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Primer for Point and Space Groups (Repost)

Posted By: AvaxGenius
Primer for Point and Space Groups (Repost)

Primer for Point and Space Groups by Richard L. Liboff
English | PDF | 2004 | 231 Pages | ISBN : 0387402489 | 20.3 MB

This text stems from a course I have taught a number of times, attended by students of material science, electrical engineering, physics, chemistry, physical chemistry and applied mathematics. It is intended as an intro­ ductory discourse to give the reader a first encounter with group theory. The work concentrates on point and space groups as these groups have the principal application in technology. Here is an outline of the salient features of the chapters. In Chapter 1, basic notions and definitions are introduced including that of Abelian groups, cyclic groups, Sylow's theorems, Lagrange's subgroup theorem and the rearrangement theorem. In Chapter 2, the concepts of classes and direct products are discussed. Applications of point groups to the Platonic solids and non-regular dual polyhedra are described. In Chapter 3, matrix representation of operators are introduced leading to the notion of irreducible representations ('irreps'). The Great Orthogonal­ ity Theorem (GOT) is also introduced, followed by six important rules relating to dimensions of irreps. Schur's lemma and character tables are described. Applications to quantum mechanics are discussed in Chapter 4 including descriptions of the rotation groups in two and three dimensions, the symmetric group, Cayley's theorem and Young diagrams. The relation of degeneracy of a quantum state of a system to dimensions of irreps of the group of symmetries of the system are discussed, as well as the basis properties of related eigenfunctions.

Smooth Manifolds and Observables

Posted By: AvaxGenius
Smooth Manifolds and Observables

Smooth Manifolds and Observables by Jet Nestruev
English | PDF (True) | 2003 | 226 Pages | ISBN : 0387955437 | 3.3 MB

This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.

Abstract Algebra

Posted By: yoyoloit
Abstract Algebra

Abstract Algebra (303 Pages)
by Shaoqiang Deng & Fuhai Zhu

English | 2024 | ISBN: 9811277664 | 304 pages | True PDF | 13.27 MB

Variational Methods in Partially Ordered Spaces

Posted By: AvaxGenius
Variational Methods in Partially Ordered Spaces

Variational Methods in Partially Ordered Spaces by Alfred Göpfert , Hassan Riahi , Christiane Tammer , Constantin Zǎlinescu
English | PDF EPUB (True) | 2023 | 576 Pages | ISBN : 303136533X | 78.1 MB

In mathematical modeling of processes occurring in logistics, management science, operations research, networks, mathematical finance, medicine, and control theory, one often encounters optimization problems involving more than one objective function so that Multiobjective Optimization (or Vector Optimization, initiated by W. Pareto) has received new impetus. The growing interest in vector optimization problems, both from the theoretical point of view and as it concerns applications to real world optimization problems, asks for a general scheme which embraces several existing developments and stimulates new ones.

Fundamentals of Diophantine Geometry

Posted By: AvaxGenius
Fundamentals of Diophantine Geometry

Fundamentals of Diophantine Geometry by Serge Lang
English | PDF | 1983 | 383 Pages | ISBN : 0387908374 | 28 MB

Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.

Numerical Challenges in Lattice Quantum Chromodynamics

Posted By: AvaxGenius
Numerical Challenges in Lattice Quantum Chromodynamics

Numerical Challenges in Lattice Quantum Chromodynamics: Joint Interdisciplinary Workshop of John von Neumann Institute for Computing, Jülich, and Institute of Applied Computer Science, Wuppertal University, August 1999 by Andreas Frommer, Thomas Lippert, Björn Medeke, Klaus Schilling
English | PDF | 2000 | 197 Pages | ISBN : 3540677321 | 24.6 MB

Lattice gauge theory is a fairly young research area in Theoretical Particle Physics. It is of great promise as it offers the framework for an ab-initio treatment of the nonperturbative features of strong interactions. Ever since its adolescence the simulation of quantum chromodynamics has attracted the interest of numerical analysts and there is growing interdisciplinary engage­ ment between theoretical physicists and applied mathematicians to meet the grand challenges of this approach. This volume contains contributions of the interdisciplinary workshop "Nu­ merical Challenges in Lattice Quantum Chromo dynamics" that the Institute of Applied Computer Science (IAI) at Wuppertal University together with the Von-Neumann-Institute-for-Computing (NIC) organized in August 1999. The purpose of the workshop was to offer a platform for the exchange of key ideas between lattice QCD and numerical analysis communities. In this spirit leading experts from both fields have put emphasis to transcend the barriers between the disciplines. The meetings was focused on the following numerical bottleneck problems: A standard topic from the infancy of lattice QCD is the computation of Green's functions, the inverse of the Dirac operator. One has to solve huge sparse linear systems in the limit of small quark masses, corresponding to high condition numbers of the Dirac matrix. Closely related is the determination of flavor-singlet observables which came into focus during the last years.

Braids and Self-Distributivity

Posted By: AvaxGenius
Braids and Self-Distributivity

Braids and Self-Distributivity by Patrick Dehornoy
English | PDF | 2000 | 637 Pages | ISBN : 3764363436 | 30.9 MB

The aim of this book is to present recently discovered connections between Artin's braid groups En and left self-distributive systems (also called LD­ systems), which are sets equipped with a binary operation satisfying the left self-distributivity identity x(yz) = (xy)(xz). (LD) Such connections appeared in set theory in the 1980s and led to the discovery in 1991 of a left invariant linear order on the braid groups. Braids and self-distributivity have been studied for a long time. Braid groups were introduced in the 1930s by E. Artin, and they have played an increas­ ing role in mathematics in view of their connection with many fields, such as knot theory, algebraic combinatorics, quantum groups and the Yang-Baxter equation, etc. LD-systems have also been considered for several decades: early examples are mentioned in the beginning of the 20th century, and the first general results can be traced back to Belousov in the 1960s. The existence of a connection between braids and left self-distributivity has been observed and used in low dimensional topology for more than twenty years, in particular in work by Joyce, Brieskorn, Kauffman and their students. Brieskorn mentions that the connection is already implicit in (Hurwitz 1891). The results we shall concentrate on here rely on a new approach developed in the late 1980s and originating from set theory.

Algebraic Integrability, Painlevé Geometry and Lie Algebras

Posted By: AvaxGenius
Algebraic Integrability, Painlevé Geometry and Lie Algebras

Algebraic Integrability, Painlevé Geometry and Lie Algebras by Mark Adler , Pierre Moerbeke , Pol Vanhaecke
English | PDF | 2004 | 487 Pages | ISBN : 354022470X | 40.7 MB

This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.

Rational Points on Elliptic Curves

Posted By: AvaxGenius
Rational Points on Elliptic Curves

Rational Points on Elliptic Curves by Joseph H. Silverman , John Tate
English | PDF | 1992| 292 Pages | ISBN : 0387978259 | 22.97 MB

In 1961 the second author deliv1lred a series of lectures at Haverford Col­ lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran­ scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por­ tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter­ est in the theory of elliptic curves for subjects ranging from cryptogra­ phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience.

Rational Algebraic Curves: A Computer Algebra Approach (Repost)

Posted By: AvaxGenius
Rational Algebraic Curves: A Computer Algebra Approach (Repost)

Rational Algebraic Curves: A Computer Algebra Approach by J. Rafael Sendra , Franz Winkler , Sonia Pérez-Díaz
English | PDF (True) | 2008 | 273 Pages | ISBN : 3540737243 | 3.68 MB

Algebraic curves and surfaces are an old topic of geometric and algebraic investigation. They have found applications for instance in ancient and m- ern architectural designs, in number theoretic problems, in models of b- logical shapes, in error-correcting codes, and in cryptographic algorithms. Recently they have gained additional practical importance as central objects in computer-aided geometric design. Modern airplanes, cars, and household appliances would be unthinkable without the computational manipulation of algebraic curves and surfaces. Algebraic curves and surfaces combine fas- nating mathematical beauty with challenging computational complexity and wide spread practical applicability.

Methods of Algebraic Geometry in Control Theory: Part II (Repost)

Posted By: AvaxGenius
Methods of Algebraic Geometry in Control Theory: Part II (Repost)

Methods of Algebraic Geometry in Control Theory: Part II Multivariable Linear Systems and Projective Algebraic Geometry by Peter Falb
English | PDF | 1999 | 382 Pages | ISBN : 0817641130 | 24.1 MB

"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry).

Automated Reasoning and Mathematics: Essays in Memory of William W. McCune

Posted By: AvaxGenius
Automated Reasoning and Mathematics: Essays in Memory of William W. McCune

Automated Reasoning and Mathematics: Essays in Memory of William W. McCune by Maria Paola Bonacina, Mark E. Stickel
English | PDF | 2013 | 276 Pages | ISBN : 3642366740 | 4.07 MB

This Festschrift volume is published in memory of William W. McCune who passed away in 2011. William W. McCune was an accomplished computer scientist all around but especially a fantastic system builder and software engineer.
The volume includes 13 full papers, which are presenting research in all aspects of automated reasoning and its applications to mathematics. These papers have been thoroughly reviewed and selected out of 15 submissions received in response to the call for paper issued in September 2011. The topics covered are: strategies, indexing, superposition-based theorem proving, model building, application of automated reasoning to mathematics, as well as to program verification, data mining, and computer formalized mathematics.

Linear Multivariable Control: a Geometric Approach: A Geometric Approach

Posted By: AvaxGenius
Linear Multivariable Control: a Geometric Approach: A Geometric Approach

Linear Multivariable Control: a Geometric Approach: A Geometric Approach by W. Murray Wonham
English | PDF | 1979 | 340 Pages | ISBN : 0387960716 | 32.9 MB

In writing this monograph my aim has been to present a "geometric" approach to the structural synthesis of multivariable control systems that are linear, time-invariant and of finite dynamic order. The book is addressed to graduate students specializing in control, to engineering scientists engaged in control systems research and development, and to mathemati­ cians with some previous acquaintance with control problems.

Datalog and Logic Databases

Posted By: AvaxGenius
Datalog and Logic Databases

Datalog and Logic Databases by Sergio Greco
English | PDF(True) | 2015 | 171 Pages | ISBN : 1627051139 | 1.17 MB

The use of logic in databases started in the late 1960s. In the early 1970s Codd formalized databases in terms of the relational calculus and the relational algebra. A major influence on the use of logic in databases was the development of the field of logic programming. Logic provides a convenient formalism for studying classical database problems and has the important property of being declarative, that is, it allows one to express what she wants rather than how to get it.

Cyclic Homology in Non-Commutative Geometry

Posted By: AvaxGenius
Cyclic Homology in Non-Commutative Geometry

Cyclic Homology in Non-Commutative Geometry by Joachim Cuntz, Georges Skandalis, Boris Tsygan
English | PDF | 2004 | 147 Pages | ISBN : 3540404694 | 12.2 MB

Cyclic homology was introduced in the early eighties independently by Connes and Tsygan. They came from different directions. Connes wanted to associate homological invariants to K-homology classes and to describe the index pair­ ing with K-theory in that way, while Tsygan was motivated by algebraic K-theory and Lie algebra cohomology. At the same time Karoubi had done work on characteristic classes that led him to study related structures, without however arriving at cyclic homology properly speaking. Many of the principal properties of cyclic homology were already developed in the fundamental article of Connes and in the long paper by Feigin-Tsygan.