الصفحة 28
الصفحة 28
Continuous Semigroups of Holomorphic Self-maps of the Unit Disc
The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Carathéodory prime ends topology and Gromov hyperbolicity theory.
Continuous Optimization : Current Trends and Modern Applications
The search for the best possible performance is inherent in human nature. Individuals, enterprises and governments all seek optimal—that is, the best—possible solutions of problems that they meet. Evidently, continuous optimization plays an increasingly significant role in everyday management and technical decisions in science, engineering and commerce. The collection of 16 refereed papers in this book covers a diverse number of topics and provides a good picture of recent research in continuous optimization. The first part of the book presents substantive survey articles in a number of important topic areas of continuous optimization. Most of the papers in the second part present results on the theoretical aspects as well as numerical methods of continuous optimization. The papers in the third part are mainly concerned with applications of continuous optimization.
Construction of Global Lyapunov Functions : Using Radial Basis Functions
In this volume, the basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented.
Constrained optimization and image space analysis ; Vol.1 : Separation of sets and optimality conditions
Constrained Optimization and Image Space Analysis unites his results and presents optimization theory and variational inequalities in their light.It presents a new approach to the theory of constrained extremum problems, including Mathematical Programming, Calculus of Variations and Optimal Control Problems. Such an approach unifies the several branches: Optimality Conditions, Duality, Penalizations, Vector Problems, Variational Inequalities and Complementarity Problems. The applications benefit from a unified theory.
Conics and Cubics : A Concrete Introduction to Algebraic Curves
Its focus on curves of degree at most three keeps results tangible and proofs transparent. Theorems follow naturally from high school algebra and two key ideas: homogenous coordinates and intersection multiplicities. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout's Theorem on the number of intersections of two curves.The book is a text for a one-semester course on algebraic curves for junior-senior mathematics majors. The only prerequisite is first-year calculus.
Conformal Groups in Geometry and Spin Structures
This book provides a self-contained overview of this important area of mathematical physics, beginning with its origins in the works of Cartan and Chevalley and progressing to recent research in spinors and conformal geometry. Key topics and features: * Focuses initially on the basics of Clifford algebras * Studies the spaces of spinors for some even Clifford algebras * Examines conformal spin geometry, beginning with an elementary study of the conformal group of the Euclidean plane * Treats covering groups of the conformal group of a regular pseudo-Euclidean space, including a section on the complex conformal group * Introduces conformal flat geometry and conformal spinoriality groups, followed by a systematic development of riemannian or pseudo-riemannian manifolds having a conformal spin structure * Discusses links between classical spin structures and conformal spin structures in the context of conformal connections * Examines pseudo-unitary spin structures and pseudo-unitary conformal spin structures using the Clifford algebra associated with the classical pseudo-unitary space
Conformal and Potential Analysis in Hele-Shaw Cells
This monograph aims at giving a presentation of recent and new ideas that arise from the problems of planar fluid dynamics and which are interesting from the point of view of geometric function theory and potential theory. In particular, this book is concerned with geometric problems for Hele-Shaw flows. Also Hele-Shaw flows on parameter spaces (e.g., the Teichmüller space) are treated and connections with string theory are revealed. Ultimately, the interaction between several branches of complex and potential analysis, and planar fluid mechanics is discussed.
Conflicts Between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany
Conflicts Between Generalization, Rigor, and Intuition undertakes a historical analysis of the development of two mathematical concepts -negative numbers and infinitely small quantities, mainly in France and Germany, but also in Britain, and the different paths taken there.This book not only discusses the history of the two concepts, but it also introduces a wealth of new knowledge and insights regarding their interrelation as necessary foundations for the emergence of the 19th century concept of analysis. The historical investigation unravels several processes underlying and motivating conceptual change: generalization (in particular, algebraization as an agent for generalizing) and a continued effort of intuitive accessibility which often conflicted with likewise desired rigor. The study focuses on the 18th and the 19th centuries.The book provides a productive unity to a large number of historical sources.
Concepts and Results in Chaotic Dynamics : A Short Course
The book is a good introduction to the field of dynamical systems with a particular emphasis on statistical properties and applications. In particular, the relations both with real experiments with numerical simulations are discussed. The book contains many figures that really help the understanding of the text. The book can be used as a text for an introductory course in dynamical systems
Conception optimale de structures = Optimal structural design
Optimal Structural Design deals with all aspects of shape optimization, parametric, geometric and topological, and gives a large place to numerical algorithms, gradient methods and stochastic methods (with an original contribution by Marc Schoenauer for this last point). In particular, most of the structural optimization algorithms have been implemented in the FreeFem ++ finite element software and the programs are freely available on the web. Optimal structural design is devoted to structural or shape optimization and is intended for a mixed audience of applied mathematicians and mechanicians. It discusses parametric, geometric and topology optimization and gives deterministic and stochastic numerical algorithms (implemented in the FreeFem ++ finite element software).
Concentrator Location in Telecommunications Networks
It presents polyhedral results and exact solution methods for location problems encountered in telecommunications but which also have applications in other areas like transportation and supply chain management.
Concentration inequalities and model selection ; Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 2003
An overview of a non-asymptotic theory for model selection is given here and some selected applications to variable selection, change points detection and statistical learning are discussed. This volume reflects the content of the course given by P. Massart in St. Flour in 2003.
Computing the Electrical Activity in the Heart
This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. The book gives an introduction to the most important models of the field, followed by a detailed description of numerical techniques for the models. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers.
Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra
This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory.
Computing in Algebraic Geometry : A Quick Start using SINGULAR
Algebraic geometry generally studies the properties of solution sets of systems of polynomial equations without direct reference to the actual polynomials used in these systems. … This is especially desirable for classwork where the development of the abstract machinery generally outlasts the patience of the students, except possibly the most motivated ones.
Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models
Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented.
Computer Algebra Recipes : An Introductory Guide to the Mathematical Models of Science
Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models. Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry.
Computer Algebra Recipes : An Advanced Guide to Scientific Modeling
The text is built around a large number of computer algebra worksheets or "recipes" that have been designed using MAPLE to provide tools for problem solving and to stimulate critical thinking.
Computational Turbulent Incompressible Flow: Applied Mathematics : Body and Soul 4
This is Volume 4 of the book series of the Body & Soul mathematics education reform program, and presents a unified new approach to computational simulation of turbulent.
Computational Physiology : Simula Summer School 2021 − Student Reports
Compiles student reports from the 2021 Simula Summer School in Computational Physiology. Interested readers will find herein a number of modern approaches to modeling excitable tissue. This should provide a framework for tools available to model subcellular and tissue-level physiology across scales and scientific questions.
