Mathematics

Linear vibrations: A theoretical treatment of multi-degree-of-freedom vibrating systems By . C. Müller, W. O. Schiehlen

Richard Dedekind, Heinrich Weber, “Theory of Algebraic Functions of One Variable”

Universal Formulas In Integral And Fractional Differential Calculus

Dependence Logic: Theory and Applications by Samson Abramsky

Euclidean Distance Geometry: An Introduction By Leo Liberti, Carlile Lavor

Linear vibrations: A theoretical treatment of multi-degree-of-freedom vibrating systems By . C. Müller, W. O. Schiehlen

English | PDF | 1985 | 332 Pages | ISBN : 9401087350 | 39.51 MB

In the last decade the development in vibration analysis was char acterized by increasing demands on precision and by the growing use of electronic computers. At present, improvements in precision are obtained by a more accurate modelling of technical systems.

Thus, for instance, a system with one degree of freedom is often not accepted, as it used to be, as a model for vibration analysis in mechanical engineering. As a rule, vehicles and machines have to be modelled as systems with many degrees of freedom such as multibody systems, finite element systems or con tinua. The mathematical description of multi-degree-of-freedom systems leads to matrix representations of the corresponding equations. These are then conveniently analyzed by means of electronic computers, that is, by the analog computer and especially by the digital machine. Hence there exists a mutually stimulating interaction between the growing require ments and the increasing computational facilities. The present book deals with linear vibration analysis of technical systems with many degrees of freedom in a form allowing the use of computers for finding solutions. Part I begins with the classification of vibrating systems. The main characteristics here are the kind of differential equation, the time depen dence of the coefficients and the attributes of the exciting process. Next it is shown by giving examples involving mechanical vibrating systems how to set up equations of motion and how to transform these into state equations.

Richard Dedekind, Heinrich Weber, “Theory of Algebraic Functions of One Variable”

2012 | ISBN-10: 0821883305 | 157 pages | PDF | 7 MB

This book is the first English translation of the classic long paper Theorie der algebraischen Functionen einer Veranderlichen (Theory of algebraic functions of one variable), published by Dedekind and Weber in 1882. The translation has been enriched by a Translator’s Introduction that provides historical background, and extensive commentary embedded in the translation itself. The translation, introduction, and commentary provide the first easy access to this important paper for a wide mathematical audience: students, historians of mathematics, and professional mathematicians. Why is the Dedekind-Weber paper important? In the 1850s, Riemann initiated a revolution in algebraic geometry by interpreting algebraic curves as surfaces covering the sphere. He obtained deep and striking results in pure algebra by intuitive arguments about surfaces and their topology. However, Riemann’s arguments were not rigorous, and they remained in limbo until 1882, when Dedekind and Weber put them on a sound foundation. The key to this breakthrough was to develop the theory of algebraic functions in analogy with Dedekind’s theory of algebraic numbers, where the concept of ideal plays a central role. By introducing such concepts into the theory of algebraic curves, Dedekind and Weber paved the way for modern algebraic geometry.

Universal Formulas In Integral And Fractional Differential Calculus

World Scientific | English | 2016 | ISBN-10: 9814675598 | 296 pages | PDF | 3.71 mb

by Khavtgai Namsrai (Author)

This reference book presents unique and traditional analytic calculations, and features more than a hundred universal formulas where one can calculate by hand enormous numbers of definite integrals, fractional derivatives and inverse operators. Despite the great success of numerical calculations due to computer technology, analytical calculations still play a vital role in the study of new, as yet unexplored, areas of mathematics, physics and other branches of sciences. Readers, including non-specialists, can obtain themselves universal formulas and define new special functions in integral and series representations by using the methods expounded in this book. This applies to anyone utilizing analytical calculations in their studies.

Dependence Logic: Theory and Applications by Samson Abramsky

English | 13 July 2016 | ISBN: 3319318012 | 292 Pages | EPUB | 3.59 MB

In this volume, different aspects of logics for dependence and independence are discussed, including both the logical and computational aspects of dependence logic, and also applications in a number of areas, such as statistics, social choice theory, databases, and computer security. The contributing authors represent leading experts in this relatively new field, each of whom was invited to write a chapter based on talks given at seminars held at the Schloss Dagstuhl Leibniz Center for Informatics in Wadern, Germany (in February 2013 and June 2015) and an Academy Colloquium at the Royal Netherlands Academy of Arts and Sciences (March 2014). Altogether, these chapters provide the most up-to-date look at this developing and highly interdisciplinary field and will be of interest to a broad group of logicians, mathematicians, statisticians, philosophers, and scientists. Topics covered include

a comprehensive survey of many propositional, modal, and first-order variants of dependence logic;

new results concerning expressive power of several variants of dependence logic with different sets of logical connectives and generalized dependence atoms;

connections between inclusion logic and the least-fixed point logic;

an overview of dependencies in databases by addressing the relationships between implication problems for fragments of statistical conditional independencies, embedded multivalued dependencies, and propositional logic;

various Markovian models used to characterize dependencies and causality among variables in multivariate systems;

applications of dependence logic in social choice theory; and

an introduction to the theory of secret sharing, pointing out connections to dependence and independence logic.

Euclidean Distance Geometry: An Introduction By Leo Liberti, Carlile Lavor

English | PDF,EPUB | 2017 | 141 Pages | ISBN : 331960791X | 8.43 MB

This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several.

Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.