High Quality Content by WIKIPEDIA articles! In complex analysis, the open mapping theorem states that if U is a connected open subset of the complex plane C and f : U ? C is a non-constant holomorphic function, then f is an open map (i.e. it sends open subsets of U to open subsets of C). The open mapping theorem points to the sharp difference between holomorphy and real-differentiability. On the real line, for example, the differentiable function f(x) = x2 is not an open map, as the image of the open interval (?1,1) is the half-open interval [0,1). The theorem for example implies that a non-constant holomorphic function cannot map an open disk onto a portion of any real line embedded in the complex plane. Данное издание...

ISBN: 978-6-1313-0486-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! OpenMath is the name of a markup language for specifying the meaning of mathematical formulae. Among other things, it can be used to complement MathML, a standard which mainly focuses on the presentation of formulae, with information about their semantic meaning. OpenMath can be encoded in XML or in a binary format.OpenMath consists of the definition of "OpenMath Objects", an abstract datatype for describing the logical structure of a mathematical formula, and the definition of "OpenMath Content Dictionaries", or collections of names for mathematical concepts. The names available from the latter type of collections are specifically intended for use in extending MathML, and conversely, a basic...

ISBN: 978-6-1313-0586-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation. The idea of representing the processes of calculus, derivation and integration, as operators has a long history that goes back to Gottfried Leibniz. The mathematician Louis Francois Antoine Arbogast was one of the first to manipulate these symbols independently of the function to which they were applied. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1305-1448-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In programming languages and mathematical notation, the associativity (or fixity) of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses. Operators may be left-associative, right-associative or non-associative. The associativity and precedence of an operator depends on the programming language in question. Consider the expression a ~ b ~ c. If the operator ~ has left associativity, this expression would be interpreted as (a ~ b) ~ c and evaluated left-to-right. If the operator has right associativity, the expression would be interpreted as a ~ (b ~ c) and evaluated right-to-left. If the operator is non-associative, the...

ISBN: 978-6-1313-0708-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! An operand is a quantity on which an operation is performed.[1] The following arithmetic expression shows an example of operators and operands: 3 + 6 = 9 In the above example, '+' is the symbol for the operation called addition. The operand '3' is one of the inputs (quantities) followed by the addition operator, and the operand '6' is the other input necessary for the operation. The result of the operation is 9. (The number '9' is also called the sum of the addend, 3 and 6.) An operand, then, is also referred to as "one of the inputs (quantities) for an operation". Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1311-3031-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the operator norm is a means to measure the "size" of certain linear operators. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.Every real m-by-n matrix yields a linear map from Rn to Rm. One can put several different norms on these spaces, as explained in the article on norms. Each such choice of norms gives rise to an operator norm and therefore yields a norm on the space of all m-by-n matrices. Examples can be found in the article on matrix norms. If we specifically choose the Euclidean norm on both Rn and Rm, then we obtain the matrix norm which to a given matrix A assigns the square root of the largest...

ISBN: 978-6-1313-0752-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, an operator is a type of function. Often, an "operator" is a function which acts on functions to produce other functions (the sense in which Oliver Heaviside used the term); or it may be a generalization of such a function, as in linear algebra, where some of the terminology reflects the origin of the subject in operations on the functions which are solutions of differential equations. An operator can perform a function on any number of operands (inputs) though most often there is only one operand. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1305-1464-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In its simplest meaning in mathematics and logic, an operation is an action or procedure which produces a new value from one or more input values. There are two common types of operations: unary and binary. Unary operations involve only one value, such as negation and trigonometric functions. Binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, and exponentiation. Operations can involve mathematical objects other than numbers. The logical values true and false can be combined using logic operations, such as and, or, and not. Vectors can be added and subtracted. Rotations can be combined using the function composition operation,...

ISBN: 978-6-1305-1436-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, operator theory is the branch of functional analysis that focuses on bounded linear operators, but which includes closed operators and nonlinear operators. Operator theory also includes the study of algebras of operators.Single operator theory deals with the properties and classification of single operators. For example, the classification of normal operators in terms of their spectra falls into this category. The theory of operator algebras brings algebras of operators such as C*-algebras to the fore. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1313-0775-1
Издательство: Книга по требованию
Дата выхода: июль 2011

In this monograph, we consider natural operations on directed graphs. And we find the connections between our operations on graphs and the groupoid-perations on "graph" groupoids. Remark that we cannot guarantee the (algebraic or categorial) groupoids generated by the grouopoid-operations; sum, product, quotient or complement; of graph groupoids are again graph groupoids. By defining suitable operations on graphs, we can conclude the groupoids generated by the groupoid-operations of graph groupoids are again graph groupoids; for example, the product groupoid of two graph groupoids is groupoid-isomorphic to the graph groupoid of the product graph, etc. This provides another bridge connceting combinatorics and algebra. Recently, the von...

ISBN: 978-3-8383-5271-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In physics, an operator is a function acting on the space of physical states. As a result of its application on a physical state, another physical state is obtained, very often along with some extra relevant information. The simplest example of the utility of operators is the study of symmetry. Because of this, they are a very useful tool in classical mechanics. In quantum mechanics, on the other hand, they are an intrinsic part of the formulation of the theory. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-3726-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(H) of bounded linear operators on a Hilbert space H.There are many topologies that can be defined on B(H) besides the ones used above. These topologies are all locally convex, which implies that they are defined by a family of seminorms. In analysis, a topology is called strong if it has many open sets and weak if it has few open sets, so that the corresponding modes of convergence are, respectively, strong and weak. (In topology proper, these terms can suggest the opposite meaning, so strong and weak are replaced with, respectively, fine and coarse.) The diagram on the right...

ISBN: 978-6-1313-0791-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings. Although it is usually classified as a branch of functional analysis, it has direct applications to representation theory, differential geometry, quantum statistical mechanics and quantum field theory. Such algebras can be used to study arbitrary sets of operators with little algebraic relation simultaneously. From this point of view, operator algebras can be regarded as a generalization of spectral theory of a single operator. In general operator algebras are non-commutative rings. Данное издание не...

ISBN: 978-6-1313-0630-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, operator K-theory is a variant of K-theory on the category of Banach algebras (In most applications, these Banach algebras are C*-algebras). Its basic feature that distinguishes it from algebraic K-theory is that it has a Bott periodicity. So there are only two K-groups, namely K0, equal to algebraic K0, and K1. As a consequence of the periodicity theorem, it satisfies excision. This means that it associates to an extension of C*-algebras an exact cyclic 6-term-sequence. Operator K-theory is a generalization of topological K-theory, defined by means of vector bundles on locally compact Hausdorff spaces. Here, an n-dimensional vector bundle over a topological space X is...

ISBN: 978-6-1313-0729-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! En mathematiques l'adjoint d'un operateur, quand il existe, est un nouvel operateur defini sur un espace vectoriel sur le corps des nombres reels ou complexes, muni d'un produit scalaire. Un tel espace est qualifie de prehilbertien. Si l'operateur initial est continu et si l'espace vectoriel est complet l'adjoint est toujours defini. Cette configuration se produit toujours en dimension finie. L'application qui, a un operateur associe son adjoint, est semilineaire continue bijective. Cette fonction est meme une isometrie involutive. L'espace des operateurs se decompose en deux sous-espaces vectoriels supplementaires orthogonaux. Ce sont des espaces propres de l'application associes aux valeurs...

ISBN: 978-6-1316-7559-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In logic and mathematics, a finitary operation is a function of the form : X1 x … x Xk -> Y. The sets Xj are the called the domains of the operation, the set Y is called the codomain of the operation, and the fixed non-negative integer k is called the arity of the operation. An operation of arity zero, called a nullary operation, is simply an element of the codomain Y. An operation of arity k is called a k-ary operation. Thus a k-ary operation is a (k+1)-ary relation that is functional on its first k domains. Elements of the functional domains are called arguments. Elements of the codomain are called values. Данное издание не является оригинальным....

ISBN: 978-6-1311-3041-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Operad theory is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity. Operads generalize the various associativity properties already observed in algebras and coalgebras such as Lie algebras or Poisson algebras by modeling computational trees within the algebra. Algebras are to operads as group representations are to groups. Originating from work in algebraic topology by Boardman and Vogt, and J. Peter May (to whom their name is due), it has more recently found many applications, drawing for example on work by Maxim Kontsevich on graph homology. Данное издание...

ISBN: 978-6-1313-0596-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the Oppenheim conjecture in the area of diophantine approximation concerns representations of numbers by real quadratic forms in several variables. It was formulated in 1929 by Alexander Oppenheim and later the conjectured property was further strengthened by Davenport and Oppenheim. Initial research on this problem took the number n of variables to be large, and applied a version of the Hardy-Littlewood circle method. The definitive work of Margulis, settling the conjecture in the affirmative, used methods arising from ergodic theory and the study of discrete subgroups of semisimple Lie groups. Данное издание не является оригинальным....

ISBN: 978-6-1313-0804-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In category theory, a branch of mathematics, the opposite category or dual category Cop of a given category C is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism. Doing the reversal twice yields the original category, so the opposite of an opposite category is the original category itself. In symbols, Cop op = C.In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions respectively to objects linked in diagrams by morphisms or arrows. One of the simplest examples of a category (which is a very important concept in topology) is that of groupoid, defined as...

ISBN: 978-6-1313-0816-1
Издательство: Книга по требованию
Дата выхода: июль 2011

The “canning problem” occurs when a process has a minimum specification such that any product produced below that minimum incurs a scrap/rework cost and any product over the minimum incurs a “give-away” cost. The objective of the canning problem is to determine the target mean for production that minimizes both of these costs. An upper screening limit can also be determined; above which give-away cost is so high that reworking the product maximizes net profit. Continuous, finite range space distributions are considered, specifically the Uniform and Triangular distributions. For the Uniform distribution, an optimum upper screening limit and an optimum value for the mean fill level is found using three net profit models. Each model...

ISBN: 978-3-6391-3540-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In statistics, an optimality criterion provides a measure of the fit of the data to a given hypothesis. The selection process is determined by the solution that optimizes the criteria used to evaluate the alternative hypotheses. The term has been used to identify the different criteria that are used to evaluate a phylogenetic tree and include maximum likelihood, Bayesian, maximum parsimony, and minimum evolution. For example, in order to determine the best topology between two phylogenetic trees using the maximum likelihood optimality criterion, one would calculate the maximum likelihood score of each tree and choose the one that had the better score. However, different optimality criteria can...

ISBN: 978-6-1313-0926-7
Издательство: Книга по требованию
Дата выхода: июль 2011

In dieser Dissertation wird eine Problemstellung der Optimalen Steuerung aus dem Bereich der Linearen Elastizitatstheorie behandelt. Die Arbeit beinhaltet folgende Schwerpunkte: Modellierung der Problemstellung, Formulierung der Optimalsteuerungsprobleme fur den zeitunabhangigen bzw. zeitabhangigen Fall, die Herleitung der notwendigen Bedingungen fur eine ermittelte optimale Losung, die Berechnung von numerischen Losungen sowie deren Uberprufung auf Erfullung der notwendigen Bedingungen. In der Modellierung werden Gleichungen zur Bestimmung der Deformation einer Zylinderschale unter rotations-symmetrischer Krafteinwirkung aus Grundgleichungen der Mechanik hergeleitet. Fur die Formulierung der Optimalsteuerungsprobleme (fur Praxis...

ISBN: 978-3-8381-2067-6
Издательство: Книга по требованию
Дата выхода: июль 2011

Seitdem es Autos gibt, schafft der standig zunehmende Gerauschpegel nicht zu uberhorende Probleme. Ein Teil des Autolarms kann vermieden werden, wenn es gelingen wird, moglichst "leisere" Reifen bzw. Reifenprofile zu konstruieren. Die Herausforderung besteht darin, ein Reifenprofil zu generieren, das optimale Gerauscheigenschaften hat. Wie soll man aber das Optimum finden, wenn selbst ein Supercomputer Jahre brauchen wird, um alle moglichen Profile auszuprobieren? Diese Aufgabe kann mit Hilfe eines heuristischen Verfahren gelost werden. Der Autor Andrei Loskutov modelliert das Problem mathematisch und untersucht dessen Losbarkeit. Dabei wird die Fourieranalyse als Basis fur die akustische Bewertung eines Reifens benutzt. Nach einer...

ISBN: 978-3-8364-6628-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum-variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and...

ISBN: 978-6-1303-3748-3
Издательство: Книга по требованию
Дата выхода: июль 2011

This study deals with the optimal control problems of the glass tube drawing processes where the aim is to control the cross-sectional area (circular) of the tube by using the adjoint variable approach. The process of tube drawing is modeled by four coupled nonlinear partial differential equations. These equations are derived by the axisymmetric Stokes equations and the energy equation by using the approach based on asymptotic expansions with inverse aspect ratio as small parameter. Existence and uniqueness of the solutions of stationary isothermal model is also proved. By defining the cost functional, we formulated the optimal control problem. Then Lagrange functional associated with minimization problem is introduced and the first and...

ISBN: 978-3-6392-5797-7
Издательство: Книга по требованию
Дата выхода: июль 2011