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Contemporary Developments in Finite Fields and Applications

Contemporary Developments in Finite Fields and Applications Author Anne Canteaut
ISBN-10 9789814719278
Release 2016-06-15
Pages 372
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The volume is a collection of 20 refereed articles written in connection with lectures presented at the 12th International Conference on Finite Fields and Their Applications ("Fq12") at Skidmore College in Saratoga Springs, NY in July 2015. Finite fields are central to modern cryptography and secure digital communication, and hence must evolve rapidly to keep pace with new technologies. Topics in this volume include cryptography, coding theory, structure of finite fields, algorithms, curves over finite fields, and further applications. Contributors will include: Antoine Joux (Fondation Partenariale de l'UPMC, France); Gary Mullen (Penn State University, USA); Gohar Kyureghyan (Otto-von-Guericke Universität, Germany); Gary McGuire (University College Dublin, Ireland); Michel Lavrauw (Università degli Studi di Padova, Italy); Kirsten Eisentraeger (Penn State University, USA); Renate Scheidler (University of Calgary, Canada); Michael Zieve (University of Michigan, USA). Contents:Divisibility of L-Polynomials for a Family of Curves (I Blanco-Chacón, R Chapman, S Fordham and G McGuire)Divisibility of Exponential Sums Associated to Binomials Over 𝔽p (F Castro, R Figueroa, P Guan and J Ortiz-Ubarri)Dickson Polynomials that are Involutions (P Charpin, S Mesnager and S Sarkar)Constructing Elliptic Curves and Curves of Genus 2 over Finite Fields (K Eisenträger)A Family of Plane Curves with Two or More Galois Points in Positive Characteristic (S Fukasawa)Permutation Polynomials of 𝔽q2 of the Form αX + Xr(q-1)+1 (X-D Hou)Character Sums and Generating Sets (M-D A Huang and L Liu)Nearly Sparse Linear Algebra and Application to Discrete Logarithms Computations (A Joux and C Pierrot)Full Degree Two del Pezzo Surfaces over Small Finite Fields (A Knecht and K Reyes)Diameter of Some Monomial Digraphs (A Kodess, F Lazebnik, S Smith and J Sporre)Permutation Polynomials of the Form X + γTr(Xk) (G Kyureghyan and M Zieve)Scattered Spaces in Galois Geometry (M Lavrauw)On the Value Set of Small Families of Polynomials over a Finite Field, III (G Matera, M Pérez and Melina Privitelli)The Density of Unimodular Matrices over Integrally Closed Subrings of Function Fields (G Micheli and R Schnyder)Some Open Problems Arising from My Recent Finite Field Research (G L Mullen)On Coefficients of Powers of Polynomials and Their Compositions over Finite Fields (G L Mullen, A Muratović-Ribić and Q Wang)On the Structure of Certain Reduced Linear Modular Systems (E Orozco)Finding a Gröbner Basis for the Ideal of Recurrence Relations on m-Dimensional Periodic Arrays (I M Rubio, M Sweedler and C Heegard)An Introduction to Hyperelliptic Curve Arithmetic (R Scheidler)On the Existence of Aperiodic Complementary Hexagonal Lattice Arrays (Y Tan and G Gong) Readership: Researchers in combinatorics and graph theory, numerical analysis and computational mathematics, and coding theory.



Model Based Development

Model Based Development Author H.S. Lahman
ISBN-10 9780132757188
Release 2011-06-14
Pages 548
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A Proven Development Methodology That Delivers On the Promise of Model-Based Approaches Software continues to become more and more complex, while software consumers’ expectations for performance, reliability, functionality, and speed-to-market are also growing exponentially. H. S. Lahman shows how to address all these challenges by integrating proven object-oriented techniques with a powerful new methodology. Model-Based Development represents Lahman’s half century of experience as a pioneering software innovator. Building on Shlaer-Mellor’s work, Lahman’s unique approach fully delivers on the promise of models and is firmly grounded in the realities of contemporary development, design, and architecture. The book introduces the methodology’s core principles, showing how it separates each of a project’s concerns, enabling practitioners to optimize each domain for its unique needs and characteristics. Next, it demonstrates how to perform more effective object-oriented analysis, emphasizing abstraction, disciplined partitioning, modeling invariants, finite state machines, and efficient communications among program units. Coverage includes How we got here: a historical perspective and pragmatic review of object principles Problem space versus computing space: reflecting crucial distinctions between customer and computer environments in your designs Application partitioning: why it matters and how do it well Building static models that describe basic application structure Modeling classes, class responsibilities, associations, and both referential and knowledge integrity Creating dynamic models that describe behavior via finite state machines Successfully using abstract action languages (AALs) and action data flow diagrams (ADFDs) Throughout, Lahman illuminates theoretical issues in practical terms, explaining why things are done as they are, without demanding rigorous math. His focus is on creating implementation-independent models that resolve functional requirements completely, precisely, and unambiguously. Whether you’re a developer, team leader, architect, or designer, Lahman’s techniques will help you build software that’s more robust, easier to maintain, supports larger-scale reuse, and whose specification is rigorous enough to enable full-scale automatic code generation.



Galois Theory and Applications

Galois Theory and Applications Author Mohamed Ayad
ISBN-10 9789813238329
Release 2018-04-26
Pages 452
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Galois Theory and Applications has been writing in one form or another for most of life. You can find so many inspiration from Galois Theory and Applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Galois Theory and Applications book for free.



Arithmetic Geometry Cryptography and Coding Theory

Arithmetic  Geometry  Cryptography and Coding Theory Author Alp Bassa
ISBN-10 9781470428105
Release 2017-03-27
Pages 199
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This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18–22, 2015. Since the first meeting almost 30 years ago, the biennial AGCT meetings have been one of the main events bringing together researchers interested in explicit aspects of arithmetic geometry and applications to coding theory and cryptography. This volume contains original research articles reflecting recent developments in the field.



Finite Fields

Finite Fields Author Rudolf Lidl
ISBN-10 0521392314
Release 1997-01-01
Pages 755
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This book is devoted entirely to the theory of finite fields.



Application of the Finite Element Method in Implant Dentistry

Application of the Finite Element Method in Implant Dentistry Author Jianping Geng
ISBN-10 3540737642
Release 2008-09-26
Pages 137
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This book creates the theoretical foundation that novices need to perform the finite element method in implant dentistry. It shows how both the implant dentist and the designer can benefit from finite element analysis. The authors explain the theory and math of the finite element method. Then, you get practical applications alongside discussions of the critical issues in using finite element analysis for dental implant design.



Elasticity

Elasticity Author Martin H. Sadd
ISBN-10 9780124104327
Release 2014-01-22
Pages 600
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Elasticity: Theory, Applications, and Numerics, Third Edition, continues its market-leading tradition of concisely presenting and developing the linear theory of elasticity, moving from solution methodologies, formulations, and strategies into applications of contemporary interest, such as fracture mechanics, anisotropic and composite materials, micromechanics, nonhomogeneous graded materials, and computational methods. Developed for a one- or two-semester graduate elasticity course, this new edition has been revised with new worked examples and exercises, and new or expanded coverage of areas such as spherical anisotropy, stress contours, isochromatics, isoclinics, and stress trajectories. Using MATLAB software, numerical activities in the text are integrated with analytical problem solutions. These numerics aid in particular calculations, graphically present stress and displacement solutions to problems of interest, and conduct simple finite element calculations, enabling comparisons with previously studied analytical solutions. Online ancillary support materials for instructors include a solutions manual, image bank, and a set of PowerPoint lecture slides. Thorough yet concise introduction to linear elasticity theory and applications Only text providing detailed solutions to problems of nonhomogeneous/graded materials New material on stress contours/lines, contact stresses, curvilinear anisotropy applications Further and new integration of MATLAB software Addition of many new exercises Comparison of elasticity solutions with elementary theory, experimental data, and numerical simulations Online solutions manual and downloadable MATLAB code



Groups Rings and Group Rings

Groups  Rings  and Group Rings Author A. Giambruno
ISBN-10 9780821847718
Release 2009
Pages 270
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This volume represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. Papers in this volume contain results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras. In particular, topics such as growth functions on varieties, groups of units in group rings, representation theory of Lie algebras, Jordan, alternative and Leibniz algebras, graded identities, automorphisms of trees, and partial actions, are discussed.



Topology and Geometry in Dimension Three

Topology and Geometry in Dimension Three Author William H. Jaco
ISBN-10 9780821852958
Release 2011
Pages 196
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This volume contains the proceedings of a conference held from June 4-6, 2010, at Oklahoma State University, in honor of William (Bus) Jaco's 70th birthday. His contributions to research in low dimensional geometry and topology and to the American mathematical community, especially through his work for the American Mathematical Society, were recognized during the conference. The focus of the conference was on triangulations and geometric structures for three-dimensional manifolds. The papers in this volume present significant new results on these topics, as well as in geometric group theory.



Finite Simple Groups Thirty Years of the Atlas and Beyond

Finite Simple Groups  Thirty Years of the Atlas and Beyond Author Manjul Bhargava
ISBN-10 9781470436780
Release 2017-07-24
Pages 229
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Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.



Automata Theory with Modern Applications

Automata Theory with Modern Applications Author James A. Anderson
ISBN-10 9781139458214
Release 2006-06-22
Pages
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Recent applications to biomolecular science and DNA computing have created a new audience for automata theory and formal languages. This is the only introductory book to cover such applications. It begins with a clear and readily understood exposition of the fundamentals that assumes only a background in discrete mathematics. The first five chapters give a gentle but rigorous coverage of basic ideas as well as topics not found in other texts at this level, including codes, retracts and semiretracts. Chapter 6 introduces combinatorics on words and uses it to describe a visually inspired approach to languages. The final chapter explains recently-developed language theory coming from developments in bioscience and DNA computing. With over 350 exercises (for which solutions are available), many examples and illustrations, this text will make an ideal contemporary introduction for students; others, new to the field, will welcome it for self-learning.



Advances in Mathematical Chemistry and Applications

Advances in Mathematical Chemistry and Applications Author Subhash C. Basak
ISBN-10 9781681080529
Release 2016-02-11
Pages 354
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Advances in Mathematical Chemistry and Applications highlights the recent progress in the emerging discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces have brought together 27 chapters written by 68 internationally renowned experts in these two volumes. Each volume comprises a wise integration of mathematical and chemical concepts and covers numerous applications in the field of drug discovery, bioinformatics, chemoinformatics, computational biology, mathematical proteomics, and ecotoxicology. Volume 2 explores deeper the topics introduced in Volume 1, with numerous additional topics such as topological approaches for classifying fullerene isomers; chemical reaction networks; discrimination of small molecules using topological molecular descriptors; GRANCH methods for the mathematical characterization of DNA, RNA and protein sequences; linear regression methods and Bayesian techniques; in silico toxicity prediction methods; drug design; integration of bioinformatics and systems biology, molecular docking, and molecular dynamics; metalloenzyme models; protein folding models; molecular periodicity; generalized topologies and their applications; and many more. Brings together both the theoretical and practical aspects of the fundamental concepts of mathematical chemistry Covers applications in diverse areas of physics, chemistry, drug discovery, predictive toxicology, systems biology, chemoinformatics, and bioinformatics About half of the book focuses primarily on current work, new applications, and emerging approaches for the mathematical characterization of essential aspects of molecular structure, while the other half describes applications of structural approach to new drug discovery, virtual screening, protein folding, predictive toxicology, DNA structure, and systems biology



The Mathematics of Coding Theory

The Mathematics of Coding Theory Author Paul B. Garrett
ISBN-10 0131019678
Release 2004
Pages 398
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This book makes a very accessible introduction to a very important contemporary application of number theory, abstract algebra, and probability. It contains numerous computational examples throughout, giving learners the opportunity to apply, practice, and check their understanding of key concepts. KEY TOPICS Coverage starts from scratch in treating probability, entropy, compression, Shannon¿s theorems, cyclic redundancy checks, and error-correction. For enthusiasts of abstract algebra and number theory.



Galois Theory

Galois Theory Author Emil Artin
ISBN-10 9780486158259
Release 2012-05-24
Pages 86
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Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.



Finite Physical Dimensions Optimal Thermodynamics 1

Finite Physical Dimensions Optimal Thermodynamics 1 Author Michel Feidt
ISBN-10 9780081023495
Release 2017-08-28
Pages 272
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Energy and the environment are inextricably linked to the economy. Thermodynamics therefore seems to be a privileged tool in overcoming the constraints associated with optimization. This first volume reports on an original, contemporary approach leading to optimal solutions in the form of trend models, proving the existence of solutions which can then be refined in a more complete and sophisticated manner. The validation of the proposed methodology is realized through real-life examples (engines, heat pumps, refrigeration systems, etc.). However, the more fundamental aspects linked to the dynamics of the transfer and conversion of energy and matter are also explored, as well as the evolution which characterizes the second law of thermodynamics. This book presents recent advances, often still undergoing research, as well as structured exercises, and is therefore aimed at both students and researchers in the field of energetics. It proposes a view of the evolution of knowledge regarding the thermodynamics modeling of systems and processes It shows results and also the existence of optimum all and along the development It focuses on multidisciplinary approach that characterizes thermodynamics



A Contemporary Study of Iterative Methods

A Contemporary Study of Iterative Methods Author A. Alberto Magrenan
ISBN-10 9780128094938
Release 2018-02-13
Pages 400
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A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand. Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography Explores the uses of computation of iterative methods across non-linear analysis Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options



Contemporary Cryptology

Contemporary Cryptology Author Gustavus J. Simmons
ISBN-10 0879422777
Release 1992
Pages 640
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The field of cryptography has experienced an unprecedented development in the past decade and the contributors to this book have been in the forefront of these developments. In an information-intensive society, it is essential to devise means to accomplish, with information alone, every function that it has been possible to achieve in the past with documents, personal control, and legal protocols (secrecy, signatures, witnessing, dating, certification of receipt and/or origination). This volume focuses on all these needs, covering all aspects of the science of information integrity, with an emphasis on the cryptographic elements of the subject. In addition to being an introductory guide and survey of all the latest developments, this book provides the engineer and scientist with algorithms, protocols, and applications. Of interest to computer scientists, communications engineers, data management specialists, cryptographers, mathematicians, security specialists, network engineers.