الصفحة 4
الصفحة 4
Algorithms in Real Algebraic Geometry
The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing.
Algorithms and data structures ; 17th International Symposium, WADS 2021, Virtual Event, August 9–11, 2021, Proceedings
This book constitutes the refereed proceedings of the 17th International Symposium on Algorithms and Data Structures, WADS 2021, held in virtually in August 2021. The 47 full papers, presented together with two invited lectures, were carefully reviewed and selected from a total of 123 submissions. They present original research on the theory, design and application of algorithms and data structures.
Algorithmic Aspects in Information and Management ; 14th International Conference, AAIM 2020, Jinhua, China, August 10–12, 2020, Proceedings
This volume constitutes the proceedings of the 14th International Conference on Algorithmic Aspects in Information and Management, AAIM 2020, held in Jinhua, China in August 2020. The 39 full papers and 17 short papers presented were carefully reviewed and selected from 76 submissions. The papers deal with emerging important algorithmic problems with a focus on the fundamental background, theoretical technology development, and real-world applications associated with information and management analysis, modeling and data mining. Special considerations are given to algorithmic research that was motivated by real-world applications.
Algèbre, Chapitre 4 à 7 = Algebra, Chapter 4 to 7
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. Deals in particular with extensions of fields and Galois theory. It includes the chaptires: 4. Polynomials and rational fractions; 5. Commutative bodies 6. Orderly groups and bodies; 7. Modules on the main rings
Algebraic Theory of Locally Nilpotent Derivations
This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such as Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler’s Theorem for the plane, right up to the most recent results, such as Makar-Limanov’s Theorem for locally nilpotent derivations of polynomial rings.
Algebraic Cycles, Sheaves, Shtukas, and Moduli : Impanga Lecture Notes
The articles in this volume are devoted to: - moduli of coherent sheaves. - principal bundles and sheaves and their moduli. - new insights into Geometric Invariant Theory. - stacks of shtukas and their compactifications. - algebraic cycles vs. commutative algebra. - Thom polynomials of singularities. - zero schemes of sections of vector bundles.
Algebraic Biology ; 2nd International Conference, AB 2007, Castle of Hagenberg, Austria, July 2-4, 2007, Proceedings
This volume constitutes the refereed proceedings of the Second International Conference on Algebraic Biology. The conference served as an interdisciplinary forum for the presentation of research on all aspects of the application of symbolic computation in biology, including computer algebra, computational logic, and related methods.
Advances in cryptology - CRYPTO -87 ; Conference on the theory and applications of cryptographic techniques : Proceedings
Zero-knowledge interactive proofsystems are a new technique which can be used as a cryptographic tool for designing provably secure protocols. Goldwasser, Micali, and Rackoff originally suggested this technique for controlling the knowledge released in an interactive proof of membership in a language, and for classification of languages. In this approach, knowledge is defined in terms of complexity to convey knowledge if it gives a computational advantage to the receiver, theory, and a message is said for example by giving him the result of an intractable computation. The formal model of interacting machines is described in. A proof-system (for a language L) is an interactive protocol by which one user, the prover, attempts to convince another user, the verifier, that a given input x is in L. We assume that the verifier is a probabilistic machine which is limited to expected polynomial-time computation, while the prover is an unlimited probabilistic machine.
Adaptive Nonlinear System Identification : The Volterra and Wiener Model Approaches
Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches introduces engineers and researchers to the field of nonlinear adaptive system identification. The book includes recent research results in the area of adaptive nonlinear system identification and presents simple, concise, easy-to-understand methods for identifying nonlinear systems. These methods use adaptive filter algorithms that are well known for linear systems identification. They are applicable for nonlinear systems that can be efficiently modeled by polynomials.After a brief introduction to nonlinear systems and to adaptive system identification, the author presents the discrete Volterra model approach. This is followed by an explanation of the Wiener model approach. Adaptive algorithms using both models are developed. The performance of the two methods are then compared to determine which model performs better for system identification applications.
Adaptive Learning of Polynomial Networks : Genetic Programming, Backpropagation and Bayesian Methods
This book provides theoretical and practical knowledge for develop ment of algorithms that infer linear and nonlinear models. It offers a methodology for inductive learning of polynomial neural network mod els from data. The design of such tools contributes to better statistical data modelling when addressing tasks from various areas like system identification, chaotic time-series prediction, financial forecasting and data mining. The main claim is that the model identification process involves several equally important steps: finding the model structure, estimating the model weight parameters, and tuning these weights with respect to the adopted assumptions about the underlying data distrib ution. When the learning process is organized according to these steps, performed together one after the other or separately, one may expect to discover models that generalize well.
A Field Guide to Algebra
Focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths. In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians.
A Course in Enumeration
Leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject.
