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6,500 | The Nash social welfare is the product of the utilities of the agents. An assignment called Nash-optimal or Maximum-Nash-Welfare if it maximizes the product of utilities. Nash-optimal allocations have some nice fairness properties.An advantage of global optimization criteria over individual criteria is that welfare-max... | Fair item allocation | 0.824052 |
6,501 | A global optimization criterion evaluates a division based on a given social welfare function: The egalitarian social welfare is minimum utility of a single agent. An item assignment is called egalitarian-optimal if it attains the maximum possible egalitarian welfare, i.e., it maximizes the utility of the poorest agent... | Fair item allocation | 0.824052 |
6,502 | Izvestiya: Mathematics is the English translation of the Russian mathematical journal Izvestiya Rossiiskoi Akademii Nauk, Seriya Matematicheskaya (Russian: Известия РАН. Серия математическая) which was founded in 1937. Since 1995, the journal has been published jointly by Turpion, the Russian Academy of Sciences, and t... | Izvestiya: Mathematics | 0.824049 |
6,503 | In functional analysis, a branch of mathematics, nest algebras are a class of operator algebras that generalise the upper-triangular matrix algebras to a Hilbert space context. They were introduced by Ringrose (1965) and have many interesting properties. They are non-selfadjoint algebras, are closed in the weak operato... | Nest algebra | 0.824047 |
6,504 | Let us work in the n {\displaystyle n} -dimensional complex vector space C n {\displaystyle \mathbb {C} ^{n}} , and let e 1 , e 2 , … , e n {\displaystyle e_{1},e_{2},\dots ,e_{n}} be the standard basis. For j = 0 , 1 , 2 , … , n {\displaystyle j=0,1,2,\dots ,n} , let S j {\displaystyle S_{j}} be the j {\displaystyle j... | Nest algebra | 0.824047 |
6,505 | Indeed, they are formally defined as the algebra of bounded operators leaving invariant each subspace contained in a subspace nest, that is, a set of subspaces which is totally ordered by inclusion and is also a complete lattice. Since the orthogonal projections corresponding to the subspaces in a nest commute, nests a... | Nest algebra | 0.824047 |
6,506 | Nest algebras are hyperreflexive with distance constant 1. | Nest algebra | 0.824047 |
6,507 | No other agent may, in this sense, be said to be better. At present the theory is limited by incomputability (the halting problem). Approximations may be used to avoid this. Processing speed and combinatorial explosion remain the primary limiting factors for artificial intelligence. | Inductive probability | 0.824047 |
6,508 | The theory of universal artificial intelligence applies decision theory to inductive probabilities. The theory shows how the best actions to optimize a reward function may be chosen. The result is a theoretical model of intelligence.It is a fundamental theory of intelligence, which optimizes the agents behavior in, Exp... | Inductive probability | 0.824047 |
6,509 | At closer inspection it turns out to be the same. Bayes' theorem is about conditional probabilities, and states the probability that event B happens if firstly event A happens: P ( A ∧ B ) = P ( B ) ⋅ P ( A | B ) = P ( A ) ⋅ P ( B | A ) {\displaystyle P(A\land B)=P(B)\cdot P(A|B)=P(A)\cdot P(B|A)} becomes in terms of m... | Inductive probability | 0.824047 |
6,510 | For a set of mutually exclusive possibilities A i {\displaystyle A_{i}} , the sum of the posterior probabilities must be 1. ∑ i P ( A i | B ) = 1 {\displaystyle \sum _{i}{P(A_{i}|B)}=1} Substituting using Bayes' theorem gives the law of total probability ∑ i P ( B | A i ) P ( A i ) = ∑ i P ( A i | B ) P ( B ) {\display... | Inductive probability | 0.824047 |
6,511 | Bayes' theorem may be used to estimate the probability of a hypothesis or theory H, given some facts F. The posterior probability of H is then P ( H | F ) = P ( H ) P ( F | H ) P ( F ) {\displaystyle P(H|F)={\frac {P(H)P(F|H)}{P(F)}}} or in terms of information, P ( H | F ) = 2 − ( L ( H ) + L ( F | H ) − L ( F ) ) {\d... | Inductive probability | 0.824047 |
6,512 | The intelligent agent may be a human or a machine. If the intelligent agent does not interact with the environment then the probability will converge over time to the frequency of the event. If however the agent uses the probability to interact with the environment there may be a feedback, so that two agents in the ide... | Inductive probability | 0.824047 |
6,513 | Chris Wallace and D. M. Boulton developed minimum message length circa 1968. Later Jorma Rissanen developed the minimum description length circa 1978. These methods allow information theory to be related to probability, in a way that can be compared to the application of Bayes' theorem, but which give a source and expl... | Inductive probability | 0.824047 |
6,514 | But Bayes' theorem always depended on prior probabilities, to generate new probabilities. It was unclear where these prior probabilities should come from. Ray Solomonoff developed algorithmic probability which gave an explanation for what randomness is and how patterns in the data may be represented by computer program... | Inductive probability | 0.824047 |
6,515 | Probability and statistics was focused on probability distributions and tests of significance. Probability was formal, well defined, but limited in scope. In particular its application was limited to situations that could be defined as an experiment or trial, with a well defined population. Bayes's theorem is named aft... | Inductive probability | 0.824047 |
6,516 | Probabilities may be calculated from the extended form of Bayes' theorem. Given all mutually exclusive hypothesis H i {\displaystyle H_{i}} which give evidence, such that, L ( H i ) + L ( F | H i ) < L ( F ) {\displaystyle L(H_{i})+L(F|H_{i}) | Inductive probability | 0.824047 |
6,517 | Make a list of all the shortest programs K i {\displaystyle K_{i}} that each produce a distinct infinite string of bits, and satisfy the relation, T n ( R ( K i ) ) = x {\displaystyle T_{n}(R(K_{i}))=x} where R ( K i ) {\displaystyle R(K_{i})} is the result of running the program K i {\displaystyle K_{i}} and T n {\dis... | Inductive probability | 0.824047 |
6,518 | Isaac Newton used inductive arguments in constructing his law of universal gravitation. Starting with the statement, The center of an apple falls towards the center of the earth.Generalizing by replacing apple for object, and earth for object gives, in a two body system, The center of an object falls towards the center... | Inductive probability | 0.824047 |
6,519 | Its basis is Bayes' theorem. Information describing the world is written in a language. For example, a simple mathematical language of propositions may be chosen. | Inductive probability | 0.824047 |
6,520 | Computer vision uses this mapping to construct 3D images from stereo image pairs. Inductive logic programming is a means of constructing theory that implies a condition. Plotkin's "relative least general generalization (rlgg)" approach constructs the simplest generalization consistent with the condition. | Inductive probability | 0.824047 |
6,521 | It is the object oriented model, in the non computer science sense. The object oriented model is constructed from our perception. In particularly vision is based on the ability to compare two images and calculate how much information is needed to morph or map one image into another. | Inductive probability | 0.824047 |
6,522 | The program with the shortest length that matches the data is the most likely to predict future data. This is the thesis behind the minimum message length and minimum description length methods. At first sight Bayes' theorem appears different from the minimimum message/description length principle. | Inductive probability | 0.824047 |
6,523 | The principle of indifference has played a key role in probability theory. It says that if N statements are symmetric so that one condition cannot be preferred over another then all statements are equally probable.Taken seriously, in evaluating probability this principle leads to contradictions. Suppose there are 3 bag... | Inductive probability | 0.824047 |
6,524 | The Journal of Computational Geometry is abstracted and indexed in MathSciNet, Zentralblatt Math, and the Emerging Sources Citation Index. Long-term preservation of journal contents are ensured by the journal's membership in the Global LOCKSS Network. | Journal of Computational Geometry | 0.824046 |
6,525 | The Journal of Computational Geometry (JoCG) is an open access mathematics journal that was established in 2010. It covers research in all aspects of computational geometry. All its papers are published free of charge to both authors and readers, and are made freely available through a Creative Commons Attribution lice... | Journal of Computational Geometry | 0.824046 |
6,526 | Microbial dark matter is unrelated to the dark matter of physics and cosmology, but is so-called for the difficulty in effectively studying it. It is hard to estimate its relative magnitude, but the accepted gross estimate is that less than one per cent of microbial species in a given ecological niche is culturable. In... | Marine phytoplankton | 0.824043 |
6,527 | ScicomP was formed in October 1999 when 285 researchers and engineers met at IBM's Advanced Computing Technology Center (ACTC) at IBM Research in Yorktown Heights, NY. The meeting was a user-oriented and planned 3-day workshop to share information on scientific computing techniques for the users of IBM SP supercomputer... | ScicomP | 0.824041 |
6,528 | Aminooxazolines can react with cyanoacetylene in a mild and highly efficient manner, controlled by inorganic phosphate, to give the cytidine ribonucleotides. Photoanomerization with UV light allows for inversion about the 1' anomeric centre to give the correct beta stereochemistry; one problem with this chemistry is th... | Peptide-RNA world | 0.824034 |
6,529 | In a series of publications, John Sutherland and his team at the School of Chemistry, University of Manchester, have demonstrated high yielding routes to cytidine and uridine ribonucleotides built from small 2- and 3-carbon fragments such as glycolaldehyde, glyceraldehyde or glyceraldehyde-3-phosphate, cyanamide, and c... | Peptide-RNA world | 0.824034 |
6,530 | In 1913, however, Bohr justified his rule by appealing to the correspondence principle, without providing any sort of wave interpretation. In 1913, the wave behavior of matter particles such as the electron was not suspected. In 1925, a new kind of mechanics was proposed, quantum mechanics, in which Bohr's model of ele... | Bohr Atomic Model | 0.824032 |
6,531 | Compound concentration tables must have samples in rows and compounds in columns. MetPA's output is a series of tables indicating which pathways are significantly enriched (along with accompanying statistics) as well as a variety of graphs or pathway maps illustrating where and how certain pathways were enriched. MetPA... | Metabolomic Pathway Analysis | 0.82402 |
6,532 | In relativistic quantum mechanics or relativistic quantum field theory, length scales are related to momentum, time and energy scales through Planck's constant and the speed of light. Often in high energy physics natural units are used where length, time, energy and momentum scales are described in the same units (usua... | Distance scale | 0.824018 |
6,533 | The idea that one can derive descriptions of physics at different length scales from one another can be quantified with the renormalization group. In quantum mechanics the length scale of a given phenomenon is related to its de Broglie wavelength ℓ = ℏ / p {\displaystyle \ell =\hbar /p} where ℏ {\displaystyle \hbar } i... | Distance scale | 0.824018 |
6,534 | In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other and are said to decouple. The decoupling of different lengt... | Distance scale | 0.824018 |
6,535 | The focus of this journal is fundamental research on the Sun and it covers all aspects of solar physics. Topical coverage includes solar-terrestrial physics and stellar research if it pertains to the focus of this journal. Publishing formats include regular manuscripts, invited reviews, invited memoirs, and topical col... | Solar Physics (journal) | 0.824012 |
6,536 | Solar Physics is a peer-reviewed scientific journal published monthly by Springer Science+Business Media. The editors-in-chief are Lidia van Driel-Gesztelyi (various affiliations), John Leibacher (National Solar Observatory, and Institut d'Astrophysique Spatiale), Cristina Mandrini (Universidad de Buenos Aires), and Iñ... | Solar Physics (journal) | 0.824012 |
6,537 | The idea of bounding probability has a very long tradition throughout the history of probability theory. Indeed, in 1854 George Boole used the notion of interval bounds on probability in his The Laws of Thought. Also dating from the latter half of the 19th century, the inequality attributed to Chebyshev described bound... | Probability bounds analysis | 0.824011 |
6,538 | Probability bounds analysis gives the same answer as interval analysis does when only range information is available. It also gives the same answers as Monte Carlo simulation does when information is abundant enough to precisely specify input distributions and their dependencies. Thus, it is a generalization of both in... | Probability bounds analysis | 0.824011 |
6,539 | Such bounds are called probability boxes, and constrain cumulative probability distributions (rather than densities or mass functions). This bounding approach permits analysts to make calculations without requiring overly precise assumptions about parameter values, dependence among variables, or even distribution shape... | Probability bounds analysis | 0.824011 |
6,540 | "Inferences in Probability Logic". Artificial Intelligence. 70 (1–2): 33–52. | Probability bounds analysis | 0.824011 |
6,541 | Bernardini, Alberto; Tonon, Fulvio (2010). Bounding Uncertainty in Civil Engineering: Theoretical Background. Berlin: Springer. ISBN 978-3-642-11189-1. | Probability bounds analysis | 0.824011 |
6,542 | Some analysts use sampling-based approaches to computing probability bounds, including Monte Carlo simulation, Latin hypercube methods or importance sampling. These approaches cannot assure mathematical rigor in the result because such simulation methods are approximations, although their performance can generally be i... | Probability bounds analysis | 0.824011 |
6,543 | Art Gallery Theorems and Algorithms is a mathematical monograph on topics related to the art gallery problem, on finding positions for guards within a polygonal museum floorplan so that all points of the museum are visible to at least one guard, and on related problems in computational geometry concerning polygons. It ... | Art Gallery Theorems and Algorithms | 0.824009 |
6,544 | The book only requires an undergraduate-level knowledge of graph theory and algorithms. However, it lacks exercises, and is organized more as a monograph than as a textbook. Despite warning that it omits some details that would be important to implementors of the algorithms that it describes, and does not describe algo... | Art Gallery Theorems and Algorithms | 0.824009 |
6,545 | The art gallery problem, posed by Victor Klee in 1973, asks for the number of points at which to place guards inside a polygon (representing the floor plan of a museum) so that each point within the polygon is visible to at least one guard. Václav Chvátal provided the first proof that the answer is at most ⌈ n / 3 ⌉ {\... | Art Gallery Theorems and Algorithms | 0.824009 |
6,546 | A multiplicity of theoretical physics research directions exist for study via a two-dimensional gas. Examples of these are Complex quantum mechanics phenomena, whose solutions may be more appropriate in a two-dimensional environment; Studies of phase transitions (e.g. melting phenomena at a planar surface); Thin film p... | Two-dimensional gas | 0.824008 |
6,547 | A two-dimensional gas is a collection of objects constrained to move in a planar or other two-dimensional space in a gaseous state. The objects can be: classical ideal gas elements such as rigid disks undergoing elastic collisions; elementary particles, or any ensemble of individual objects in physics which obeys laws ... | Two-dimensional gas | 0.824008 |
6,548 | Research at Princeton University in the early 1960s posed the question of whether the Maxwell–Boltzmann statistics and other thermodynamic laws could be derived from Newtonian laws applied to multi-body systems rather than through the conventional methods of statistical mechanics. While this question appears intractabl... | Two-dimensional gas | 0.824008 |
6,549 | The collection of all algebraic structures of a given type will usually be a proper class. Examples include the class of all groups, the class of all vector spaces, and many others. In category theory, a category whose collection of objects forms a proper class (or whose collection of morphisms forms a proper class) is... | Class (set theory) | 0.824007 |
6,550 | The structure of a disulfide bond can be described by its χss dihedral angle between the Cβ−Sγ−Sγ−Cβ atoms, which is usually close to ±90°. The disulfide bond stabilizes the folded form of a protein in several ways: It holds two portions of the protein together, biasing the protein towards the folded topology. That is,... | Disulfide bonds | 0.824001 |
6,551 | Symmetrical disulfides are compounds of the formula R2S2. Most disulfides encountered in organo sulfur chemistry are symmetrical disulfides. Unsymmetrical disulfides (also called heterodisulfides) are compounds of the formula RSSR'. They are less common in organic chemistry, but most disulfides in nature are unsymmetri... | Disulfide bonds | 0.824001 |
6,552 | TPTP (Thousands of Problems for Theorem Provers) is a freely available collection of problems for automated theorem proving. It is used to evaluate the efficacy of automated reasoning algorithms. Problems are expressed in a simple text-based format for first order logic or higher-order logic. TPTP is used as the source... | Thousands of Problems for Theorem Provers | 0.823991 |
6,553 | Molecular Probes was a biotechnology company located in Eugene, Oregon specializing in fluorescence. The company was founded in 1975 by Richard and Rosaria Haugland in their kitchen in Minnesota, then moved briefly to Texas and finally to Oregon in the early 1980s. In 1989, Molecular Probes moved from Junction City to ... | Molecular Probes | 0.823988 |
6,554 | Several important problems can be phrased in terms of eigenvalue decompositions or singular value decompositions. For instance, the spectral image compression algorithm is based on the singular value decomposition. The corresponding tool in statistics is called principal component analysis. | Numerical analyst | 0.823988 |
6,555 | In 1995, Clifford Adelman, a senior research analyst for the U.S. Department of Education, reviewed student transcripts from more than 3,000 universities and reported that student grades had actually declined slightly over the prior 20 years. A report issued by the National Center for Education Statistics surveyed all ... | Grade inflation | 0.823982 |
6,556 | This suggests that a candidate rejected with a U classification in mathematics in 1988 would likely be awarded a B/C grade in 2012, while in all subjects a 1980s C candidate would now be awarded an A*/A.The OECD noted in 2012, that the same competing commercial entities are licensed to award A-Levels as GCSEs (see abov... | Grade inflation | 0.823982 |
6,557 | As of 2007, 40% of Ontario high school graduates leave with A averages – 8 times as many as would be awarded in the traditional British system. In Alberta, as of 2007, just over 20% of high school graduates leave with an A average. This discrepancy may be explained that all Alberta high school students must write provi... | Grade inflation | 0.823982 |
6,558 | Nevertheless, there remains strong incentives for "gaming" and "teaching to the test". In response to allegations of grade inflation, a number of schools have switched to other exams, such as the International GCSE, or the International Baccalaureate middle years programme. Source: Joint Council for General Qualificati... | Grade inflation | 0.823982 |
6,559 | Louis Goldman, professor at Wichita State University, states that an increase of .404 points was reported from a survey in 134 colleges from 1965 to 1973. A second study in 180 colleges, showed a .432 GPA increase from 1960 to 1974, both indicating grade inflation.Stuart Rojstaczer, a retired geophysics professor at Du... | Grade inflation | 0.823982 |
6,560 | CBSE decided to lead by example and promised not to inflate its results. But although the 2017 results have seen a small correction, the board has clearly not discarded the practice completely. Almost 6.5 per cent of mathematics examinees in 2017 scored 95 or more — 10 times higher than in 2004 — and almost 6 per cent ... | Grade inflation | 0.823982 |
6,561 | Higher grades at some schools may reflect better performance than others (although with no national standard, there can be no way to compare one school to another by grades). Although grade inflation does not evenly distribute through departments, it is arguable due to the subjective nature of grades, that interdepartm... | Grade inflation | 0.823982 |
6,562 | The number of third class honours, "ordinary" (i.e. pass), and unclassified awards dropped substantially during the same period. During this time, the total number of first degrees awarded in the UK increased by 56%, from 212,000 to 331,000.Grade inflation in UK universities appears to be caused by administrators wishi... | Grade inflation | 0.823982 |
6,563 | The Higher Education Statistics Agency gathers and publishes annual statistics relating to the higher qualifications awarded in the UK. The Students and Qualifiers data sets indicate that the percentage of "GOOD" first degree classifications have increased annually since 1995. For example, 7% of all first-degree studen... | Grade inflation | 0.823982 |
6,564 | 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... | American Invitational Mathematics Examination | 0.823971 |
6,565 | For example, the problem of translating a natural language sentence into a syntactic representation such as a parse tree can be seen as a structured prediction problem in which the structured output domain is the set of all possible parse trees. Structured prediction is also used in a wide variety of application domain... | Structured perceptron | 0.82397 |
6,566 | Structured prediction or structured (output) learning is an umbrella term for supervised machine learning techniques that involves predicting structured objects, rather than scalar discrete or real values.Similar to commonly used supervised learning techniques, structured prediction models are typically trained by mean... | Structured perceptron | 0.82397 |
6,567 | Sequence tagging is a class of problems prevalent in natural language processing, where input data are often sequences (e.g. sentences of text). The sequence tagging problem appears in several guises, e.g. part-of-speech tagging and named entity recognition. In POS tagging, for example, each word in a sequence must rec... | Structured perceptron | 0.82397 |
6,568 | Probabilistic graphical models form a large class of structured prediction models. In particular, Bayesian networks and random fields are popular. Other algorithms and models for structured prediction include inductive logic programming, case-based reasoning, structured SVMs, Markov logic networks, Probabilistic Soft L... | Structured perceptron | 0.82397 |
6,569 | The Texas A&M Institute for Genomic Medicine (TIGM) is a research institute of Texas A&M AgriLife Research. It was founded in 2005 under a $50 million award from the Texas Enterprise Fund to accelerate the pace of medical discoveries and foster the development of the biotechnology industry in Texas. TIGM helps research... | Texas Institute for Genomic Medicine | 0.823962 |
6,570 | Knapp, Anthony W. (2006), Basic algebra, Springer, ISBN 978-0-8176-3248-9 Rotman, Joseph J. (1995), An introduction to the theory of groups, Graduate texts in mathematics, vol. 148, Springer, ISBN 978-0-387-94285-8 Smith, Geoff; Tabachnikova, Olga (2000), Topics in group theory, Springer undergraduate mathematics serie... | Simple group | 0.823961 |
6,571 | In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, namely a nontrivial normal subgroup and the corresponding quotient group. This process can be repeated, and for finite groups one... | Simple group | 0.823961 |
6,572 | The full classification is generally accepted as starting with the Feit–Thompson theorem of 1962–63, largely lasting until 1983, but only being finished in 2004. Soon after the construction of the Monster in 1981, a proof, totaling more than 10,000 pages, was supplied that group theorists had successfully listed all fi... | Simple group | 0.823961 |
6,573 | These groups (the groups of Lie type, together with the cyclic groups, alternating groups, and the five exceptional Mathieu groups) were believed to be a complete list, but after a lull of almost a century since the work of Mathieu, in 1964 the first Janko group was discovered, and the remaining 20 sporadic groups were... | Simple group | 0.823961 |
6,574 | Later Jordan's results on classical groups were generalized to arbitrary finite fields by Leonard Dickson, following the classification of complex simple Lie algebras by Wilhelm Killing. Dickson also constructed exception groups of type G2 and E6 as well, but not of types F4, E7, or E8 (Wilson 2009, p. 2). | Simple group | 0.823961 |
6,575 | According to the College Board:An AP course in calculus consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both, from institutions of high... | AP Calculus | 0.823957 |
6,576 | According to the College Board, Calculus BC is a full-year course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics...Students who take an AP Calculus course should do so with the intention of placing out of a comparable college calculus course. | AP Calculus | 0.823957 |
6,577 | The College Board intentionally schedules the AP Calculus AB exam at the same time as the AP Calculus BC exam to make it impossible for a student to take both tests in the same academic year, though the College Board does not make Calculus AB a prerequisite class for Calculus BC. Some schools do this, though many other... | AP Calculus | 0.823957 |
6,578 | The multiple choice section is scored by computer, with a correct answer receiving 1 point, with omitted and incorrect answers not affecting the raw score. This total is multiplied by 1.2 to calculate the adjusted multiple-choice score.The free response section is hand-graded by hundreds of educators each June. The raw... | AP Calculus | 0.823957 |
6,579 | The material includes the study and application of differentiation and integration, and graphical analysis including limits, asymptotes, and continuity. An AP Calculus AB course is typically equivalent to one semester of college calculus. Analysis of graphs (predicting and explaining behavior) Limits of functions (one ... | AP Calculus | 0.823957 |
6,580 | Advanced Placement (AP) Calculus (also known as AP Calc, Calc AB / Calc BC or simply AB / BC) is a set of two distinct Advanced Placement calculus courses and exams offered by the American nonprofit organization College Board. AP Calculus AB covers basic introductions to limits, derivatives, and integrals. AP Calculus ... | AP Calculus | 0.823957 |
6,581 | AP Calculus BC is equivalent to full year regular college course, covering both Calculus I and II. After passing the class, students may move on to Multivariable calculus. | AP Calculus | 0.823957 |
6,582 | AP Calculus BC includes all of the topics covered in AP Calculus AB, as well as the following: Convergence tests for series Taylor series Parametric equations Polar functions (including arc length in polar coordinates and calculating area) Arc length calculations using integration Integration by parts Improper integral... | AP Calculus | 0.823957 |
6,583 | AP Calculus AB is an Advanced Placement calculus course. It is traditionally taken after precalculus and is the first calculus course offered at most schools except for possibly a regular calculus class. The Pre-Advanced Placement pathway for math helps prepare students for further Advanced Placement classes and exams. | AP Calculus | 0.823957 |
6,584 | All of them may be described by the same second-order partial differential equation, the wave equation, which allows us to think of light and sound as forms of waves, much like familiar waves in the water. Conduction of heat, the theory of which was developed by Joseph Fourier, is governed by another second-order parti... | Second order equation | 0.823953 |
6,585 | However, diverse problems, sometimes originating in quite distinct scientific fields, may give rise to identical differential equations. Whenever this happens, mathematical theory behind the equations can be viewed as a unifying principle behind diverse phenomena. As an example, consider the propagation of light and so... | Second order equation | 0.823953 |
6,586 | Differential equations play an important role in modeling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have... | Second order equation | 0.823953 |
6,587 | The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasize... | Second order equation | 0.823953 |
6,588 | These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. Stochastic partial differential equations generalize partial differential ... | Second order equation | 0.823953 |
6,589 | A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (This is in contrast to ordinary differential equations, which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving func... | Second order equation | 0.823953 |
6,590 | Many fundamental laws of physics and chemistry can be formulated as differential equations. In biology and economics, differential equations are used to model the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated ... | Second order equation | 0.823953 |
6,591 | The target material can be polarised longitudinal or transverse to the beam axis. For unpolarised physics, mostly liquid hydrogen is used, allowing to study the proton properties. For other physics, where high atomic numbers are needed, nickel, lead and other nuclear targets are used. | COMPASS experiment | 0.823945 |
6,592 | According to the physics goal, a suitable target is needed. For polarised physics, the spins of the target material need to be oriented in one direction. The target cell contains either ammonium or deuterium, which are polarised by the means of microwave radiation and strong magnetic fields. To keep up the polarisation... | COMPASS experiment | 0.823945 |
6,593 | The versatile set-up, the use of different targets and particle beams allow the investigation of various processes. The main physics goals are the investigation of the nucleon spin structure and hadron spectroscopy. The collaboration consists of 220 physicists from 13 different countries, involving 28 universities and ... | COMPASS experiment | 0.823945 |
6,594 | The NA58 experiment, or COMPASS (standing for "Common Muon and Proton Apparatus for Structure and Spectroscopy") is a 60-metre-long fixed-target experiment at the M2 beam line of the SPS at CERN. The experimental hall is located at the CERN North Area, close to the French village of Prévessin-Moëns. The experiment is a... | COMPASS experiment | 0.823945 |
6,595 | Solid geometry or stereometry is the geometry of three-dimensional Euclidean space.A solid figure is the region bounded by a two-dimensional surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms (and ... | Geometric solid | 0.823945 |
6,596 | The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra. Classic Euler angl... | Extrinsic rotations | 0.823939 |
6,597 | The DFT has been shown to account for many puzzling findings regarding human choice behavior including violations of stochastic dominance, violations of strong stochastic transitivity, violations of independence between alternatives, serial-position effects on preference, speed accuracy tradeoff effects, inverse relati... | Decision field theory | 0.823938 |
6,598 | Diffusion models, such as the decision field theory, can be viewed as stochastic recurrent neural network models, except that the dynamics are approximated by linear systems. The linear approximation is important for maintaining a mathematically tractable analysis of systems perturbed by noisy inputs. In addition to th... | Decision field theory | 0.823938 |
6,599 | The Decision Field Theory has demonstrated an ability to account for a wide range of findings from behavioral decision making for which the purely algebraic and deterministic models often used in economics and psychology cannot account. Recent studies that record neural activations in non-human primates during perceptu... | Decision field theory | 0.823938 |
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