Security of data by means of cryptography is becoming more and more important in many areas of our lives. Public-key cryptosystems (PKC) form an important part of cryptography as they allow convenient and secure communication between all users. The objective is to develop PKCs that provide a high level of security while being fast and easy to use. The author Robert Niebuhr analyses the application of Algebraic-Geometric Codes (AGC) in Cryptographic Systems. Starting with a brief discussion of Algebraic Geometry and the general construction of PKCs, he shows how to use AGC including encoding, decoding and error-correction. To demonstrate the concrete application he develops a Cryptosystem using the McEliece Scheme and evaluates its...
ISBN: 978-3-6390-4517-8
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! L'algebre, mot d'origine arabe al-jabr, est la branche des mathematiques qui etudie, d'une facon generale, les structures algebriques. L'etude des structures algebriques peut etre faite de maniere unifiee dans la cadre de l'algebre universelle. L'etude epistemologique de l'algebre a ete introduite par Jules Vuillemin. Les anciens Babyloniens et Egyptiens savaient deja resoudre des problemes qui peuvent etre traduits en equations du premier ou second degre. Par exemple, le Papyrus Rhind (conserve au British Museum de Londres, il date de -1650, ere chretienne) comporte l'enonce suivant : On doit diviser 100 miches de pain entre dix hommes comprenant un navigateur, un contremaitre et un gardien,...
ISBN: 978-6-1308-7271-7
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High Quality Content by WIKIPEDIA articles! L’algebre lineaire est la branche des mathematiques qui s'interesse a l'etude des espaces vectoriels (ou espaces lineaires), de leurs elements les vecteurs, des transformations lineaires et des systemes d'equations lineaires (theorie des matrices). Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1316-8322-0
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. In category theoretic terms, an algebraic group is a group object in the category of algebraic varieties. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1307-1321-8
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
In mathematics, an algebraic variety is the set of solutions of a system of polynomial equations. Algebraic varieties are one of the central objects of study in classical (and to some extent, modern) algebraic geometry. The word "variety" is employed in the sense of a mathematical manifold, for which, in Romance languages, cognates of the word "variety" are used. Historically, the fundamental theorem of algebra established a link between algebra and geometry by saying that a monic polynomial in one variable over the complex numbers is determined by the set of its roots, which can be considered a geometric object. Building on this result, Hilbert's Nullstellensatz provides a fundamental correspondence between ideals of polynomial rings...
ISBN: 978-6-1307-8603-8
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! En mathematiques, l’algebre multilineaire etend les methodes de l’algebre lineaire. Tout comme l’algebre lineaire est batie sur le concept d’un vecteur et developpe la theorie des espaces vectoriels, l’algebre multilineaire est batie sur le concept d’un tenseur et developpe la theorie des espaces tensoriels. Dans les applications, de nombreux types de tenseurs surviennent. La theorie se veut exhaustive et comprend un certain nombre d'espaces et l'expose de leurs relations. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1325-8426-7
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! En mathematiques, les algebres de Clifford sont des algebres associatives importantes au sein des theories des formes quadratiques, des groupes orthogonaux et en physique. Elles peuvent etre vues comme l'une des generalisations possibles des nombres complexes et des quaternions. Elles ont ete nommees en l'honneur du mathematicien anglais William Kingdon Clifford. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1325-8435-9
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! En mathematiques, une algebre geometrique est une algebre multilineaire avec une interpretation geometrique (le terme est aussi utilise dans un sens plus general pour decrire l'etude et l'application de ces algebres : l'algebre geometrique est l'etude des algebres geometriques). Officieusement, une algebre geometrique est une algebre de Clifford qui inclut un produit geometrique. L'algebre geometrique est utile dans les problemes de physique qui impliquent des rotations, des phases ou des nombres imaginaires. Les partisans de l'algebre geometrique disent qu'elle fournit une description plus compacte et intuitive de la mecanique quantique et classique, de la theorie electromagnetique et de la...
ISBN: 978-6-1326-3324-8
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
En mathematiques, une algebre de Lie, nommee en l'honneur du mathematicien Sophus Lie, est un espace vectoriel qui est muni d'un crochet de Lie bilineaire, antisymetrique et qui verifie l'identite de Jacobi. Une algebre de Lie est un cas particulier d'algebre sur un corps. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1326-3309-5
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! The algebra of sets develops and describes the basic properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality (mathematics) and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1326-8310-6
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra. It is one of the youngest combinatorial disciplines. Thus, in the preface to his Combinatorial Theory, published in 1979, Martin Aigner wrote about "growing consensus that combinatorics should be divided into three parts", without even mentioning algebraic combinatorics by name. Through the early or mid 1990s, typical combinatorial objects of interest in algebraic combinatorics either admitted a lot of symmetries or possessed a rich algebraic...
ISBN: 978-6-1327-2899-9
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! In the algebraic axiomatization of probability theory, the primary concept is not that of probability of an event, but rather that of a random variable. Probability distributions are determined by assigning an expectation to each random variable. The measurable space and the probability measure arise from the random variables and expectations by means of well-known representation theorems of analysis. One of the important features of the algebraic approach is that apparently infinite-dimensional probability distributions are not harder to formalize than finite-dimensional ones. Данное издание не является оригинальным. Книга печатается по...
ISBN: 978-6-1327-4269-8
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Дата выхода: июль 2011
Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics. Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1327-6045-6
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Дата выхода: июль 2011
Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! In computer programming, particularly functional programming and type theory, an algebraic data type is a datatype each of whose values is data from other datatypes wrapped in one of the constructors of the datatype. Any wrapped datum is an argument to the constructor. In contrast to other datatypes, the constructor is not executed and the only way to operate on the data is to unwrap the constructor using pattern matching. The most common algebraic data type is a list with two constructors: Nil or [] for an empty list, and Cons, ::, or : for the combination of a new element with a shorter list. Special cases of algebraic types are product types i.e. tuples and records, sum types or tagged...
ISBN: 978-6-1327-7200-8
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! Algebraic Modeling Languages (AML) are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation (i.e. large scale optimization type problems). One particular advantage of AMLs like AIMMS, AMPL, GAMS, LPL and OPL is the similarity of its syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization, which is supported by certain language elements like sets, indices, algebraic expressions, powerful sparse index and data handling variables, constraints with arbitrary names. The algebraic formulation of a model does not...
ISBN: 978-6-1327-9627-1
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Дата выхода: июль 2011
Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1328-0210-1
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! The algebraic connectivity of a graph G is the second-smallest eigenvalue of the Laplacian matrix of G. This eigenvalue is greater than 0 if and only if G is a connected graph. This is a corollary to the fact that the number of times 0 appears as an eigenvalue in the Laplacian is the number of connected components in the graph. The magnitude of this value reflects how well connected the overall graph is, and has been used in analysing the synchronizability of networks. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1328-0769-4
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Дата выхода: июль 2011
Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! In mathematics, an algebraic set over a field K is the set of solutions in Kn of a set of simultaneous equations. Algebraic sets are the primitive objects of algebraic geometry. To get the standard concept of algebraic variety, however, two extra aspects need to be introduced: K should be an algebraically closed field, for example the complex numbers. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1328-1057-1
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Дата выхода: июль 2011
Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! In number theory, an algebraic integer is a complex number that is a root of some monic polynomial (leading coefficient 1) with coefficients in ?. The set of all algebraic integers is closed under addition and multiplication and therefore is a subring of complex numbers denoted by A. The ring A is the integral closure of regular integers ? in complex numbers. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1328-1314-5
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Дата выхода: июль 2011
Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! In mathematics, an algebraic space is a generalization of the schemes of algebraic geometry introduced by Michael Artin for use in deformation theory. Intuitively, an algebraic space is a scheme modulo a "nice" equivalence relation; the resulting category of algebraic spaces extends the category of schemes and allows to carry out several natural constructions that are needed for example in deformation theory or in the construction of moduli spaces but are not possible in the smaller category of schemes. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...
ISBN: 978-6-1328-2391-5
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Дата выхода: июль 2011
Frederic P. Miller, Agnes F. Vandome, John McBrewster
In mathematical logic, algebraic logic is the study of logic presented in an algebraic style. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1306-5981-3
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Дата выхода: июль 2011
Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
High Quality Content by WIKIPEDIA articles! In mathematics, an algebraic cycle on an algebraic variety V is, roughly speaking, a homology class on V that is represented by a linear combination of subvarieties of V. Therefore the algebraic cycles on V are the part of the algebraic topology of V that is directly accessible in algebraic geometry. With the formulation of some fundamental conjectures in the 1950s and 1960s, the study of algebraic cycles became one of the main objectives of the algebraic geometry of general varieties. The nature of the difficulties is quite plain: the existence of algebraic cycles is easy to predict, but the methods of construction of them are currently deficient. The major conjectures on algebraic cycles...
ISBN: 978-6-1311-9103-9
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Imran Anwar, Ghulam Qanber Abbasi, Waqas Ahmad Baig
The aim of this book is to explore the algebraic and combinatorial properties of simplicial complexes. Let S = k[x1, x2, ..., xn] be a polynomial ring over an infinite field k. Note that, there is a natural bijection between the square-free monomial ideals (so called non facet ideals) and simplicial complexes introduced by R.P. Stanley. Later Faridi introduced another correspondence betweeen the square-free monomial ideals (so called facet ideals) and simplicial complexes. So, corresponding to a square-free monomial ideal I in S, one can consider I as the facet ideal of one simplicial complex and as the non-face ideal for another . In this book, we mainly discuss the invariants between these two simplicail complexes. Also we have discuss...
ISBN: 978-3-8383-5895-6
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Frederic P. Miller, Agnes F. Vandome, John McBrewster
High Quality Content by WIKIPEDIA articles! In mathematics, in the realm of group theory, a group A is algebraically closed if any finite set of equations and inequations that "make sense" in A already have a solution in A . This idea will be made precise later in the article. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.
ISBN: 978-6-1337-7781-1
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Дата выхода: июль 2011
Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Algebraic Code Excited Linear Prediction (ACELP) is a patented speech coding algorithm by VoiceAge Corporation in which a limited set of pulses is distributed as excitation to linear prediction filter. The ACELP method is widely employed in current speech coding standards such as AMR, EFR, AMR-WB (G.722.2), VMR-WB, EVRC, EVRC-B, SMV, TETRA, PCS 1900, MPEG-4 CELP and ITU-T G-series standards G.729, G.729.1 (first coding stage) and G.723.1.The ACELP algorithm is also used in the proprietary ACELP.net codec. ACELP is a patented technology and registered trademark of VoiceAge Corporation[6] in Canada and/or other...
ISBN: 978-6-1346-1978-3
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Дата выхода: июль 2011
