"), definite integrals, and limits. | {"source": "wikipedia", "start_index": 0, "docstore_id": "849"} |
Sorting by Insertion 5.2.2. Sorting by Exchanging 5.2.3. Sorting by Selection 5.2.4. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2444"} |
E.g. binary search algorithm. Linear time: if the time is proportional to the input size. E.g. the traverse of a list. | {"source": "wikipedia", "start_index": 0, "docstore_id": "889"} |
Backtracking for this problem consists of choosing some order of the matrix elements and recursively placing ones or zeros, while checking that in every row and column the number of elements that have not been assigned plus the number of ones or zeros are both at least n / 2. While more sophisticated than brute force, this approach will visit every solution once, making it impractical for n larger than six, since the number of solutions is already 116,963,796,250 for n = 8, as we shall see. Dynamic programming makes it possible to count the number of solutions without visiting them all. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2055"} |
For some problems they can find the optimal solution while for others they stop at local optima, that is, at solutions that cannot be improved by the algorithm but are not optimum. The most popular use of greedy algorithms is for finding the minimal spanning tree where finding the optimal solution is possible with this method. Huffman Tree, Kruskal, Prim, Sollin are greedy algorithms that can solve this optimization problem. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1834"} |
‘While’ is an algorithm very similar to the operation of a ‘for’ algorithm, where a task is completed a number of times. However, in ‘while’ algorithms, the program computes the task a number of times before a conditional statement is met. This means that the ‘while’ algorithm can perform its task a different number of times for each time it is run. | {"source": "wikipedia", "start_index": 0, "docstore_id": "326"} |
Ethanol-water mixtures have less volume than the sum of their individual components at the given fractions. Mixing equal volumes of ethanol and water results in only 1.92 volumes of mixture. Mixing ethanol and water is exothermic, with up to 777 J/mol being released at 298 K. Mixtures of ethanol and water form an azeotrope at about 89 mole-% ethanol and 11 mole-% water or a mixture of 95.6% ethanol by mass (or about 97% alcohol by volume) at normal pressure, which boils at 351 K (78 °C). | {"source": "wikipedia", "start_index": 0, "docstore_id": "4764"} |
Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock. Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer. Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4761"} |
Only if the test path was precisely 6 times the reference path would fringes be seen. Repeated applications of this procedure allowed precise measurement of distances up to 864 meters. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2224"} |
In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data. Root-mean-square speedIn the physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is calculated using the following equation: v RMS = 3 R T M {\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}} where R represents the gas constant, 8.314 J/(mol·K), T is the temperature of the gas in kelvins, and M is the molar mass of the gas in kilograms per mole. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1819"} |
Without a convection flow, the midpoint and the lower tube end are the best locations for heat transfer. With convection, a compromise position halfway between the two points is normally chosen, which depends on the amount of heat added. One characteristic length associated with frequency is tube length L. Another characteristic length associated with sound power is αL, the position of the gauze. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3653"} |
If the relationship between the angles is specified, the shapes of both wheels can often be determined analytically as well.It is more convenient to use the circular variable z = e i θ {\displaystyle z=e^{i\theta }} when analyzing this problem. Assuming the radius of the first gear wheel is known as a function of z, and using the relationship d z = i z d θ {\displaystyle dz=iz\,d\theta } , the above two equations can be combined to yield the differential equation: d z 2 z 2 = r 1 ( z 1 ) a − r 1 ( z 1 ) d z 1 z 1 {\displaystyle {\frac {dz_{2}}{z_{2}}}={\frac {r_{1}(z_{1})}{a-r_{1}(z_{1})}}\,{\frac {dz_{1}}{z_{1}}}} where z 1 {\displaystyle z_{1}} and z 2 {\displaystyle z_{2}} describe the rotation of the first and second gears respectively. This equation can be formally solved as: ln ( z 2 ) = ln ( K ) + ∫ r 1 ( z 1 ) a − r 1 ( z 1 ) d z 1 z 1 {\displaystyle \ln(z_{2})=\ln(K)+\int {\frac {r_{1}(z_{1})}{a-r_{1}(z_{1})}}\,{\frac {dz_{1}}{z_{1}}}} where ln ( K ) {\displaystyle \ln(K)} is a constant of integration. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3010"} |
An identity is an equation that is true for all possible values of the variable(s) it contains. Many identities are known in algebra and calculus. In the process of solving an equation, an identity is often used to simplify an equation, making it more easily solvable. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3369"} |
The subgroup H chosen is 31+12.2.Suz.2, where Suz is the Suzuki group. Elements of the monster are stored as words in the elements of H and an extra generator T. It is reasonably quick to calculate the action of one of these words on a vector in V. Using this action, it is possible to perform calculations (such as the order of an element of the monster). Wilson has exhibited vectors u and v whose joint stabilizer is the trivial group. Thus (for example) one can calculate the order of an element g of the monster by finding the smallest i > 0 such that giu = u and giv = v. This and similar constructions (in different characteristics) were used to find some of the non-local maximal subgroups of the monster group. In 2023, Seysen's mmgroup software package was used by Dietrich et al. in announcing that they had completed the classification of the maximal subgroups of the monster group. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4320"} |
About the Burnside problem: Very much like Fermat's Last Theorem in number theory, Burnside’s problem has acted as a catalyst for research in group theory. The fascination exerted by a problem with an extremely simple formulation which then turns out to be extremely difficult has something irresistible about it to the mind of the mathematician. Before the work of Novikov and Adian an affirmative answer to the problem was known only for n ∈ { 2 , 3 , 4 , 6 } {\displaystyle n\in \{2,3,4,6\}} and the matrix groups. However, this did not hinder the belief in an affirmative answer for any period n {\displaystyle n} . | {"source": "wikipedia", "start_index": 0, "docstore_id": "1678"} |
(the factorial of the order |G| of the group G). The degrees of generators need not satisfy Noether's bound when the characteristic of the field divides the number |G|, but Noether was not able to determine whether this bound was correct when the characteristic of the field divides |G|! but not |G|. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3969"} |
The USIYPT consists of six preliminary rounds and a set of final rounds. In each round, called a "Physics Fight," a student from the reporting team presents a 10-minute summary of their research into one of the four official tournament problems. Next, a student from another team engages the reporter in a 12-minute conversation about the reporting team's project. This opponent is charged with helping the audience understand the strengths and weaknesses of the report by means of a series of discussion questions. Only after this conversation is complete are jury members allowed to question the presenting students directly. Teams are judged as much on their ability to ask and answer questions in the physics fight as on the quality of their initial presentations. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3372"} |
Intransitive dice: One can have three dice, called A, B, and C, such that A is likely to win in a roll against B, B is likely to win in a roll against C, and C is likely to win in a roll against A. Monty Hall problem: An unintuitive consequence of conditional probability. Necktie paradox: A wager between two people seems to favour them both. Very similar in essence to the Two-envelope paradox. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3570"} |
Icelandic Junior College Mathematics Competition (Stærðfræðikeppni framhaldsskólanema) is an annual mathematical olympiad first held in the winter of 1984–1985. It is hosted by the Icelandic Mathematical Organization (Íslenska stærðfræðafélagið) and the Natural Sciences's Teacher Association, and the largest competition of its kind in the country. Its goals include increasing the interest of Icelandic secondary school students towards mathematics, and other fields built on a mathematical foundation. The contest is held in two parts every winter. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1765"} |
Bioinformatics is the field that deals with the analysis, Sucking, and use of biological data. This usually means topics such as genomics and proteomics, and sometimes also includes medical image computing. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1298"} |
Preparation of the sample is critical to maintaining cell morphology, tissue architecture and the antigenicity of target epitopes. This requires proper tissue collection, fixation and sectioning. A solution of formalin is often used to fix tissue, but other methods may be used. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4678"} |
The technologies include nanowires, a new class of quasi-one-dimensional materials that have demonstrated superior electrical, optical, mechanical, and thermal properties and can be used potentially as biological sensors. Research under Lieber has delved into the use of nanowires mapping brain activity.Shimon Weiss, a professor at the University of California, Los Angeles, is known for his research of fluorescent semiconductor nanocrystals, a subclass of quantum dots, for biological labeling.Paul Alivisatos, from the University of California, Berkeley, is also notable for his research on the fabrication and use of nanocrystals. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3400"} |
All known extant (surviving) organisms are based on the same biochemical processes: genetic information encoded as nucleic acid (DNA, or RNA for many viruses), transcribed into RNA, then translated into proteins (that is, polymers of amino acids) by highly conserved ribosomes. Perhaps most tellingly, the Genetic Code (the "translation table" between DNA and amino acids) is the same for almost every organism, meaning that a piece of DNA in a bacterium codes for the same amino acid as in a human cell. ATP is used as energy currency by all extant life. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3552"} |
Since the 1980s, molecular biology and bioinformatics have created the need for DNA annotation. DNA annotation or genome annotation is the process of identifying the locations of genes and all of the coding regions in a genome and determining what those genes do. An annotation (irrespective of the context) is a note added by way of explanation or commentary. Once a genome is sequenced, it needs to be annotated to make sense of it. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1842"} |
For each of the 50 multiple choice questions, students received 1 point for every correct answer, lost ¼ of a point for each incorrect answer, and received 0 points for questions left blank. This created a raw score, which was then converted into a scaled score. The conversion between these numbers varied depending on the difficulty of a particular test administration. The scaled score was the only score reported to either students or colleges, and ranged from 200 to 800, with 800 being the best possible score. The standard deviation of the test scores in 2006 was 105.15 percent of the 2012 college-bound seniors taking the test received a perfect score of 800. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4740"} |
This gives a ratio of width to length of 4:9, and the same for height to width. Putting these together gives height:width:length of 16:36:81, or to the delight of the Pythagoreans 42:62:92. This sets the module as 0.858 m. A 4:9 rectangle can be constructed as three contiguous rectangles with sides in the ratio 3:4. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4737"} |
The maximum possible score is 25 × 6 = 150 {\displaystyle 25\times 6=150} points; in 2020, the AMC 12 had a total of 18 perfect scores between its two administrations, and the AMC 10 also had 18. From 1974 until 1999, the competition (then known as the American High School Math Examination, or AHSME) had 30 questions and was 90 minutes long, scoring 5 points for correct answers. Originally during this time, 1 point was awarded for leaving an answer blank, however, it was changed in the late 1980s to 2 points. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1416"} |
An equivalent definition of group consists of replacing the "there exist" part of the group axioms by operations whose result is the element that must exist. So, a group is a set G {\displaystyle G} equipped with a binary operation G × G → G {\displaystyle G\times G\rightarrow G} (the group operation), a unary operation G → G {\displaystyle G\rightarrow G} (which provides the inverse) and a nullary operation, which has no operand and results in the identity element. Otherwise, the group axioms are exactly the same. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2076"} |
For example, the set of all positive and negative multiples of 2 along with 0 form an ideal of the integers, and this ideal is generated by the integer 2. In fact, every ideal of the ring of integers is principal. Like a group, a ring is said to be simple if it is nonzero and it has no proper nonzero two-sided ideals. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2557"} |
The dimensions that can be formed from a given collection of basic physical dimensions, such as T, L, and M, form an abelian group: The identity is written as 1; L0 = 1, and the inverse of L is 1/L or L−1. L raised to any integer power p is a member of the group, having an inverse of L−p or 1/Lp. The operation of the group is multiplication, having the usual rules for handling exponents (Ln × Lm = Ln+m). Physically, 1/L can be interpreted as reciprocal length, and 1/T as reciprocal time (see reciprocal second). | {"source": "wikipedia", "start_index": 0, "docstore_id": "1231"} |
It is a common convention that for an abelian group either additive or multiplicative notation may be used, but for a nonabelian group only multiplicative notation is used. Several other notations are commonly used for groups whose elements are not numbers. For a group whose elements are functions, the operation is often function composition f ∘ g {\displaystyle f\circ g} ; then the identity may be denoted id. In the more specific cases of geometric transformation groups, symmetry groups, permutation groups, and automorphism groups, the symbol ∘ {\displaystyle \circ } is often omitted, as for multiplicative groups. Many other variants of notation may be encountered. | {"source": "wikipedia", "start_index": 0, "docstore_id": "704"} |
Facilities burden (space, power, and cooling). When more power is used, a portable system will have a shorter battery life and require recharging more often. A server that consumes more power and/or space may not be able to fit within existing data center resource constraints, including cooling limitations. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4583"} |
To a certain extent, emotional security is a function of brain chemistry: some people are naturally predisposed to feel less happy, and to be more adversely affected by natural events, for example in the case of hypothyroidism. Certain medications, such as SSRI's or even stimulants, are often prescribed to address such natural deficiencies. The side-effects of these medications, however, in many cases can negate their positive effects, for example when certain anti-depressants make it difficult or impossible to experience orgasm by making the brain incapable of cutting off the flow of certain hormones usually associated with positive emotions but necessary to suddenly block for short periods of time in order for orgasm to occur. It is also said that such medications blunt both 'the highs and the lows,' sapping, for some people, a valuable, inspiring energy from life. However, weighing the pros against the cons of such situations is something different for each individual, and in many cases the dangers of naturally low emotional security may be worse than the side-effects of the appropriate medication, especially such as when a person is suicidal. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1303"} |
Danazol, also known as 2,3-isoxazol-17α-ethynyltestosterone or as 17α-ethynyl-17β-hydroxyandrost-4-en-isoxazole, is a synthetic androstane steroid and a derivative of testosterone and ethisterone (17α-ethynyltestosterone). It is specifically the derivative of ethisterone where the C3 ketone is replaced with a 2,3-isoxazole moiety (i.e., an isoxazole ring is fused to the A ring at the C2 and C3 positions). Ethisterone is a weak progestin with weak androgenic activity. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4385"} |
Spironolactone is also known by the following equivalent chemical names: 7α-Acetylthio-17α-hydroxy-3-oxopregn-4-ene-21-carboxylic acid γ-lactone 7α-Acetylthio-3-oxo-17α-pregn-4-ene-21,17β-carbolactone 3-(3-Oxo-7α-acetylthio-17β-hydroxyandrost-4-en-17α-yl)propionic acid lactone 7α-Acetylthio-17α-(2-carboxyethyl)androst-4-en-17β-ol-3-one γ-lactone 7α-Acetylthio-17α-(2-carboxyethyl)testosterone γ-lactone | {"source": "wikipedia", "start_index": 0, "docstore_id": "1580"} |
MPA is a synthetic pregnane steroid and a derivative of progesterone and 17α-hydroxyprogesterone. Specifically, it is the 17α-acetate ester of medroxyprogesterone or the 6α-methylated analogue of hydroxyprogesterone acetate. MPA is known chemically as 6α-methyl-17α-acetoxyprogesterone or as 6α-methyl-17α-acetoxypregn-4-ene-3,20-dione, and its generic name is a contraction of 6α-methyl-17α-hydroxyprogesterone acetate. MPA is closely related to other 17α-hydroxyprogesterone derivatives such as chlormadinone acetate, cyproterone acetate, and megestrol acetate, as well as to medrogestone and nomegestrol acetate. 9α-fluoromedroxyprogesterone acetate (FMPA), the C9α fluoro analogue of MPA and an angiogenesis inhibitor with two orders of magnitude greater potency in comparison to MPA, was investigated for the potential treatment of cancers but was never marketed. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3970"} |
In power engineering, the voltage between two phases in a three-phase system equals 3 {\textstyle {\sqrt {3}}} times the line to neutral voltage. This is because any two phases are 120° apart, and two points on a circle 120 degrees apart are separated by 3 {\textstyle {\sqrt {3}}} times the radius (see geometry examples above). | {"source": "wikipedia", "start_index": 0, "docstore_id": "3735"} |
So in equation (1) above, the second term dominates. Therefore, in magnetic circuits with an air gap, the strength of the magnetic field B depends strongly on the length of the air gap, and the length of the flux path in the core doesn't matter much. Given an air gap of 1mm, a magnetomotive force of about 796 Ampere-turns is required to produce a magnetic field of 1T. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3926"} |
In living cells, DNP acts as a proton ionophore, an agent that can shuttle protons (hydrogen cations) across biological membranes. It dissipates the proton gradient across the mitochondria membranes, collapsing the proton motive force that the cell uses to produce most of its ATP chemical energy. Instead of producing ATP, the energy of the proton gradient is lost as heat.DNP is often used in biochemistry research to help explore the bioenergetics of chemiosmotic and other membrane transport processes. | {"source": "wikipedia", "start_index": 0, "docstore_id": "91"} |
Before mercury can be methylated, it must be transported into the cell through the lipid membrane. Mercury ions are bound by a mercury scavenger protein, MerP. MerP transfers the mercury ion to a cytoplasmic membrane transporter, MerT, then to the active site of mercuric reductase or mercury(II) reductase in the cytoplasm.Normally mercury would be toxic to the cell, but some microorganisms are resistant to mercury ion due to an inducible mer operon. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4444"} |
N-Acetylgalactosamine N-Acetylglucosamine N-Acetylmuramic acid N-type calcium channel NMDA receptor Nanobiomechanics Nanodisc Nav1.1 Nav1.2 Nav1.4 Nav1.5 Nectin Neurophysins Nicolas Rashevsky Nicotinic acetylcholine receptor Niosome Norepinephrine transporter Nuclear pore | {"source": "wikipedia", "start_index": 0, "docstore_id": "4601"} |
Dopamine is synthesized in a restricted set of cell types, mainly neurons and cells in the medulla of the adrenal glands. The primary and minor metabolic pathways respectively are: Primary: L-Phenylalanine → L-Tyrosine → L-DOPA → Dopamine Minor: L-Phenylalanine → L-Tyrosine → p-Tyramine → Dopamine Minor: L-Phenylalanine → m-Tyrosine → m-Tyramine → DopamineThe direct precursor of dopamine, L-DOPA, can be synthesized indirectly from the essential amino acid phenylalanine or directly from the non-essential amino acid tyrosine. These amino acids are found in nearly every protein and so are readily available in food, with tyrosine being the most common. Although dopamine is also found in many types of food, it is incapable of crossing the blood–brain barrier that surrounds and protects the brain. | {"source": "wikipedia", "start_index": 0, "docstore_id": "926"} |
Motor proteins are a class of molecular motors that can move along the cytoplasm of animal cells. They convert chemical energy into mechanical work by the hydrolysis of ATP. A good example is the muscle protein myosin which "motors" the contraction of muscle fibers in animals. Motor proteins are the driving force behind most active transport of proteins and vesicles in the cytoplasm. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4022"} |
"n effect, the is a nanomachine composed of perhaps over 600 proteins in molecular complexes, many of which also function independently as nanomachines...Flexible linkers allow the mobile protein domains connected by them to recruit their binding partners and induce long-range allostery via protein domain dynamics. Other biological machines are responsible for energy production, for example ATP synthase which harnesses energy from proton gradients across membranes to drive a turbine-like motion used to synthesise ATP, the energy currency of a cell. Still other machines are responsible for gene expression, including DNA polymerases for replicating DNA, RNA polymerases for producing mRNA, the spliceosome for removing introns, and the ribosome for synthesising proteins. | {"source": "wikipedia", "start_index": 0, "docstore_id": "236"} |
In other words, compressive strength resists compression (being pushed together), whereas tensile strength resists tension (being pulled apart). In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently. Computational fluid dynamicsThe numerical solution of flow equations in practical problems such as aircraft design or hydraulic structures. | {"source": "wikipedia", "start_index": 0, "docstore_id": "1217"} |
When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2931"} |
{\displaystyle \mathrm {Area} ={\frac {4ab}{n}}\mathrm {B} \!\left({\frac {1}{n}},{\frac {1}{n}}+1\right).} The pedal curve is relatively straightforward to compute. Specifically, the pedal of is given in polar coordinates by | {"source": "wikipedia", "start_index": 0, "docstore_id": "1647"} |
The gravitational force pulling down on the mass is no longer equal to the upward elastic force of the spring. In the terminology of the previous section, F1 and F3 are no longer equal. However, it is still true that F1 = F2 and F3 = F4, as this is required by Newton's third law. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4144"} |
Note that air flow changes as the square root of the pressure. Thus, doubling the pressure will only increase the flow 1.41 (√2) times, not twice as might be assumed. Another way of looking at this is that the pressure must go up by a factor of four to double the flow rate. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4908"} |
The following discussion uses the simplest case, where the system has two lumped springs and two lumped masses, and only two mode shapes are assumed. Hence M = and K = . A mode shape is assumed for the system, with two terms, one of which is weighted by a factor B, e.g. Y = + B. Simple harmonic motion theory says that the velocity at the time when deflection is zero, is the angular frequency ω {\displaystyle \omega } times the deflection (y) at time of maximum deflection. In this example the kinetic energy (KE) for each mass is 1 2 ω 2 Y 1 2 m 1 {\textstyle {\frac {1}{2}}\omega ^{2}Y_{1}^{2}m_{1}} etc., and the potential energy (PE) for each spring is 1 2 k 1 Y 1 2 {\textstyle {\frac {1}{2}}k_{1}Y_{1}^{2}} etc. We also know that without damping, the maximal KE equals the maximal PE. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3991"} |
It therefore does not perdure in any single body during the course of its interaction with other corporeal substances. Since it is comprehensible as the internal action acted upon by some other body or bodies, the capacity to resist... penetration and changes in their states of motion. Derivative passive force (vis passiva derivativa) is the purely quantitative modification of primitive passive force in terms of the measures of any material mass’s resistance to penetration and change in its state of motion. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3434"} |
For example, when a person runs out of drinking water in the middle of a hiking trip, they could employ the skills associated with logical reasoning to decide whether to boil and drink water from a stream that might contain dangerous microorganisms rather than break off the trip and hike back to the parking lot. This could include considering factors like assessing how dangerous the microorganisms are and the likelihood that they survive the boiling procedure. It may also involve gathering relevant information to make these assessments, for example, by asking other hikers.Time also plays a central role in logical reasoning. | {"source": "wikipedia", "start_index": 0, "docstore_id": "3419"} |
Legibility: information is easy to read. Comprehensibility: the meaning is clearly understandable, unambiguous, interpretable, and recognizable.The user guidance in Part 13 of the ISO 9241 standard describes that the user guidance information should be readily distinguishable from other displayed information and should be specific for the current context of use. User guidance can be given by the following five means: Prompts indicating explicitly (specific prompts) or implicitly (generic prompts) that the system is available for input. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4880"} |
Adaptive tests tend to administer easier items after a person answers incorrectly. Supposedly, an astute test-taker could use such clues to detect incorrect answers and correct them. Or, test-takers could be coached to deliberately pick wrong answers, leading to an increasingly easier test. | {"source": "wikipedia", "start_index": 0, "docstore_id": "4278"} |
Adaptive tests can provide uniformly precise scores for most test-takers. In contrast, standard fixed tests almost always provide the best precision for test-takers of medium ability and increasingly poorer precision for test-takers with more extreme test scores. An adaptive test can typically be shortened by 50% and still maintain a higher level of precision than a fixed version. This translates into time savings for the test-taker. | {"source": "wikipedia", "start_index": 0, "docstore_id": "2880"} |
Given two examinees with different ability parameters β 1 {\displaystyle \beta _{1}} and β 2 {\displaystyle \beta _{2}} and an arbitrary item with difficulty δ i {\displaystyle \delta _{i}} , compute the difference in logits for these two examinees by ( β 1 − δ i ) − ( β 2 − δ i ) {\displaystyle (\beta _{1}-\delta _{i})-(\beta _{2}-\delta _{i})} . This difference becomes β 1 − β 2 {\displaystyle \beta _{1}-\beta _{2}} . Conversely, it can be shown that the log odds of a correct response by the same person to one item, conditional on a correct response to one of two items, is equal to the difference between the item locations. | {"source": "wikipedia", "start_index": 0, "docstore_id": "904"} |
For the best performance in the context of generalization, the complexity of the hypothesis should match the complexity of the function underlying the data. If the hypothesis is less complex than the function, then the model has under fitted the data. If the complexity of the model is increased in response, then the training error decreases. | {"source": "wikipedia", "start_index": 0, "docstore_id": "810"} |
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