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c_uf319fy5q741 | For example, one definition of the set N {\displaystyle \mathbb {N} } of natural numbers is: 1 is in N . {\displaystyle \mathbb {N} .} If an element n is in N {\displaystyle \mathbb {N} } then n + 1 is in N . | Recursive definition |
c_h9g5s7qrlmtc | {\displaystyle \mathbb {N} .} N {\displaystyle \mathbb {N} } is the intersection of all sets satisfying (1) and (2).There are many sets that satisfy (1) and (2) – for example, the set {1, 1.649, 2, 2.649, 3, 3.649, …} satisfies the definition. However, condition (3) specifies the set of natural numbers by removing the ... | Recursive definition |
c_urldzsqz9cw4 | Note that this definition assumes that N {\displaystyle \mathbb {N} } is contained in a larger set (such as the set of real numbers) — in which the operation + is defined. Properties of recursively defined functions and sets can often be proved by an induction principle that follows the recursive definition. For exampl... | Recursive definition |
c_mfipi0dyz3y9 | In mathematics and computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root v to any other vertex u in T is the shortest path distance from v to u in G. In connected graphs where shortest paths are well-defined (i.e. ... | Shortest-path tree |
c_9o77try5j5gx | Construct the shortest-path tree using the edges between each node and its parent.The above algorithm guarantees the existence of shortest-path trees. Like minimum spanning trees, shortest-path trees in general are not unique. In graphs for which all edge weights are equal, shortest path trees coincide with breadth-fir... | Shortest-path tree |
c_89x16y99zl2s | In graphs that have negative cycles, the set of shortest simple paths from v to all other vertices do not necessarily form a tree. For simple connected graphs, shortest-path trees can be used to suggest a non-linear relationship between two network centrality measures, closeness and degree. By assuming that the branche... | Shortest-path tree |
c_q5xs31uvc2fc | In mathematics and computer science, a splicing rule is a transformation on formal languages which formalises the action of gene splicing in molecular biology. A splicing language is a language generated by iterated application of a splicing rule: the splicing languages form a proper subset of the regular languages. | Splicing rule |
c_w1isi3mwbm8g | In mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure. The stack-sortable permutations are exactly the permutations that do not contain the permut... | Stack-sortable permutation |
c_xu5a34xyue8t | In mathematics and computer science, a string metric (also known as a string similarity metric or string distance function) is a metric that measures distance ("inverse similarity") between two text strings for approximate string matching or comparison and in fuzzy string searching. A requirement for a string metric (e... | String similarity |
c_y1p8newdbmpt | The most widely known string metric is a rudimentary one called the Levenshtein distance (also known as edit distance). It operates between two input strings, returning a number equivalent to the number of substitutions and deletions needed in order to transform one input string into another. Simplistic string metrics ... | String similarity |
c_wh7cnpb3l6gl | In mathematics and computer science, an algorithm ( ) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to d... | Algorithmic problem |
c_pv41dnmvv97b | Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus".In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in ... | Algorithmic problem |
c_sqj8ly4gr0jk | In mathematics and computer science, an algorithmic technique is a general approach for implementing a process or computation. | Algorithmic technique |
c_n5b15zrxhkjz | In mathematics and computer science, an event structure represents a set of events, some of which can only be performed after another (there is a dependency between the events) and some of which might not be performed together (there is a conflict between the events). | Event structure |
c_1igepieyyvbo | In mathematics and computer science, an unrooted binary tree is an unrooted tree in which each vertex has either one or three neighbors. | Unrooted binary tree |
c_1t6dwiykrwku | In mathematics and computer science, apply is a function that applies a function to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages. It has a role in the study of the denotational semantics of computer programs, because it is a co... | Apply |
c_c54r9k2ctfgx | Apply is also a continuous function in homotopy theory, and, indeed underpins the entire theory: it allows a homotopy deformation to be viewed as a continuous path in the space of functions. Likewise, valid mutations (refactorings) of computer programs can be seen as those that are "continuous" in the Scott topology. T... | Apply |
c_sxpcsmgpm5fc | In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and n... | Computable analysis |
c_9v3r3pm2nnbh | This might be considered surprising as an integral is (loosely speaking) an infinite sum. While this result could be explained by the fact that every computable function from {\displaystyle \mathbb {} to R {\displaystyle \mathbb {R} } is uniformly continuous, the notable thing is that the modulus of continuity can alw... | Computable analysis |
c_6wgbojg20hhc | In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to dio... | Algorithmic number theory |
c_ggf29mw3aiy5 | In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be consider... | Symbolic reasoning |
c_ke2qtl8h7ang | In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The conne... | 4-connected graph |
c_ndw7ss49411i | In mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments into evaluating a sequence of functions, each with a single argument. For example, currying a function f {\displaystyle f} that takes three arguments creates a nested unary function g... | Currying |
c_3maae4oi1934 | {\displaystyle Z.} This is a natural one-to-one correspondence between these two types of functions, so that the sets together with functions between them form a Cartesian closed category. | Currying |
c_nltohq8aftwv | The currying of a function with more than two arguments can then be defined by induction. Currying is related to, but not the same as, partial application. Currying is useful in both practical and theoretical settings. | Currying |
c_p2baqory3v2m | In functional programming languages, and many others, it provides a way of automatically managing how arguments are passed to functions and exceptions. In theoretical computer science, it provides a way to study functions with multiple arguments in simpler theoretical models which provide only one argument. The most ge... | Currying |
c_nvi2e6taxsj4 | It was introduced by Gottlob Frege, developed by Moses Schönfinkel, and further developed by Haskell Curry.Uncurrying is the dual transformation to currying, and can be seen as a form of defunctionalization. It takes a function f {\displaystyle f} whose return value is another function g {\displaystyle g} , and yields ... | Currying |
c_sh51tudkqvt4 | In mathematics and computer science, graph edit distance (GED) is a measure of similarity (or dissimilarity) between two graphs. The concept of graph edit distance was first formalized mathematically by Alberto Sanfeliu and King-Sun Fu in 1983. A major application of graph edit distance is in inexact graph matching, su... | Graph edit distance |
c_1dvhlhqdgycz | In mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into the space of all possible words. It ... | Perfect code |
c_kzf1ih2zknap | In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers, wher... | Mutually recursive |
c_5j2361hnpd2x | In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number of multiplications. Using the form of the shortest addition chain, with multiplication instead of addition, computes the desired exponent (instead of multip... | Addition-chain exponentiation |
c_t56avwizclcx | More generally, addition-chain exponentiation may also refer to exponentiation by non-minimal addition chains constructed by a variety of algorithms (since a shortest addition chain is very difficult to find). The shortest addition-chain algorithm requires no more multiplications than binary exponentiation and usually ... | Addition-chain exponentiation |
c_haghbmgj1z83 | (binary, 6 multiplications) a 15 = ( 2 × a ) 3 {\displaystyle a^{15}=(^{2}\times a)^{3}\!} (shortest addition chain, 5 multiplications). a 15 = a 3 × ( 2 ) 2 {\displaystyle a^{15}=a^{3}\times (^{2})^{2}\!} | Addition-chain exponentiation |
c_d8by5ak1w44v | (also shortest addition chain, 5 multiplications).On the other hand, the determination of a shortest addition chain is hard: no efficient optimal methods are currently known for arbitrary exponents, and the related problem of finding a shortest addition chain for a given set of exponents has been proven NP-complete. Ev... | Addition-chain exponentiation |
c_r3uzynzaho1r | There are also several methods to approximate a shortest addition chain, and which often require fewer multiplications than binary exponentiation; binary exponentiation itself is a suboptimal addition-chain algorithm. The optimal algorithm choice depends on the context (such as the relative cost of the multiplication a... | Addition-chain exponentiation |
c_7n9k53xdvv7q | In mathematics and computer science, polynomial evaluation refers to computation of the value of a polynomial when its indeterminates are substituted for some values. In other words, evaluating the polynomial P ( x 1 , x 2 ) = 2 x 1 x 2 + x 1 3 + 4 {\displaystyle P(x_{1},x_{2})=2x_{1}x_{2}+x_{1}^{3}+4} at x 1 = 2 , x 2... | Polynomial evaluation |
c_hkjc1610wkhd | See also Polynomial ring § Polynomial evaluation For evaluating the univariate polynomial a n x n + a n − 1 x n − 1 + ⋯ + a 0 , {\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{0},} the most naive method would use n {\displaystyle n} multiplications to compute a n x n {\displaystyle a_{n}x^{n}} , use n − 1 {\display... | Polynomial evaluation |
c_h0utzp12q0zl | In mathematics and computer science, symbolic-numeric computation is the use of software that combines symbolic and numeric methods to solve problems. | Symbolic-numeric computation |
c_u2z38kcy11ky | In mathematics and computer science, the BIT predicate, sometimes written BIT ( i , j ) {\displaystyle {\text{BIT}}(i,j)} , is a predicate that tests whether the j {\displaystyle j} th bit of the number i {\displaystyle i} (starting from the least significant digit) is 1, when i {\displaystyle i} is written as a binary... | BIT predicate |
c_ajnl6cmh4kom | In mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "yes" or "no" according to whether the statement is universa... | Entscheidungsproblem |
c_d9ourbrbubzf | In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and finite simple groups that are combined ... | Krohn–Rhodes theory |
c_mts3eavjwyoh | In mathematics and computer science, the binary Goppa code is an error-correcting code that belongs to the class of general Goppa codes originally described by Valerii Denisovich Goppa, but the binary structure gives it several mathematical advantages over non-binary variants, also providing a better fit for common usa... | Binary Goppa code |
c_ss7ykgc5o3ps | In mathematics and computer science, the critical exponent of a finite or infinite sequence of symbols over a finite alphabet describes the largest number of times a contiguous subsequence can be repeated. For example, the critical exponent of "Mississippi" is 7/3, as it contains the string "ississi", which is of lengt... | Critical exponent of a word |
c_cjtfdtqxdogl | In mathematics and computer science, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x).For examp... | Floor function |
c_yumfdaxuqq3w | In mathematics and computer science, the gradations of applicable meaning of a fuzzy concept are described in terms of quantitative relationships defined by logical operators. Such an approach is sometimes called "degree-theoretic semantics" by logicians and philosophers, but the more usual term is fuzzy logic or many-... | Fuzzy concept |
c_qhanq04bwc8c | Susan Haack comments: "Whereas in classical set theory an object either is or is not a member of a given set, in fuzzy set theory membership is a matter of degree; the degree of membership of an object in a fuzzy set is represented by some real number between 0 and 1, with 0 denoting no membership and 1 full membership... | Fuzzy concept |
c_f3lzccahovxi | In mathematics and computer science, the middle-square method is a method of generating pseudorandom numbers. In practice it is a highly flawed method for many practical purposes, since its period is usually very short and it has some severe weaknesses; repeated enough times, the middle-square method will either begin ... | Middle-square method |
c_tzo367lwywdq | In mathematics and computer science, the pinwheel scheduling problem is a problem in real-time scheduling with repeating tasks of unit length and hard constraints on the time between repetitions. | Pinwheel scheduling |
c_mhd6vmokoiwh | In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also generalizes the concepts of a Ma... | Probabilistic finite automata |
c_kqnhenw71hd3 | The number of stochastic languages is uncountable. The concept was introduced by Michael O. Rabin in 1963; a certain special case is sometimes known as the Rabin automaton (not to be confused with the subclass of ω-automata also referred to as Rabin automata). In recent years, a variant has been formulated in terms of ... | Probabilistic finite automata |
c_3bm62n7lsn7t | In mathematics and computer science, the probabilistic method is used to prove the existence of mathematical objects with desired combinatorial properties. The proofs are probabilistic — they work by showing that a random object, chosen from some probability distribution, has the desired properties with positive probab... | Method of conditional probabilities |
c_h71hy3anxbcb | That is, the method derandomizes the proof. The basic idea is to replace each random choice in a random experiment by a deterministic choice, so as to keep the conditional probability of failure, given the choices so far, below 1. The method is particularly relevant in the context of randomized rounding (which uses the... | Method of conditional probabilities |
c_ei5gy1k3zrk7 | In mathematics and computer science, the right quotient (or simply quotient) of a language L 1 {\displaystyle L_{1}} with respect to language L 2 {\displaystyle L_{2}} is the language consisting of strings w such that wx is in L 1 {\displaystyle L_{1}} for some string x in L 2 {\displaystyle L_{2}} . Formally: In other... | Quotient of a formal language |
c_qbjww7dzld0m | In mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by Hugo Steinhaus for the analysis of comparison sort algorithms. These numbers give the worst-case number of comparisons used by both binary insertion sort and merge sort. However, there are other algorithms that use ... | Sorting number |
c_ex7o13ntb6rl | In mathematics and computer science, the syntactic monoid M ( L ) {\displaystyle M(L)} of a formal language L {\displaystyle L} is the smallest monoid that recognizes the language L {\displaystyle L} . | Syntactic semigroup |
c_v6264kqf17cw | In mathematics and computer science, trace theory aims to provide a concrete mathematical underpinning for the study of concurrent computation and process calculi. The underpinning is provided by an algebraic definition of the free partially commutative monoid or trace monoid, or equivalently, the history monoid, which... | Trace theory |
c_dp1s986391xa | In mathematics and computer science, truncation is limiting the number of digits right of the decimal point. | Trunc (command) |
c_gc846x90554g | In mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end. The Fibonacci code is closely rela... | Fibonacci coding |
c_destnf10w1s9 | In mathematics and computing, a radix point or radix character is a symbol used in the display of numbers to separate the integer part of the value from its fractional part. In English and many other languages (including many that are written right-to-left), the integer part is at the left of the radix point, and the f... | Decimal comma |
c_kp1mccmyd4s6 | It is important to know which notation is being used when working in different software programs. The respective ISO standard defines both the comma and the small dot as decimal markers, but does not explicitly define universal radix marks for bases other than 10. Fractional numbers are rarely displayed in other number... | Decimal comma |
c_m1mplxs5zoo7 | In mathematics and computing, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f, from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number x such that f(x) = 0. As, generally, the zeros of a functi... | Root-finding algorithms |
c_xvu7i8ci91fx | However, most root-finding algorithms do not guarantee that they will find all the roots; in particular, if such an algorithm does not find any root, that does not mean that no root exists. Most numerical root-finding methods use iteration, producing a sequence of numbers that hopefully converges towards the root as it... | Root-finding algorithms |
c_qm2bozx6oba1 | Since the iteration must be stopped at some point, these methods produce an approximation to the root, not an exact solution. Many methods compute subsequent values by evaluating an auxiliary function on the preceding values. | Root-finding algorithms |
c_lrtz9m55ygv9 | The limit is thus a fixed point of the auxiliary function, which is chosen for having the roots of the original equation as fixed points, and for converging rapidly to these fixed points. The behavior of general root-finding algorithms is studied in numerical analysis. However, for polynomials, root-finding study belon... | Root-finding algorithms |
c_9dwdb87d4r1r | The efficiency of an algorithm may depend dramatically on the characteristics of the given functions. For example, many algorithms use the derivative of the input function, while others work on every continuous function. In general, numerical algorithms are not guaranteed to find all the roots of a function, so failing... | Root-finding algorithms |
c_nx8bc693scnk | In mathematics and computing, a triangular array of numbers, polynomials, or the like, is a doubly indexed sequence in which each row is only as long as the row's own index. That is, the ith row contains only i elements. | Triangular array |
c_gz5ckgoqqgv8 | In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting. The LMA interpolates between the Gauss–Newton algorithm ... | Levenberg–Marquardt nonlinear least squares fitting algorithm |
c_lq4hwlnq95un | The LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be slower than the GNA. LMA can also be viewed as Gauss–Newton using a trust region approach. | Levenberg–Marquardt nonlinear least squares fitting algorithm |
c_3pbpzvr4005s | The algorithm was first published in 1944 by Kenneth Levenberg, while working at the Frankford Army Arsenal. It was rediscovered in 1963 by Donald Marquardt, who worked as a statistician at DuPont, and independently by Girard, Wynne and Morrison.The LMA is used in many software applications for solving generic curve-fi... | Levenberg–Marquardt nonlinear least squares fitting algorithm |
c_sqlxjco7x6nl | In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to... | Hex format |
c_9zq3opwa1a0h | For example, an 8-bit byte can have values ranging from 00000000 to 11111111 (0 to 255 decimal) in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value 24,779 would be expressed in hexadecimal as ... | Hex format |
c_x891cuaczbo3 | In programming, several notations denote hexadecimal numbers, usually involving a prefix. The prefix 0x is used in C, which would denote this value as 0x60CB. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digit... | Hex format |
c_2th1bobxt3ev | In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to... | Hex digit |
c_mo75ylou42ku | For example, an 8-bit byte can have values ranging from 00000000 to 11111111 (0 to 255 decimal) in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value 30,227 would be expressed in hexadecimal as ... | Hex digit |
c_jtuyhz1bvbxt | In programming, several notations denote hexadecimal numbers, usually involving a prefix. The prefix 0x is used in C, which would denote this value as 0x7613. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digit... | Hex digit |
c_b8gz7qcn3bx7 | In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (or mechanism) for addition throughout the whole range. For a given number of places half of the possible representations of numbers encode t... | Method of complements |
c_qgy9anfcuu3r | Changing the sign of any number is encoded by generating its complement, which can be done by a very simple and efficient algorithm. This method was commonly used in mechanical calculators and is still used in modern computers. The generalized concept of the radix complement (as described below) is also valuable in num... | Method of complements |
c_5ze8jv4fxkta | The nines' complement of a number given in decimal representation is formed by replacing each digit with nine minus that digit. To subtract a decimal number y (the subtrahend) from another number x (the minuend) two methods may be used: In the first method the nines' complement of x is added to y. Then the nines' compl... | Method of complements |
c_ec5kx4ec1ese | The leftmost digit '1' of the result is then discarded. Discarding the leftmost '1' is especially convenient on calculators or computers that use a fixed number of digits: there is nowhere for it to go so it is simply lost during the calculation. The nines' complement plus one is known as the ten's complement. The meth... | Method of complements |
c_hur12lq1sjg2 | In mathematics and computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions with a certain mathematical property (see definition below). This guarantees a low number of collisions in expectation, even if the data is chosen b... | Universal hashing |
c_omjrjkwpk60j | In mathematics and control theory, H2, or H-square is a Hardy space with square norm. It is a subspace of L2 space, and is thus a Hilbert space. In particular, it is a reproducing kernel Hilbert space. | H square |
c_auu8sqb6sfyr | In mathematics and economics, a corner solution is a special solution to an agent's maximization problem in which the quantity of one of the arguments in the maximized function is zero. In non-technical terms, a corner solution is when the chooser is either unwilling or unable to make a trade-off between goods. | Corner solution |
c_wyvigo10khl8 | In mathematics and economics, the arc elasticity is the elasticity of one variable with respect to another between two given points. It is the ratio of the percentage change of one of the variables between the two points to the percentage change of the other variable. It contrasts with the point elasticity, which is th... | Arc elasticity |
c_cwsxhfnuemc2 | In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem. As we change parameters of the objective, the envelope theorem shows that, in a certain sense, changes in the optimizer of the objective do not contr... | Envelope Theorem |
c_ku5u514td43m | In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources. The problem was formalized by the French mathematician Gaspard Monge in 1781.In the 1920s A.N. Tolstoi was one of the first to study the transportation problem math... | Optimal transport problem |
c_d2rx7mwccggr | In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics. These codes are n... | Extended binary Golay code |
c_lsjbnx6camt4 | In mathematics and electronics, Cavity perturbation theory describes methods for derivation of perturbation formulae for performance changes of a cavity resonator. These performance changes are assumed to be caused by either introduction of a small foreign object into the cavity, or a small deformation of its boundary.... | Cavity Perturbation Theory |
c_s796isfiui6a | In mathematics and empirical science, quantification (or quantitation) is the act of counting and measuring that maps human sense observations and experiences into quantities. Quantification in this sense is fundamental to the scientific method. | Quantification (science) |
c_k0kl7c15qr15 | In mathematics and especially complex geometry, the Kobayashi metric is a pseudometric intrinsically associated to any complex manifold. It was introduced by Shoshichi Kobayashi in 1967. Kobayashi hyperbolic manifolds are an important class of complex manifolds, defined by the property that the Kobayashi pseudometric i... | Kobayashi metric |
c_32u903wwo443 | In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnoldus Schouten and David van Dantzig in 1930, and then introduced by Erich Kähl... | Kähler manifold |
c_kt9uqgesy9dd | Kähler geometry refers to the study of Kähler manifolds, their geometry and topology, as well as the study of structures and constructions that can be performed on Kähler manifolds, such as the existence of special connections like Hermitian Yang–Mills connections, or special metrics such as Kähler–Einstein metrics. Ev... | Kähler manifold |
c_ndc2mvwexh2e | In mathematics and especially game theory, the airport problem is a type of fair division problem in which it is decided how to distribute the cost of an airport runway among different players who need runways of different lengths. The problem was introduced by S. C. Littlechild and G. Owen in 1973. Their proposed solu... | Airport problem |
c_3jhzdao9207s | In mathematics and especially in algebraic combinatorics, the Stanley symmetric functions are a family of symmetric functions introduced by Richard Stanley (1984) in his study of the symmetric group of permutations. Formally, the Stanley symmetric function Fw(x1, x2, ...) indexed by a permutation w is defined as a sum ... | Stanley symmetric function |
c_hb6s0ymk2dbr | They were introduced in the course of Stanley's enumeration of the reduced decompositions of permutations, and in particular his proof that the permutation w0 = n(n − 1)...21 (written here in one-line notation) has exactly ( n 2 ) ! 1 n − 1 ⋅ 3 n − 2 ⋅ 5 n − 3 ⋯ ( 2 n − 3 ) 1 {\displaystyle {\frac {{\binom {n}{2}}! }{1... | Stanley symmetric function |
c_gz5wm5fpifpl | In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers π i , j {\displaystyle \pi _{i,j}} (with positive integer indices i and j) that is nonincreasing in both indices. This means that π i , j ≥ π i , j + 1 {\displaystyle \pi _{i,j}\geq \pi _{i,j+1}} and π i... | Plane partition |
c_xfwfppqfadq5 | The image has matrix form 4 4 3 2 1 4 3 1 1 3 2 1 1 {\displaystyle {\begin{matrix}4&4&3&2&1\\4&3&1&1\\3&2&1\\1\end{matrix}}} Plane partitions are also often described by the positions of the unit cubes. From this point of view, a plane partition can be defined as a finite subset P {\displaystyle {\mathcal {P}}} of posi... | Plane partition |
c_thzuv6otezio | {\displaystyle n=\sum _{i,j}\pi _{i,j}.} The sum describes the number of cubes of which the plane partition consists. Much interest in plane partitions concerns the enumeration of plane partitions in various classes. | Plane partition |
c_nr9pj4ji6a05 | The number of plane partitions with sum n is denoted by PL(n). For example, there are six plane partitions with sum 3 3 2 1 1 1 1 2 1 1 1 1 1 1 1 {\displaystyle {\begin{matrix}3\end{matrix}}\qquad {\begin{matrix}2&1\end{matrix}}\qquad {\begin{matrix}1&1&1\end{matrix}}\qquad {\begin{matrix}2\\1\end{matrix}}\qquad {\begi... | Plane partition |
c_5yr2sxu8fhx8 | In mathematics and especially number theory, the sum of reciprocals generally is computed for the reciprocals of some or all of the positive integers (counting numbers)—that is, it is generally the sum of unit fractions. If infinitely many numbers have their reciprocals summed, generally the terms are given in a certai... | Sum of reciprocals |
c_stcrxeb2pfi9 | In mathematics and functional analysis a direct integral or Hilbert integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was introduced in 1949 by John von Neumann in one of the papers in ... | Decomposable operator |
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