Over the last sixty years, the study of network flows has led to some of the most appealing and useful results in applied mathematics, including efficient algorithms for certain linear and combinatorial optimization problems. This text continues this journey and presents a novel approach to relate binary-constrained integer programs to a new class of (semi-)simultaneous network flows. The exposition of the material is fully self-contained and first provides a thorough review of the most important concepts from both integer and network flow programming, as well as the theory of computational complexity. All new results are developed and explained in much detail, illustrated on over 20 examples and more than 30 figures, and used for the...

ISBN: 978-3-6390-7228-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A semi-Markov process is a process that changes states according to a discrete time Markov Chain but stays at each state for a random amount of time with distribution Hn. A Continuous Time Markov Chain is a special case of a semi-Markov process in which the transition times are exponentially distributed with rate ?. A Markov process, named after the Russian mathematician Andrey Markov, is a mathematical model for the random evolution of a memoryless system, that is, one for which the likelihood of a given future state, at any given moment, depends only on its present state, and not on any past states. In a common description, a stochastic process with the Markov property, or memorylessness, is...

ISBN: 978-6-1303-3366-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A continuous-time stochastic process is called a semi-Markov process or 'Markov renewal process' if the embedded jump chain (the discrete process registering what values the process takes) is a Markov Chain, and where the holding times (time between jumps) are random variables with any distribution, whose distribution function may depend on the two states between which the move is made. A semi-Markov process where all the holding times are exponentially distributed is called a continuous time Markov chain/process (CTMC). Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1304-9229-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, a semialgebraic set is a subset S of real n-dimensional space defined by a finite sequence of polynomial equations and inequalities; or any finite union of such sets. Such sets are studied as an extension of real algebraic geometry, in which only equations would be used, and in mathematical logic. Similarly to algebraic subvarieties, finite unions and intersections of semialgebraic sets are still semialgebraic sets. Furthermore, unlike subvarieties, the complement of a semialgebraic set is again semialgebraic. Finally, and most importantly, the Tarski–Seidenberg theorem says that they are also closed under the projection operation:...

ISBN: 978-6-1311-5803-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, especially in real algebraic geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraic set. Let U be an open subset of Rn for some n. A semialgebraic function on U is defined to be a continuous real-valued function on U whose restriction to any semialgebraic set contained in U has a graph which is a semialgebraic subset of the product space RnxR. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-5787-5
Издательство: Книга по требованию
Дата выхода: июль 2011

We study semiclassical properties of quantum systems with internal degrees of freedom. While translational degrees of freedom are described as coordinates on the cotangent bundle of a configuration manifold, the internal ones find their classical description on more general symplectic manifolds. The quantum space for the translational degrees of freedom, square integrable functions on the configuration space, has to be "tensored" with the representation space for the internal ones. Consequently, quantum observables are operators that take values in the endomorphisms of the representation space for internal degrees of freedom. One part of this work is concerned with the generalization of semiclassical techniques to the non-scalar setting....

ISBN: 978-3-6390-3201-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Semidefinite embedding (SDE) or maximum variance unfolding (MVU) is an algorithm in computer science, that uses semidefinite programming to perform non-linear dimensionality reduction of high-dimensional vectorial input data. Non-linear dimensionality reduction algorithms attempt to map high-dimensional data onto a low-dimensional Euclidean vector space. Maximum variance Unfolding is a member of the manifold learning family, which also include algorithms such as isomap and locally linear embedding. In manifold learning, the input data is assumed to be sampled from a low dimensional manifold that is embedded inside of a higher dimensional vector space. The main intuition behind MVU is to exploit...

ISBN: 978-6-1304-9256-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, specifically in the area of abstract algebra known as group theory, a semidirect product is a particular way in which a group can be put together from two subgroups, one of which is a normal subgroup. A semidirect product is a generalization of a direct product. A semidirect product is a cartesian product as a set, but with a particular multiplication operation. If G is the semidirect product of the normal subgroup N and the subgroup H, and both N and H are finite, then the order of G equals the product of the orders of N and H. Note that, as opposed to the case with the direct product, a semidirect product of two groups is not, in general, unique; if G and G? are two groups...

ISBN: 978-6-1305-7675-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function over the intersection of the cone of positive semidefinite matrices with an affine space. Semidefinite programming is a relatively new field of optimization which is of growing interest for several reasons. Many practical problems in operations research and combinatorial optimization can be modeled or approximated as semidefinite programming problems. In automatic control theory, SDP's are used in the context of linear matrix inequalities. SDPs are in fact a special case of cone programming and can be efficiently solved by...

ISBN: 978-6-1311-5817-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, a semifield is an algebraic structure with two binary operations, addition and multiplication, which is similar to the field, but with some axioms relaxed. There are at least two conflicting conventions of what constitutes a semifield. In projective geometry and finite geometry (MSC 51A, 51E, 12K10), a semifield is a ring (S,+,·) where (S,+) is an abelian group with identity element 0, the multiplication is distributive with respect to the addition on the left and on the right, and (S,·) is a division ring that is not assumed to be commutative or associative. This structure is a special case of a quasifield. If S is a finite set,...

ISBN: 978-6-1311-6093-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. In mathematics, a semigroup is an algebraic structure consisting of a nonempty set S together with an associative binary operation. In other words, a semigroup is an associative magma. The terminology is derived from the anterior notion of a group. A semigroup differs from a group in that for each of its elements there may not exist an inverse; further, there may not exist an identity element. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1305-7739-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In algebra and theoretical computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such a way that the product of two elements of the semigroup (using the semigroup operation) is associated with the composite of the two corresponding transformations. The terminology conveys the idea that the elements of the semigroup are acting as transformations of the set. From an algebraic perspective, a semigroup action is a generalization of the notion of a group action in group theory. From the computer science point of view, semigroup actions are closely related to automata: the set models the state of the...

ISBN: 978-6-1305-7704-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, in semigroup theory, an involution in a semigroup is a transformation of the semigroup which is its own inverse and which is an anti-automorphism of the semigroup. A semigroup in which an involution is defined is called a semigroup with involution. In the multiplicative semigroup of real square matrices of order n, the map which sends a matrix to its transpose is an involution. In the free semigroup generated by a nonempty set the operation which reverses the order of the letters in a word is an involution. A semigroup with an involution is also called a *– semigroup. Данное издание не является оригинальным. Книга печатается...

ISBN: 978-6-1305-7714-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a semigroup is an algebraic structure consisting of a nonempty set S together with an associative binary operation. In other words, a semigroup is an associative magma. The terminology is derived from the anterior notion of a group. A semigroup differs from a group in that for each of its elements there may not exist an inverse; further, there may not exist an identity element. The binary operation of a semigroup is most often denoted multiplicatively: x * y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair (x, y). Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1303-3057-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a join-semilattice is a partially ordered set which has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset. Every join-semilattice is a meet-semilattice in the inverse order and vice versa. Semilattices can also be defined algebraically: join and meet are associative, commutative, idempotent binary operations, and any such operation induces a partial order (and the respective inverse order) such that the result of the operation for any two elements is the least upper bound (or greatest lower bound) of the elements with respect to this partial...

ISBN: 978-6-1305-7767-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In the branch of mathematics known as order theory, a semimodular lattice, is a lattice that satisfies the following condition: Semimodular law a ? b <: a implies b <: a ? b. The notation a <: b means that b covers a, i.e. a < b and there is no element c such that a < c < b. An atomistic (hence algebraic) semimodular bounded lattice is called a matroid lattice because such lattices are equivalent to (simple) matroids. An atomistic semimodular bounded lattice of finite length is called a geometric lattice and corresponds to a matroid of finite rank. Semimodular lattices are also known as upper semimodular lattices; the dual notion is...

ISBN: 978-6-1311-5833-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In probability theory, a real valued process X is called a semimartingale if it can be decomposed as the sum of a local martingale and an adapted finite-variation process. Semimartingales are "good integrators", forming the largest class of processes with respect to which the It? integral can be defined. The class of semimartingales is quite large (including, for example, all continuously differentiable processes, Brownian motion and Poisson processes). Submartingales and supermartingales together represent a subset of the semimartingales. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1304-9275-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, the Seminaire de Geometrie Algebrique du Bois Marie was an influential seminar run by Alexander Grothendieck. It was a unique phenomenon of research and publication outside of the main mathematical journals that ran from 1960 to 1969 at the IHES near Paris. (The name came from the small wood on the estate in Bures-sur-Yvette where the IHES was located from 1962.) The seminar notes were eventually published in twelve volumes, all except one in the Springer Lecture Notes in Mathematics series. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1311-5844-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! The Seminaire Nicolas Bourbaki (Bourbaki Seminar) is a series of seminars (in fact public lectures with printed notes distributed) that has been held in Paris since 1948. It is one of the major institutions of contemporary mathematics, and a barometer of mathematical achievement, fashion, and reputation. It is named after Nicolas Bourbaki, a group of French and other mathematicians of variable membership. The Poincare Seminars are a series of talks on physics inspired by the Bourbaki seminars on mathematics. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1311-6061-5
Издательство: Книга по требованию
Дата выхода: июль 2011

This dissertation comes to answer an increasing need for an analysis tool that enables to analyze and evaluate electronic mathematical texts which populate the internet and serve the mathematics teacher as additional texts for school students. These texts are web based and include dynamic components which the user can work with, in order to learn mathematics. The dissertation contains two parts: the first part provides an analyzing system for electronic mathematical texts. This analyzing system was founded on Morris's (1938) formal semiotics and Halliday's (1985) and Morgan's (1998) social semiotics. The second part of the dissertation describes preservice teachers' work with the semiotic system for analyzing and evaluating electronic...

ISBN: 978-3-6391-4288-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. A semiperfect number is necessarily either perfect or abundant; an abundant number which is not semiperfect is called a weird number. With the exception of 2, all primary pseudoperfect numbers are semiperfect. Every practical number that is not a power of two is semiperfect. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1311-5852-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, especially in the area of algebra known as ring theory, a semiprimitive ring is a type of ring more general than a semisimple ring, but where simple modules still provide enough information about the ring. Important rings such as the ring of integers are semiprimitive, and an artinian semiprimitive ring is just a semisimple ring. Semiprimitive rings can be understood as subdirect products of primitive rings, which are described by the Jacobson density theorem. The quotient of every ring by its Jacobson radical is semiprimitive, allowing every ring to be understood to some extent through...

ISBN: 978-6-1311-5641-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a semiprime (also called biprime or 2-almost prime, or pq number) is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... (sequence A001358 in OEIS). As of September 2008, the largest known semiprime is (243,112,609 ? 1)2, which has over 25 million digits. This is the square of the largest known prime. The square of any prime number is a semiprime, so the largest known semiprime will always be the square of the largest known prime, unless the factors of the semiprime are not known. It is conceivable that a way could be found to prove a larger number is a semiprime without...

ISBN: 978-6-1311-6025-7
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. Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non-abelian Lie algebras g whose only ideals are {0} and g itself. A consequence of semisimplicity is a theorem due to Weyl: every finite-dimensional representation is completely reducible; that is for every invariant subspace of the representation there is an invariant complement. While in other contexts, complete reducibility is equivalent to being semisimple, for Lie algebras the two...

ISBN: 978-6-1311-5911-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring which is a semisimple module over itself is known as an artinian semisimple ring. Some important rings, such as group rings of finite groups over fields of characteristic zero, are semisimple rings. An artinian ring is initially understood via its largest semisimple quotient. The structure of artinian semisimple rings is well understood by the Artin–Wedderburn theorem, which exhibits these rings as direct products of matrix rings. Данное издание не является...

ISBN: 978-6-1305-7770-4
Издательство: Книга по требованию
Дата выхода: июль 2011