High Quality Content by WIKIPEDIA articles! In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold. It is one of many mathematical objects named after Bernhard Riemann. The key difference between a Riemannian manifold and a pseudo-Riemannian manifold is that on a pseudo-Riemannian manifold the metric tensor need not be positive-definite. Instead a weaker condition of nondegeneracy is imposed. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-4287-6
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In convex analysis and the calculus of variations, branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minimima, but need not actually be convex. Informally, a differentiable function is pseudoconvex if it is increasing in any direction where it has a positive directional derivative. Every convex function is pseudoconvex, but the converse is not true. For example, the function (x) = x + x3 is pseudoconvex but not convex. Any pseudoconvex function is quasiconvex, but the converse is not true since the function (x) = x3 is quasiconvex...

ISBN: 978-6-1347-1442-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation (i.e., a transformation that rotates vectors and pseudovectors by an arbitrary angle about an arbitrary axis), but gains an additional sign flip under an improper rotation: a transformation that can be expressed as a proper rotation of a mirror image, or equivalently as an inversion through the origin followed by a proper rotation. The conceptual opposite of a pseudovector is a (true) vector or a polar vector (more formally, a contravariant vector). Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1303-7193-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under a proper rotation, but gains an additional sign flip under an improper rotation (a transformation that can be expressed as an inversion followed by a proper rotation). There is a second meaning for pseudotensor, restricted to general relativity; tensors obey strict transformation laws, whilst pseudotensors are not so constrained. Consequently the form of a pseudotensor will, in general, change as the frame of reference is altered. An equation which holds in a frame containing pseudotensors will not necessarily hold in a different frame; this makes pseudotensors of limited relevance because they...

ISBN: 978-6-1303-4337-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A pseudoprime is a probable prime (an integer which shares a property common to all prime numbers) which is not actually prime. Pseudoprimes can be classified according to which property they satisfy.The most important class of pseudoprimes come from Fermat's little theorem and hence are called Fermat pseudoprimes. This theorem states that if p is prime and a is coprime to p, then ap?1 ? 1 is divisible by p. If a number x is not prime, a > 1 is coprime to x and x divides ax?1 ? 1, then x is called a pseudoprime to base a. Some sources use variations of this definition, for example to only allow odd numbers to be pseudoprimes.A number x that is a pseudoprime for all values of a that are...

ISBN: 978-6-1303-4297-5
Издательство: Книга по требованию
Дата выхода: июль 2011

Spectral methods have a long history of application to fluid flow simulations. Their main advantages are high-order accuracy and convergence properties. The basic spectral methods only work on rectangular or circular domains. A very important and active research area is to adapt spectral methods for domains with complex boundary. In this monograph the application of pseudospectral (PS) method to viscous flow over a two-dimensional cylinder with dimples on the boundary is presented. By using a series of coordinate transformations, the exterior domain is mapped to the interior of the unit disk. Then the Fourier-Chebyshev PS approximation is applied to the transformed system of partial differential equations. Both steady and unsteady...

ISBN: 978-3-8364-8853-2
Издательство: Книга по требованию
Дата выхода: июль 2011

Pseudo-differential operators(p.d.o.)which originated as powerful tool in the study of partial differential equation,have now become an independent field of research. In fact, p.d.o are generalizations of partial differential operators. These operators have been defined on various functions and distribution spaces using various transformations. Pseudo-differential operators arise naturally in the solution of boundary value problemsfor partial differential equations. Hankel transformation is used in the solution of cylindrical boundary value problems. Therefore, the theory ofp.d.o involving Hankel transform will find applications in the characterizing solutions of cylindrical boundary value problems, which occur mostcommonly in nature....

ISBN: 978-3-6392-1812-1
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, specifically in topology, a pseudo-Anosov map is a type of a diffeomorphism or homeomorphism of a surface. It is a generalization of a linear Anosov diffeomorphism of the torus. Its definition relies on the notion of a measured foliation invented by William Thurston, who also coined the term "pseudo-Anosov diffeomorphism" when he proved his classification of diffeomorphisms of a surface. A measured foliation F on a closed surface S is a geometric structure on S which consists of a singular foliation and a measure in the transverse direction. In some neighborhood of a regular point of F, there is...

ISBN: 978-6-1347-0895-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Pseudomathematics is a form of mathematics-like activity that does not work within the framework, definitions, rules, or rigor of formal mathematical models. While any given pseudomathematical approach may work within some of these boundaries, for instance, by accepting or invoking most known mathematical definitions that apply, pseudomathematics inevitably disregards or explicitly discards a well-established or proven mechanism, falling back upon any number of demonstrably non-mathematical principles. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1304-0788-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Puiseux series are a generalization of formal power series, first introduced by Victor Puiseux in 1850[1], that allows for negative and fractional exponents of the indeterminate.The Puiseux expansion is a generalization of the Laurent series expansion (hence also of the formal series expansion), initially defined for algebraic functions or (equivalently) branches of algebraic curves (a fact also referred to as Puiseux's theorem) and which can be generalized to various settings. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-4356-9
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a pullback bundle or induced bundle is a useful construction in the theory of fiber bundles. Given a fiber bundle : E -> B and a continuous map f : B -> B one can define a "pullback" of E by f as a bundle f*E over B . The fiber of f*E over a point x in B is just the fiber of E over f(x). Thus f*E is the disjoint union of all these fibers equipped with a suitable topology. In mathematics, and particularly topology, a fiber bundle (or, in BrE, fibre bundle) is intuitively a space E which locally "looks" like a product space B x F, but globally may have a different topological structure....

ISBN: 978-6-1348-3909-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Suppose that ?:M? N is a smooth map between smooth manifolds M and N; then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by ?), and is frequently denoted by ?*. More generally, any covariant tensor field – in particular any differential form – on N may be pulled back to M using ?. When the map ? is a diffeomorphism, then the pullback, together with the pushforward, can be used to transform any tensor field from N to M or vice-versa. In particular, if ? is a diffeomorphism between open subsets of Rn and Rn, viewed as a change of coordinates...

ISBN: 978-6-1303-4385-9
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the attractor of a random dynamical system may be loosely thought of as a set to which the system evolves after a long enough time. The basic idea is the same as for a deterministic dynamical system, but requires careful treatment because random dynamical systems are necessarily non-autonomous. This requires one to consider the notion of a pullback attractor or attractor in the pullback sense. In mathematics, a random dynamical system is a measure-theoretic formulation of a dynamical system with an element of "randomness", such as the dynamics of solutions to a stochastic differential equation....

ISBN: 978-6-1348-3828-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In category theory, a branch of mathematics, a pullback (also called a fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X ? Z and g : Y ? Z with a common codomain; it is the limit of the cospan X rightarrow Z leftarrow Y. The pullback is often written P = X times_Z Y., In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects linked in diagrams by morphisms or arrows. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1303-4371-2
Издательство: Книга по требованию
Дата выхода: июль 2011

We examine the problem of solving hyperbolic initial boundary value problems in several space dimensions on parallel computers using domain decomposition. Imposing continuity conditions across an inter-domain boundary in several space dimensions is in general not well posed. If however the boundary moves faster than the fastest wave associated with the hyperbolic equation then the problem becomes well posed. We minimize a function which is the sum of squares of the L2 norm of the residuals in the partial differential equation, initial and boundary conditions and a penalty term which is the sum of squares of the L2 norm of the jumps in the function across inter-domain boundaries. The inter-domain boundaries are made to move back and forth...

ISBN: 978-3-6393-2518-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. It is distinguished by its rigour, abstraction, and beauty. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of navigation, astronomy, physics, engineering, and so on. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-4399-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Suppose that ? : M ? N is a smooth map between smooth manifolds; then the differential of ? at a point x is, in some sense, the best linear approximation of ? near x. It can be viewed as generalization of the total derivative of ordinary calculus. Explicitly, it is a linear map from the tangent space of M at x to the tangent space of N at ?(x). Hence it can be used to push forward tangent vectors on M to tangent vectors on N. The differential of a map ? is also called, by various authors, the derivative or total derivative of ?, and is sometimes itself called the pushforward. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1303-4427-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamed sum) is the colimit of a diagram consisting of two morphisms f : Z ? X and g : Z ? Y with a common domain: it is the colimit of the span X leftarrow Z rightarrow Y. Here are some examples of pushouts in familiar categories. Note that in each case, we are only providing a construction of an object in the isomorphism class of pushouts; as mentioned above, there may be other ways to construct it, but they are all equivalent.The pushout is the categorical dual of the pullback. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1303-4439-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to piece together objects (puzzle pieces) in a logical way in order to come up with the desired shape, picture or solution. Puzzles are often contrived as a form of entertainment, but they can also stem from serious mathematical or logistical problems — in such cases, their successful resolution can be a significant contribution to mathematical research. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-2282-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base. An n-sided pyramid will have n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are self-dual. When unspecified, the base is usually assumed to be square. If the base is a regular polygon and the apex is above the center of the polygon, an n-gonal pyramid will have Cnv symmetry. Pyramids are a subclass of the prismatoids. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1303-4458-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team "should" have won based on the number of runs they scored and allowed. Comparing a team's actual and Pythagorean winning percentage can be used to evaluate how lucky (or alternatively how "clutch") that team was (by examining the variation between the two winning percentages). The term is derived from the formula's resemblance to the Pythagorean theorem. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1304-9733-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples. For instance, the triangle with sides a = b = 1 and c = ?2...

ISBN: 978-6-1303-4474-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae (see Angle sum and difference identities) it is the basic relation among the sin and cos functions from which all others may be derived. If the trigonometric functions are defined in terms of the unit circle, the proof is immediate: given an angle ?, there is a unique point P on the unit circle centered at the origin in the Euclidean plane at an angle ? from the x-axis, and cos ?, sin ? are respectively the x- and y-coordinates of P. By definition of the unit circle, the sum of the squares of these coordinates is 1,...

ISBN: 978-6-1303-0642-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Pythagore serait ne aux environs de 580 av. J.-C. a Samos, une ile de la mer Egee au Sud-Est de la ville d'Athenes ; on etablit sa mort vers 497 av. J.-C., a l'age de 83 ans. Le nom de Pythagore ou Pyth-agore, etymologiquement « celui qui a ete annonce par la Pythie », decoule de l'annonce de sa naissance faite a son pere lors d'un voyage a Delphes. La vie enigmatique de Pythagore permet difficilement d'eclaircir l'histoire de ce reformateur religieux, mathematicien, philosophe et thaumaturge. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1308-6683-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, in the area of combinatorics and special functions, a q-analog is, roughly speaking, a theorem or identity in the variable q that gives back a known result in the limit, as q ? 1 (from inside the complex unit circle in most situations). The earliest q-analog studied in detail is the basic hypergeometric series, which was introduced in the 19th century.q-analogs find applications in a number of areas, including the study of fractals and multi-fractal measures, and expressions for the entropy of chaotic dynamical systems. The relationship to fractals and dynamical systems results from the fact that many fractal patterns have the symmetries of Fuchsian groups in general (see, for...

ISBN: 978-6-1303-1636-5
Издательство: Книга по требованию
Дата выхода: июль 2011