الصفحة 2
الصفحة 2
Gene Expression Programming : Mathematical Modeling by an Artificial Intelligence
This monograph provides all the implementation details of GEP so that anyone with elementary programming skills will be able to implement it themselves. The book also includes a self-contained introduction to this new exciting field of computational intelligence, including several new algorithms for decision tree induction, data mining, classifier systems, function finding, polynomial induction, times series prediction, evolution of linking functions, automatically defined functions, parameter optimization, logic synthesis, combinatorial optimization, and complete neural network induction. The book also discusses some important and controversial evolutionary topics that might be refreshing to both evolutionary computer scientists and biologists.
Galois Theory
Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra.The book discusses Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it concludes with a discussion of the algebraic closure and of infinite Galois extensions.
Galerkin Finite Element Methods for Parabolic Problems
This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution.
Functional Approach to Optimal Experimental Design
The book presents a novel approach for studying optimal experimental designs. The functional approach consists of representing support points of the designs by Taylor series. It is thoroughly explained for many linear and nonlinear regression models popular in practice including polynomial, trigonometrical, rational, and exponential models. Using the tables of coefficients of these series included in the book, a reader can construct optimal designs for specific models by hand. The book is suitable for researchers in statistics and especially in experimental design theory as well as to students and practitioners with a good mathematical background.
Frontiers in Algorithmics ; 14th International Workshop, FAW 2020, Haikou, China, October 19-21, 2020, Proceedings
This book constitutes the proceedings of the 14th International Workshop on Frontiers in Algorithmics, FAW 2020, held in Haikou, China, in May 2020. The conference was held virtually due to the COVID-19 pandemic. The 12 full papers presented in this volume were carefully reviewed and selected from 15 submissions. The workshop provides a focused forum on current trends of research on algorithms, discrete structures, and their applications, and brings together international experts at the research frontiers in these areas to exchange ideas and to present significant new results. The papers detail graph theory, scheduling and algorithm and complexity.
Fields and Galois Theory
The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra. This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection.
Field Theory ; 2nd ed.
This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study.There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.
Factorization of Matrix and Operator Functions : The State Space Method
The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization.
Essays in Constructive Mathematics
This book aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it, by basing all definitions and proofs on finite algorithms. The topics covered derive from classic works of nineteenth century mathematics---among them Galois' theory of algebraic equations, Gauss's theory of binary quadratic forms and Abel's theorem about integrals of rational differentials on algebraic curves. It is not surprising that the first two topics can be treated constructively---although the constructive treatments shed a surprising amount of light on them---but the last topic, involving integrals and differentials as it does, might seem to call for infinite processes. In this case too, however, finite algorithms suffice to define the genus of an algebraic curve, to prove that birationally equivalent curves have the same genus, and to prove the Riemann-Roch theorem. The main algorithm in this case is Newton's polygon, which is given a full treatment. Other topics covered include the fundamental theorem of algebra, the factorization of polynomials over an algebraic number field, and the spectral theorem for symmetric matrices.
Error-Correcting Linear Codes : Classification by Isometry and Applications
This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group actions that allows the classification of codes by isometry. The book provides in-depth coverage of important topics like cyclic codes and the coding theory used in compact disc players. The final four chapters cover advanced and algorithmic topics like the classification of linear codes by isometry, the enumeration of isometry classes, random generation of codes, the use of lattice basis reduction to compute minimum distances, the explicit construction of codes with given parameters, as well as the systematic evaluation of representatives of all isometry classes of codes.
Discrete Spectral Synthesis and Its Applications
In order to study discrete Abelian groups with wide range applications, the use of classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups is required. This book covers several different problems in this field and is unique in being the only comprehensive coverage of this topic.
Diophantine Approximation : Festschrift for Wolfgang Schmidt
This volume contains 22 research and survey papers on recent developments in the field of diophantine approximation. The first article by Hans Peter Schlickewei is devoted to the scientific work of Wolfgang Schmidt. Further contributions deal with the subspace theorem and its applications to diophantine equations and to the study of linear recurring sequences. The articles are either in the spirit of more classical diophantine analysis or of geometric or combinatorial flavor. In particular, estimates for the number of solutions of diophantine equations as well as results concerning congruences and polynomials are established. Furthermore, the volume contains transcendence results for special functions and contributions to metric diophantine approximation and to discrepancy theory.
Difference Equations : From Rabbits to Chaos
Difference equations are models of the world around us. From clocks to computers to chromosomes, processing discrete objects in discrete steps is a common theme. Difference equations arise naturally from such discrete descriptions and allow us to pose and answer such questions as: How much? How many? How long? Difference equations are a necessary part of the mathematical repertoire of all modern scientists and engineers.The book cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron—Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply polynomials quickly.
Difference Algebra
This book reflects the contemporary level of difference algebra; it contains a systematic study of partial difference algebraic structures and their applications, as well as the coverage of the classical theory of ordinary difference rings and field extensions. The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. It will be also of interest to researchers in computer algebra, theory of difference equations and equations of mathematical physics. The book is self-contained; it requires no prerequisites other than knowledge of basic algebraic concepts and mathematical maturity of an advanced undergraduate.
Developments in language theory ; 8th International Conference, DLT 2004, Auckland, New Zealand, December 13-17, Proceedings
Basic Notions of Reaction Systems / A Kleene Theorem for a Class of Communicating Automata with Effective Algorithms / Algebraic and Topological Models for DNA Recombinant Processes / Contributed Papers : Regular Expressions for Two-Dimensional Languages Over One-Letter Alphabet / On Competence in CD Grammar Systems / The Dot-Depth and the Polynomial Hierarchy Correspond on the Delta Levels, and other
Determinantal Ideals
Determinantal ideals are ideals generated by minors of a homogeneous polynomial matrix. Some classical ideals that can be generated in this way are the ideal of the Veronese varieties, of the Segre varieties, and of the rational normal scrolls. Determinantal ideals are a central topic in both commutative algebra and algebraic geometry, and they also have numerous connections with invariant theory, representation theory, and combinatorics. Due to their important role, their study has attracted many researchers and has received considerable attention in the literature. In this book three crucial problems are addressed: CI-liaison class and G-liaison class of standard determinantal ideals; the multiplicity conjecture for standard determinantal ideals; and unobstructedness and dimension of families of standard determinantal ideals.
Design and Analysis of Simulation Experiments
This is an advanced expository book on statistical methods for the Design and Analysis of Simulation Experiments (DASE). Though the book focuses on DASE for discrete-event simulation (such as queuing and inventory simulations), it also discusses DASE for deterministic simulation (such as engineering and physics simulations). The text presents both classic and modern statistical designs. Classic designs (e.g., fractional factorials) assume only a few factors with a few values per factor. The resulting input/output data of the simulation experiment are analyzed through low-order polynomials, which are linear regression (meta)models. Modern designs allow many more factors, possible with many values per factor. These designs include group screening (e.g., Sequential Bifurcation, SB) and space filling designs (e.g., Latin Hypercube Sampling, LHS). The data resulting from these modern designs may be analyzed through low-order polynomials for group screening and various metamodel types (e.g., Kriging) for LHS.
Decoupling Control
Decoupling or non-interactive control has attracted considerable research attention since the 1960s when control engineers started to deal with multivariable systems. The theory and design techniques for decoupling control have now, more or less matured for linear time-invariant systems, yet there is no single book which focuses on such an important topic. The present monograph fills this gap by presenting a fairly comprehensive and detailed treatment of decoupling theory and relevant design methods. Decoupling control under the framework of polynomial transfer function and frequency response settings, is included as well as the disturbance decoupling problem. The emphasis here is on special or relatively new compensation schemes such as (true and virtual) feedforward control and disturbance observers, rather than use of feedback control alone. The results are presented in a self-contained way and only the knowledge of basic linear systems theory is assumed of the reader.
Cryptography Arithmetic : Algorithms and Hardware Architectures
Modern cryptosystems, used in numerous applications that require secrecy or privacy - electronic mail, financial transactions, medical-record keeping, government affairs, social media etc. - are based on sophisticated mathematics and algorithms that in implementation involve much computer arithmetic. And for speed it is necessary that the arithmetic be realized at the hardware (chip) level. This book is an introduction to the implementation of cryptosystems at that level.
Courbes algébriques planes = Plane Algebraic Curves
Resulting from a master's course at the University of Paris VII, this text is re-edited as it appeared in 1978. Various tools are introduced in connection with Bézout's theorem necessary for the development of the notion of the multiplicity of intersection of two algebraic curves in the complex projective plane. Starting from elementary notions on affine and projective algebraic subsets, we define the intersection multiplicities and interpret their sum in terms of the resultant of two polynomials. The local study is a pretext for the introduction of formal or convergent series rings; it culminates in Puiseux's theorem, the convergence of which is reduced by splits to that of the theorem of implicit functions. Various figures illuminate the text: we "see" in particular that the homogeneous equation x3 + y3 + z3 = 0 defines a torus in the complex projective plane.
