Introduction to Continuous Semigroups

In the academic year 1994/95 I lectured on semigroups in the Scuola Normale Superiore and in the Politecnico di Torino. The purpose of the lectures was to present to an audience of graduate students a

In these notes the abstract theory of analytic one-parameter semigroups in Banach algebras is discussed, with the Gaussian, Poisson and fractional integral semigroups in convolution Banach algebras serving as motivating examples. Such semigroups are constructed in a Banach algebra with a bounded approximate identity. Growth restrictions on the semigroup are linked to the structure of the underlying Banach algebra. The Hille-Yosida Theorem and a result of J. Esterle's on the nilpotency of semigroups are proved in detail. The lecture notes are an expanded version of lectures given by the author at the University of Edinburgh in 1980 and can be used as a text for a graduate course in functional analysis.

The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications.

Practical optimization problems are often hard to solve, in particular when they are black boxes and no further information about the problem is available except via function evaluations. This work in

This text provides a basis for the analysis of optimization models and candidate optimal solutions, especially for continuous optimization models. The treatment focuses on the analysis and algebra tha

This bookis anelementary introduction to the theory of discrete dynamical systems, alsostressing the topological background of the topic. It treats all important concepts needed to understand recent l

This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated

This book is about stability of linear dynamical systems, discrete and continuous. More precisely, we discuss convergence to zero of strongly continuous semigroups of operators and of powers of a boun

This book introduces the basic tools of the qualitative theory of ordinary differential equations. It is ideal for a first course in the qualitative theory of differential equations or dynamical syste

This monograph provides a modern introduction to the theory of quantales.First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and l

Unusually clear, accessible coverage of set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals and more. Written for junior and senior underg

This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

Created by the continuous feedback of a "student-tested, faculty-approved" process, SOC4 delivers all the key terms and all of the core concepts for the introductory sociology course through a visuall

This text is an unbound, binder-ready edition. Introduction to Heat Transfer is the gold standard of heat transfer pedagogy for more than 30 years, with a commitment to continuous improvement by four

The proposed book explores the science and technology related to terahertz wave technologies, including the latest research on electromagnetic waves with an introduction to continuous wave THz technol

Thoroughly revised for its second edition, this advanced textbook provides an introduction to the basic methods of computational physics, and an overview of progress in several areas of scientific computing by relying on free software available from CERN. The book begins by dealing with basic computational tools and routines, covering approximating functions, differential equations, spectral analysis, and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as molecular dynamics, modeling continuous systems, Monte Carlo methods, genetic algorithm and programming, and numerical renormalization. It includes many more exercises. This can be used as a textbook for either undergraduate or first-year graduate courses on computational physics or scientific computation. It will also be a useful reference for anyone involved in computational research.

Thoroughly revised for its second edition, this advanced textbook provides an introduction to the basic methods of computational physics, and an overview of progress in several areas of scientific computing by relying on free software available from CERN. The book begins by dealing with basic computational tools and routines, covering approximating functions, differential equations, spectral analysis, and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as molecular dynamics, modeling continuous systems, Monte Carlo methods, genetic algorithm and programming, and numerical renormalization. It includes many more exercises. This can be used as a textbook for either undergraduate or first-year graduate courses on computational physics or scientific computation. It will also be a useful reference for anyone involved in computational research.

This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1), piecewise - terministic control problems

Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, the technique of continuous analysi

The first book on Modelica, a modeling language that can be used to simulate both continuous and discrete behavior, Introduction to Physical Modeling with Modelica provides the necessary background to

This graduate-level text offers a concise but wide-ranging introduction to methods of approximating continuous functions by functions depending only on a finite number of parameters. It places particu

This book is about dynamical systems that are "hybrid" in the sense that they contain both continuous and discrete state variables. Recently there has been increased research interest in the study of

Quantum information processing offers fundamental improvements over classical information processing, such as computing power, secure communication, and high-precision measurements. However, the best way to create practical devices is not yet known. This textbook describes the techniques that are likely to be used in implementing optical quantum information processors. After developing the fundamental concepts in quantum optics and quantum information theory, the book shows how optical systems can be used to build quantum computers according to the most recent ideas. It discusses implementations based on single photons and linear optics, optically controlled atoms and solid-state systems, atomic ensembles, and optical continuous variables. This book is ideal for graduate students beginning research in optical quantum information processing. It presents the most important techniques of the field using worked examples and over 120 exercises.

The book discusses both continuous and discrete systems in a systematic and sequential approaches for all aspects of nonlinear dynamics. The content structure is logical and its sequential orientation

Metabolic and Cellular Engineering (MCE) is more than an exciting scientific enterprise. It has become the cornerstone for coping with the challenges ahead of mankind. Continuous developments, new con

Metabolic and Cellular Engineering (MCE) is more than an exciting scientific enterprise. It has become the cornerstone for coping with the challenges ahead of mankind. Continuous developments, new con

This book provides a concrete introduction to quantum fields on a lattice: a precise and non-perturbative definition of quantum field theory obtained by replacing continuous space-time by a discrete set of points on a lattice. The path integral on the lattice is explained in concrete examples using weak and strong coupling expansions. Fundamental concepts such as 'triviality' of Higgs fields and confinement of quarks and gluons into hadrons are described and illustrated with the results of numerical simulations. The book also provides an introduction to chiral symmetry and chiral gauge theory, as well as quantized non-abelian gauge fields, scaling and universality. Based on the lecture notes of a course given by the author, this book contains many explanatory examples and exercises, and is suitable as a textbook for advanced undergraduate and graduate courses.

The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including Black-Scholes) are developed. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms

The theory of von Neumann algebras has undergone rapid development since the work of Tonita, Takesaki and Conner. These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the subject and demonstrate the important role of the theory of crossed products. Part I deals with general continuous crossed products and proves the commutation theorem and the duality theorem. Part II discusses the structure of Type III von Neumann algebras and considers crossed products with modular actions. Restricting the treatment to the case of o-finite von Neumann algebras enables the author to work with faithful normal states.

Now in its sixth edition, this historically organized introductory text treats philosophy as a dramatic and continuous story--a conversation about humankind's deepest and most persistent concerns. Tra

This book is the only source available that presents a unified view of the theory and applications of discrete and continuous- time signals. This is the only book to present the mathematical p

This text is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. It aims at providing some insight into basic abstract analysis which is now the contextual language of much modern mathematics. Although it is assumed that the student will have familiarity with elementary real and complex analysis and linear algebra and have studied a course in the analysis of metric spaces, a knowledge of integration theory or general topology is not required. The theme of this text concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. But the implications of the general theory are illustrated with a great variety of example spaces.

An accessible introduction to the use of regression analysis in the social sciencesRegression with Social Data: Modeling Continuous and Limited Response Variables represents the most complete and full