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Radical Classes & Semi-Simple Classes of Rings

für 53.10€ kaufen ···· Rheinberg-Buch.de - Bücher, eBooks, DVD & Blu-ray
The concept of a radical was introduced by J. H. M. Wedderburn in 1908, for determination of structures of algebras and later on various radicals have been proposed by Artin, Baer, Jacobson, Brown-McCoy, Levitzki etc. for study of rings in the forties. The general theory of radicals was initiated by Kurosh (1953) and Amitsur in the early fifties. Andrunakievic, Sulinski, Divinsky and many others have followed up the works of Kurosh and Amitsur. The first example of a radical was the nilradical introduced in (Köthe 1930), based on a suggestion in (Wedderburn 1908). In the next few years several other radicals were discovered, of which the most important example is the Jacobson radical. The general theory of radicals was defined independently by (Amitsur 1952, 1954, 1954b) and Kurosh (1953). ····· 10361664

Riemann-Hilbert Problem and Quantum Field Theory

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In this monograph, firstly, we introduce integrable renormalization formalism as a method of studying quantum integrable systems underlying the Hopf algebra of Feynman diagrams. Besides we consider an alternative approach to these systems which is connected with the Lie group of diffeographisms of a physical theory. Secondly, we consider the process which allows us to develop the Connes-Marcolli approach to the study of nonperturbative QFT. For this purpose, at the first step, we work on a new Hall tree type framework of the universal Hopf algebra of renormalization which can be lifted onto the level of universal counterterms. At the second step, we associate a categorical construction to each equation DSE which can encode this class of equations with respect to a special family of connections. At the third step, we consider the universality of the category of the equisingular flat vector bundles at the level of DSEs. At the fourth step, applying the mentioned categorical investigation, we determine a new family of Picard-Fuchs type equations related to each DSE. Further, we relate a category of Feynman motivic sheaves as a subcategory of the Arapura category to each DSE. ····· 10361577

Advanced Global Analysis

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This book is composed of several sections which follow one another for flow. The focus is on the Whitehead theorem which implies that a space W is contractible if and only if W is both acyclic and has trivial fundamental group. So one would expect the fundamental group of an acyclic space to contain a lot of information. Moreover, acyclic spaces can be characterized in this way. This book contains super results for modern global analysis. ····· 10361557

Orbits of the Dissected Polygons of the Generalized Catalan Numbers

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Catalan numbers occur regularly throughout many different areas of mathematics. They date back all the way to Euler, and today there are literally hundreds of different realizations of the Catalan number. We can extend the idea of a Catalan number to a generalized Catalan number by adding and extra parameter. In particular, one realization of the generalized Catalan numbers is the number of ways to dissect a regular polygon with (p-1)k+2 sides into k disjoint p+1-gons using (k-1) non-intersecting diagonals. The action of the dihedral group partitions these dissections into some number of orbits. Our main goal of this paper is to find a way to count these orbits for given p and k. In order to do this, we introduce the notion of p-ary trees. We show that the number of diagonalizations of our polygon is equivalent to the number of p-ary trees with k source nodes. Finally, we use Burnside`s Lemma as a way to count the number of orbits for a given tree core and extract formulas for the number of orbits for many tree cores that exist for large enough p and k. ····· 10361496

Solutions of some Problems in Mechanics of Elastic Media

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Elasticity is a fundamental property of all substances occurring in nature. The theory of elasticity is concerned with the study of the response of elastic bodies to the action of forces. The importance of the application of the theory of elasticity in physics and technical mechanics involved in the stated problems from the viewpoint of mathematical analysis attracted the attention of the greatest investigators of the 20th centuries to this branch of science. This thesis is devoted to study some problems in the mechanics of elastic bodies, which might have some interesting applications in the Earthquake science, Geophysics,..., etc. or in the industry, under certain boundary conditions. The topics discussed here are classified into two parts. The first and second chapters are concerned with the determination of frequency in orthotropic non-homogeneous cylinder and sphere. The third and fourth chapters are concerned with the determination of stress in a dynamical non-homogeneous cylinder containing core, using the stresses-strains relationship in which the elastic constants and density are taken as functions of the radial coordinates in the absence of the body forces. ····· 10361446

Asymptotic behavior of viscous fluids on rough boundaries

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A relevant problem in fluid mechanics is the appropriate choice of the boundary conditions. For a viscous fluid in a 3D domain, a well accepted hypothesis is that if the boundary is impermeable, then the fluid adheres completely to it. This condition is called adherence condition. However, some other boundary conditions are often used which may be more realistic from a physical point of view. In this sense, for a viscous fluid governed by the Stokes or Navier-Stokes system, Navier proposed a slip-friction boundary condition. In this work we study the relation between both the adherence and the Navier conditions imposed on different types of rough boundaries: periodic and non-periodic. ····· 10361429

HQFTs and Quantum Groups

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The thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one of the thesis generalizes the de_nition of an n-dimensional HQFT in terms of a monoidal functor from a rigid symmetric monoidal category X_Cobn to any monoidal category A. In particular, 2-dimensional HQFTs with target K(G,1) taking values in A are generated from any Turaev G-crossed system in A and vice-versa. This is the generalization of Turaev`s theory into a purely categorical set-up. Part two of the thesis generalizes the concept of a group-coalgebra, Hopf group-coalgebra, crossed Hopf group-coalgebra and quasitriangular Hopf group-coalgebra over a group scheme. Quantum double of a crossed Hopf group-scheme coalgebra is constructed in the a_ne case and conjectured for non-a_ne case. We can construct 3-dimensional HQFTs from modular crossed G-categories. The category of representations of a quantum double of a crossed Hopf group-coalgebra is a ribbon(quasitriangular) crossed group-category. Hence generates 3-dimensional HQFTs under certain conditions if the category becomes modular. However, systematic _nding of modular crossed G-categories is largely open. ····· 10361426

Multi-criteria Supply Chain Network Design under Uncertainty

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This work contributes to the debate on how uncertainty and concepts of sustainable development can be put into modern Supply Chain Network (SCN). First, we study the literature review, which is a review of the current state of the art of Supply Chain Network Design (SCND) approaches and resolution methods. Second, we propose a new methodology for multi-criteria SCND as well as its application to real SCN, in order to satisfy the customers demand and respect the environmental, social, legislative, and economical requirements. Third, we present a multi-objective model that captures a compromise between the total cost and the environment influence. After that, we develop a novel heuristic solution method based on decomposition technique, to solve large scale SCND problems. Finally, we use two-stage stochastic programming approach to model the SCN under demand uncertainty. Then, we address uncertainty in all SCN parameters, we use possibilistic linear programming approach to model the problem and we validate both approaches in a large application case. ····· 10361377

Some Problems in the Spectral Theory of Separated Dirac Operators

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This work describes a representation of the spectral function for the Dirac operator, and includes an application of this representation to the problem of bounding the points of spectral concentration of the operator. Conditions on the potential function under which an absolutely continuous spectrum exists are given. A connection is made between the Dirac system and a Riccati equation, and the spectral derivative is expressed using a series solution of the Riccati equation. Conditions under which this series converges are given. The terms of the series are then differentiated to obtain a representation of the second derivative of the spectral function. The question of relative asymptotic sizes of the terms of this representation are addressed. The construction and application of the representation are similar to those used to investigate the spectrum of the Sturm-Liouville operator. ····· 10361371

Modifications of Homotopy Analysis Method for Differential Equations

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This book bring new solutions for various types of differential equations. Approximate analytic solution was obtained for system of differential equations specially that has chaotic behavior, delay differential equations, Schrodinger and coupled Schrodinger equation, fractional differential equations, differential algebraic equations and some other fluid mechanic models. Accurate and simple solution was presented via several modifications for homotopy analysis method. ····· 10361367

Insertion of a function

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1-Insertion of a function belonging to a certain subclass of ${ bb r}^x$}. 2-Insertion of a continuous function between two comparable precontinuous (semi-continuous) functions. 3-Strong insertion of a continuous function between two comparable precontinuous (semi-continuous )functions. 4-Insertion of a contra-continuous function. 5-Strong insertion of a contra-continuous function. 6-insertion of an $alpha-$continuous function. 7-Insertion of a continuous function between two comparable $alpha $continuous ($c-$continuous) functions. ····· 10361230

Detecting Conjunctions Using Cluster Volumes

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In brain mapping literatures, the experiment is repeated on several different subjects or for several different stimuli on the same subject, and the researcher is interested in the common points in the brain where activation occurs in all test statistic images. The conjunction is thus defined as those points in the brain that show activation in all images. We are interested in which parts of the conjunction are noise, and which show true activation in all test statistic images. Our main result is an approximate P-value for this in the case of the conjunction of two Gaussian or chi square test statistic images. The results are applied to a functional magnetic resonance experiment in pain perception. ····· 10361123

On Second Order Diff. Operators with Different B. C.& Weight Functions

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The aim of this book is to present some types of spectral problems, which includes second order differential equation with different boundary conditions for each type. The book studies the properties of eigenvalues and estimation of normalized eigenfunctions with different cases of weight functions, in both regular and irregular cases. It also estimates the Green s functions to the spectral problem. Firstly, the spectrum to model, which is defined in chapter two, are real and the normalized eigenfunctions to that model with different cases of weight functions are estimated. Secondly, it is shown that the eigenvalues are located in upper half plane and are complex (i.e. pure imaginary) the asymptotic behavior of eigenvalues is shown through the model approaches to the infinity and the normalized eigenfunctions are proved to be uniformly bounded in both regular and irregular cases, whenever the weight functions are smooth and (x) C^2 (0,a) and q(x) C(0,a). Finally, we found the upper bound for norm to the Green s function which is defined in chapter four in the regular case. ····· 10361107

Operators on Weighted Hardy Spaces

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The main purpose of this book is to introduce the generalized composition operators and the generalized multiplication operators on weighted Hardy spaces . Composition operators have been the subject matter of intensive study over past several decades and they find applications in ergodic theory ,quantum mechanics and other branches of mathematical and physical sciences . The 1st chapter of the book contains introductory material . The compact, Fredholm generalized composition operators are characterized in the second chapter. The Hermitian,Normal ,Quasi normal ,Isometric and co isometric generalized composition operators are presented in the third chapter. It is shown that most of the properties of the generalized multiplication operators differ from the multiplication operators acting on other function spaces .eg:- On most of the function spaces multiplication operators are normal .But this result is not valid incase of generalized multiplication operators on weighted Hardy spaces . In this book some light is thrown on differential and anti-differential operators acting on weighted Hardy spaces . ····· 1036198

Summability Methods And Its Applications

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The non-ending span of space, the ever lasting stream of time and the non-terminating chain of counting numbers are some of the realities that inevitably lead to the concept of unattainable limitless infinity. With the introduction of the operations of arithmetic in the domain of numbers, there emerged the concept of infinite series. In 1821, Cauchy clearly defined the sum of an infinite series based on the concept of limit developed by him. Since then, the Mathematicians are trying to find the sum of an infinite series by adopting different techniques. This Book contains the investigations on absolute Nörlund-Banach Summability of Fourier series and conjugate Fourier series, on index summability factors of Fourier series, on the local property of indexed Nörlund summability of a factored fourier series, on indexed product summability of an infinite series and on index summability of an infinite series. ····· 1036151

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