الصفحة 43
الصفحة 43
Arithmetical investigations : Representation theory, orthogonal polynomials, and quantum interpolations
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
Approval Voting
The book proposes a compelling way to elect some 500,000 officials in public elections. After a generation of discussion and debate on the subject, the authors remain convinced that Approval Voting is as relevant today.
Appropriate Dose Selection - How to Optimize Clinical Drug Development
Optimal dose individualization has become more important in improving clinical efficacy and safety, given the variability in drug response, e.g., due to concurrent illnesses or co-medications. Therefore, the role of optimal dose finding in early clinical drug development so as to maximize successful clinical use is emphasized. The continued use of biomarkers – based on the (known) pharmacology of the drug and/or biology of the underlying disease – along with exposure–response evaluation throughout all phases of drug development can quantitatively integrate clinical pharmacology knowledge, provide early proof of concept, and help in rational dose selection and rational drug product labeling for clinical use.
Approaches to Fundamental Physics : An Assessment of Current Theoretical Ideas
This book presents contributions on particle theory, quantum field theory, general relativity, quantum gravity, string theory and cosmology. These represent the outcome of numerous discussions, taking place among the authors over a period of several years, about the research landscape of present-day fundamental theoretical physics. Indeed, the resultant book documents their attempt, out of their respective and highly specialized scientific positions, to find a way of communicating about methods, achievements and promises of the different approaches which shape the development of this field. It is therefore also an attempt to elucidate the connections between these approaches, and present them not as disjoint ventures but rather as facets of a common quest for understanding. Readers interested in fundamental approaches of theoretical physics will find this book highly stimulating and enlightening.
Applied Stochastic Control of Jump Diffusions
The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications.
Applied Quantitative Finance
Applied Quantitative Finance (2nd edition) provides a comprehensive and state-of-the-art treatment of cutting-edge topics and methods. It provides solutions to and presents theoretical developments in many practical problems such as risk management, pricing of credit derivatives, quantification of volatility and copula modelling. The synthesis of theory and practice supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on practical implementation and theoretical concepts. This linkage between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners comfortable access to new techniques in quantitative finance.
Applied Multivariate Statistical Analysis
This book presents the tools and concepts of multivariate data analysis in a way that is understandable for non-mathematicians and practitioners who face statistical data analysis.
Applied cryptography and network security ; 18th International Conference, ACNS 2020, Rome, Italy, October 19–22, 2020, Proceedings, Part II
This two-volume set of LNCS 12146 and 12147 constitutes the refereed proceedings of the 18th International Conference on Applied Cryptography and Network Security, ACNS 2020, held in Rome, Italy, in October 2020.The conference was held virtually due to the COVID-19 pandemic. The 46 revised full papers presented were carefully reviewed and selected from 214 submissions. The papers were organized in topical sections named: cryptographic protocols cryptographic primitives, attacks on cryptographic primitives, encryption and signature, blockchain and cryptocurrency, secure multi-party computation, post-quantum cryptography.
Applied Cryptography and Network Security ; 18th International Conference, ACNS 2020, Rome, Italy, October 19–22, 2020, Proceedings, Part I
This two-volume set of LNCS 12146 and 12147 constitutes the refereed proceedings of the 18th International Conference on Applied Cryptography and Network Security, ACNS 2020, held in Rome, Italy, in October 2020. The conference was held virtually due to the COVID-19 pandemic. The 46 revised full papers presented were carefully reviewed and selected from 214 submissions. The papers were organized in topical sections named: cryptographic protocols cryptographic primitives, attacks on cryptographic primitives, encryption and signature, blockchain and cryptocurrency, secure multi-party computation, post-quantum cryptography.
Applied computational materials modeling : Theory, simulation and experiment
this book provides the average person working in the materials field with a more balanced perspective of the role that computational modeling can play in every day research and development efforts. This is done by presenting a series of examples of the successful application of various computational modeling procedures (everything from first principles to quantum approximate to CALPHAD methods) to real life surface and bulk alloy problems.This book should have a large appeal in the materials community, both for experimentalists who would greatly benefit from adding computational methods to their everyday research regimes, as well as for those scientists/engineers familiar with a particular computational method who would like to add complementary techniques to their arsenal of research and development tools
Applied Civil Engineering Risk Analysis
Povides readers with the tools needed to determine the probability of failure, and when multiplied by the consequences of failure, illustrates how to assess the risk of civil engineering problems. Presenting methods for quantifying uncertainty that exists in engineering analysis and design, with an emphasis on fostering more accurate analysis and design.
Applications of random matrices in physics
Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics.
Anti-Spam Measures : Analysis and Design
The goal of this book is the methodical analysis of the potential, limitations, advantages, and drawbacks of anti-spam measures. These determine to which extent the measures can contribute to the reduction of spam in the long run. The range of considered anti-spam measures includes legislative, organizational, behavioral and technological ones. Furthermore, the conceptual development and analysis of an infrastructural email framework that features such a complementary application, is pointed out. The technological and organizational facets, the framework is analyzed twofold: its theoretical effectiveness is assessed with the aid of the formal model mentioned above, its storage and traffic requirements are analyzed quantitatively.
Anaphora and Type Logical Grammar
This book develops a hybrid architecture that allows to incorporate anaphora resolution into grammatical deduction while avoiding these consequences. To this end, the grammar logic is enriched with a connective that specifically deals with anaphora.After giving a self-contained introduction into Type Logical Grammar in general, the book discusses the formal properties of this connective. In the sequel, Jäger applies this machinery to numerous linguistic phenomena pertaining to the interaction of pronominal anaphora, VP ellipsis and quantification. In the final chapter, the framework is extended to indefiniteness, specificity and sluicing.
Analytical Dynamics : Theory and Applications
This book takes a traditional approach to the development of the methods of analytical dynamics, using two types of examples throughout: simple illustrations of key results and thorough applications to complex, real-life problems
Analytical Chemistry : Theoretical and Metrological Fundamentals
Fundamentals of Analytical Chemistry are usually presented as a sum of chemical and physical foundations, laws, axioms and equations for analytical methods and procedures. In contrast, this book delivers a practice-oriented, general guiding theory valid for all methods and techniques. Starting with a closer look to analytical signals and their dependencies, all the important figures of merit characterizing the power of analytical procedures and the reliability of analytical results are discussed and quantified, such as sensitivity, precision, accuracy and ruggedness. Elements of signal theory, information theory, statistics and fundamentals of calibration are also presented for this aim.
Analysis, Modeling and Simulation of Multiscale Problems
This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.
An Invitation to Quantum Cohomology : Kontsevich's Formula for Rational Plane Curves
This book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint is mostly that of enumerative geometry, and the red thread of the exposition is the problem of counting rational plane curves. Kontsevich's formula is initially established in the framework of classical enumerative geometry, then as a statement about reconstruction for Gromov–Witten invariants, and finally, using generating functions, as a special case of the associativity of the quantum product.
An Introduction to the Relativistic Theory of Gravitation
The geometric interpretation of gravitation is one of the major foundations of modern theoretical physics. This primer introduces classical general relativity with emphasis on the clarity of conceptual structure and on the basic mathematical methods to build up systematically application skills. The wealth of physical phenomena entailed by the Einstein‘s equations is revealed with the help of specific models describing gravitomagnetism, gravitational waves, cosmology, gravitational collapse and black holes. End-of-chapter exercises complete the main text.
An Introduction to the Mathematics of Money : Saving and Investing
This is an undergraduate textbook on the basic aspects of personal savings and investing with a balanced mix of mathematical rigor and economic intuition. It uses routine financial calculations as the motivation and basis for tools of elementary real analysis rather than taking the latter as given. Proofs using induction, recurrence relations and proofs by contradiction are covered. Inequalities such as the Arithmetic-Geometric Mean Inequality and the Cauchy-Schwarz Inequality are used. Basic topics in probability and statistics are presented.
