High Quality Content by WIKIPEDIA articles! Recursion, in mathematics and computer science, is a method of defining functions in which the function being defined is applied within its own definition. The term is also used more generally to describe a process of repeating objects in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-4577-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A recursive language in mathematics, logic and computer science is a type of formal language which is also called decidable or Turing-decidable. The class of all recursive languages is often called R, although this name is also used for the class RP. This type of language was not defined in the Chomsky hierarchy of (Chomsky 1959). All recursive languages are also recursively enumerable. All regular, context-free and context-sensitive languages are recursive. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1313-0692-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematical logic and computer science, a recursive definition (or inductive definition) is used to define an object in terms of itself (Aczel 1978:740ff). A recursive definition of a function defines values of the functions for some inputs in terms of the values of the same function for other inputs. For example, the factorial function n! is defined by the rules. 0! = 1. (n+1)! = (n+1)·n!. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1313-0671-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Recursion, in mathematics and computer science, is a method of defining functions in which the function being defined is applied within its own definition. The term is also used more generally to describe a process of repeating objects in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-4566-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing-recognizable if: There is an algorithm that, when given an input number, eventually halts if and only if the input is an element of S. Or, equivalently, there is an algorithm that enumerates the members of S. That means that its output is simply a list of the members of S: s1, s2, s3, ... . If necessary, this algorithm may run forever. The first condition suggests why the term semidecidable is sometimes used; the second suggests why computably enumerable is used. The abbreviations r.e. and c.e. are often used, even...

ISBN: 978-6-1303-8936-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, logic and computer science, a recursively enumerable language is a type of formal language which is also called partially decidable or Turing-recognizable. It is known as a type-0 language in the Chomsky hierarchy of formal languages. The class of all recursively enumerable languages is called RE. There exist three equivalent major definitions for the concept of a recursively enumerable language. All regular, context-free, context-sensitive and recursive languages are recursively enumerable. Post's theorem shows that RE, together with its complement co-RE, correspond to the first level of the arithmetical hierarchy. Данное издание не является...

ISBN: 978-6-1313-0715-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In computability theory, a set of natural numbers is called recursive, computable or decidable if there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set. A set which is not computable is called noncomputable or undecidable. A more general class of sets consists of the recursively enumerable sets. For these sets, it is only required that there is an algorithm that correctly decides when a number is in the set; the algorithm may give no answer (but not the wrong answer) for numbers not in the set. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1313-0700-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In computability theory, a set is decidable, computable, or recursive if there is an algorithm that terminates after a finite amount of time and correctly decides whether or not a given object belongs to the set. Decidability of a set is of particular interest when the set is viewed as a decision problem; a decidable set is also a decidable problem, computable problem, and recursive problem. The remainder of this article uses the term decidable, although recursive and computable are equivalent in this context. A language is a set of finite strings over a particular alphabet. A language is decidable (also computable, recursive) if it is a decidable set. A set, language, or decision problem that...

ISBN: 978-6-1303-4593-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In the study of ancient Egyptian mathematics, red auxiliary numbers were numbers used in a large number of arithmetic problems. In the 1650 BCE Rhind Mathematical Papyrus (RMP), the additive set of integers were written in red ink. The red auxiliary numbers were created from a common multiple, often a least common multiple (LCM) of the denominators of the unit fractions. Ahmes the RMP author, for example, practiced the selection of red auxiliary numbers in RMP 21,22, and 23 and fully detailed in RMP 36. Learning the method, red auxiliary numbers were used for several purposes. The main purpose was listed in 2/n tables citing the scribe's skill in generally converting rational numbers to...

ISBN: 978-6-1313-0746-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The red clump is a feature in the Hertzsprung-Russell diagram of stars. The red clump is considered the metal-rich counterpart to the horizontal branch. It corresponds to stars more luminous than main sequence stars of the same surface temperature (or colder than main sequence stars of comparable luminosity), or above and to the right of the main sequence on the Hertzsprung-Russell diagram. This period in a star's evolution corresponds to the core helium-burning phase, whereas the main sequence is the core hydrogen-burning phase. In theory, the absolute luminosities of stars in the red clump are fairly independent of stellar composition or age so that consequently they make good standard...

ISBN: 978-6-1310-6357-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A red-black tree is a type of self-balancing binary search tree, a data structure used in computing science, typically used to implement associative arrays. The original structure was invented in 1972 by Rudolf Bayer: who called them "symmetric binary B-trees", but acquired its modern name in a paper in 1978 by Leonidas J. Guibas and Robert Sedgewick. It is complex, but has good worst-case running time for its operations and is efficient in practice: it can search, insert, and delete in O(log n) time, where n is total number of elements in the tree. Put very simply, a red-black tree is a binary search tree which inserts and removes intelligently, to ensure the tree is reasonably balanced....

ISBN: 978-6-1303-4607-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Redescending M-estimators are very popular ?-type M-estimators which have ? functions that are non-decreasing near the origin, but decreasing toward 0 far from the origin. Their ? functions can be chosen to redescend smoothly to zero, so that they usually satisfy ?(x) = 0 for all x with |x| > r, where r is referred to as the minimum rejected point. Due to these properties of the ? function, these kinds of estimators are very efficient, have a high breakdown point, and, unlike other outlier rejection techniques, they do not suffer from a masking effect. Their efficiency results from the fact that they completely reject gross outliers, and do not completely ignore moderately large outliers...

ISBN: 978-6-1313-0774-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In computability theory and computational complexity theory, a reduction is a transformation of one problem into another problem. Depending on the transformation used this can be used to define complexity classes on a set of problems. Intuitively, problem A is reducible to problem B if solutions to B exist and give solutions to A whenever A has solutions. Thus, solving A cannot be harder than solving B. We write A ?m B, usually with a subscript on the ? to indicate the type of reduction being used (m : mapping reduction,p : polynomial reduction). Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1329-4199-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics a deformation of a mathematical object is either a single nearby object ('nearby' in some appropriate sense depending on the context), or a family of such nearby objects, and often an object is understood better by understanding its possible deformations. Examples are very numerous: deformations of group actions, of maps, of algebraic varieties, of algebras (eg deformation quantization), dynamical systems (bifurcation theory), complex structures (deformation theory).At this very general level, it is not possible (?) to give a formal definition of deformation, so in this article we describe different definitions for different contexts.In many cases, the possible deformations of a...

ISBN: 978-6-1311-3130-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In computability theory, many reducibility relations (also called reductions, reducibilities, and notions of reducibility) are studied. They are motivated by the question: given sets A and B of natural numbers, is it possible to effectively convert a method for deciding membership in B into a method for deciding membership in A? If the answer to this question is affirmative then A is said to be reducible to B. The study of reducibility notions is motivated by the study of decision problems. For many notions of reducibility, if any noncomputable set is reducible to a set A then A must also be noncomputable. This gives a powerful technique for proving that many sets are noncomputable....

ISBN: 978-6-1313-0916-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator an integer) is called "reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reducing a radical". Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1313-0893-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a reductive group is a smooth affine algebraic group G such that the (geometric) unipotent radical of G (i.e., maximal smooth connected unipotent normal subgroup over an algebraic closure of the ground field) is trivial. Any semisimple algebraic group is reductive, as is any algebraic torus and any general linear group. The name comes from the complete reducibility of linear representations of such a group, which is a property in fact holding over fields of characteristic zero. Haboush's theorem shows that a certain rather weaker property holds for reductive groups in the general case. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1313-0982-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the reduced derivative is a generalization of the notion of derivative that is well-suited to the study of functions of bounded variation. Although functions of bounded variation have derivatives in the sense of Radon measures, it is desirable to have a derivative that takes values in the same space as the functions themselves. In mathematical analysis, a function of bounded variation, also known as a BV function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a single variable, being of bounded variation means that the distance along the direction...

ISBN: 978-6-1311-2252-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Reduction of order is a technique in mathematics for solving second-order ordinary differential equations. It is employed when one solution y1(x) is known and a second linearly independent solution y2(x) is desired. Consider the general second-order constant coefficient ODE a y''(x) + b y'(x) + c y(x) = 0, ; where a,b,c are real non-zero coefficients. Furthermore, assume that the associated characteristic equation a lambda^{2} + b lambda + c = 0 ; has repeated roots (i.e. the discriminant, b2 ? 4ac, vanishes). Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1313-0930-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, in particular the theory of principal bundles, one can ask if a G-bundle "comes from" a subgroup H < G. This is called reduction of the structure group (to H), and makes sense for any map H to G, which need not be an inclusion (despite the terminology).Formally, given a G-bundle B and a map H ? G (which need not be an inclusion), a reduction of the structure group (from G to H) is an H-bundle BH such that the pushout B_H times_H G is isomorphic to B. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1313-0950-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In computability theory and computational complexity theory, a reduction is a transformation of one problem into another problem. Depending on the transformation used this can be used to define complexity classes on a set of problems. Intuitively, problem A is reducible to problem B if solutions to B exist and give solutions to A whenever A has solutions. Thus, solving A cannot be harder than solving B. We write A ? B, usually with a subscript on the ? to indicate the type of reduction being used. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1313-0876-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a Lie algebra is reductive if its adjoint representation in completely reducible, whence the name. More concretely, a Lie algebra is reductive if is a direct sum of a semisimple Lie algebra and an abelian Lie algebra: mathfrak{g} = mathfrak{s} oplus mathfrak{a}; there are alternative characterizations, given below.The most basic example is the Lie algebra mathfrak{gl}_n of n times n matrices with the commutator as Lie bracket, or more abstractly as the endomorphism algebra of an n-dimensional vector space, mathfrak{gl}(V). This is the Lie algebra of the general linear group GL(n), and is reductive as it decomposes as mathfrak{gl}_n = mathfrak{sl}_n oplus mathfrak{k},...

ISBN: 978-6-1313-0995-3
Издательство: Книга по требованию
Дата выхода: июль 2011

The author introduces and addresses the problem of redundancy in semidefinite programming. This work is motivated by the increasing interest in semidefinite programming and the associated demand for ways of eliminating redundant linear matrix inequality constraints in large semidefinite programming problems. This book develops different techniques for identifying nonredundant and eliminating redundant linear matrix inequality constraints. It discusses both probabilistic and deterministic methods. The first probabilistic method, called the semidefinite-stand-hit method (SSH), applies to general linear matrix inequality constraints and extends the stand-and-hit (SH) method of linear programming. The author also extends the Hypersphere...

ISBN: 978-3-6392-0155-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations. RBR is unlike usual binary numeral systems, including two's complement, which use a single bit for each digit. Many of RBR's properties differ from those of regular binary representation systems. Most importantly, RBR allows addition without using a typical carry. When compared to non-redundant representation, RBR makes bitwise logical operation slower, but Arithmetic operation are faster when large bit width are used. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1313-0994-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Reeb sphere theorem, named after Georges Reeb, states that A closed oriented connected manifold M n that admits a singular foliation having only centers is homeomorphic to the sphere Sn and the foliation has exactly two singularities. A singularity of a foliation F is of Morse type if in its small neighborhood all leaves of the foliation are levels of a Morse function, being the singularity a critical point of the function. The singularity is a center if it is a local extremum of the function; otherwise, the singularity is a saddle. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1313-1025-6
Издательство: Книга по требованию
Дата выхода: июль 2011