الصفحة 2
الصفحة 2
Variational Methods in Shape Optimization Problems
The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems.
Variational Methods : Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
Gives a concise introduction to variational methods and presents an overview of areas of current research in the calculus of variations. The fourth edition gives a survey on new developments in the field. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Also the recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. Aside from these more significant additions, a number of smaller changes throughout the text have been made and the references have been updated.
Variational and Quasi-Variational Inequalities in Mechanics
The variational method is a powerful tool to investigate states and processes in technical devices, nature, living organisms, systems, and economics. The power of the variational method consists in the fact that many of its sta- ments are physical or natural laws themselves. The essence of the variational approach for the solution of problems rel- ing to the determination of the real state of systems or processes consists in the comparison of close states. The selection criteria for the actual statesmust be such that all the equations and conditions of the mathematical model are satis?ed. Historically, the first variational theory was the Lagrange theory created to investigate the equilibrium of finite-dimensional mechanical systems under holonomic bilateral constraints (bonds). The selection criterion proposed by Lagrange is the admissible displacement principle.
Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes
The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potential representations, and the solution of the latter in Sobolev spaces.
Variation et optimisation de formes : Une analyse géométrique = Variation and optimization of shapes : A geometric analysis
An introduction to modern approaches to the mathematical optimization of shapes. It is based solely on first-year Master's level mathematics knowledge, but already allows readers to address open questions in this rapidly evolving field. It develops the methodology as well as the mathematical analysis and geometric tools necessary for studying domain variations. It includes a systematic study of geometric questions associated with the Laplace operator, classical capacity, and differentiation with respect to a shape, as well as a FAQ on common topologies of domains and on the geometric properties of optimal shapes, including what happens when they do not exist, all accompanied by a substantial bibliography.
Uses of technology in upper secondary mathematics education
This survey addresses the use of technology in upper secondary mathematics education from four points of view: theoretical analysis of epistemological and cognitive aspects of activity in new technology mediated learning environments, the changes brought by technology in the interactions between environment, students and teachers, the interrelations between mathematical activities and technology, skills and competencies that must be developed in teacher education. Research shows that the use of some technologies may deeply change the solving processes and contribute to impact the learning processes. The questions are which technologies to choose for which purposes, and how to integrate them, so as to maximize all students’ agency. In particular the role of the teacher in classrooms and the content of teacher education programs are critical for taking full advantage of technology in teaching practice.
Uniformly Accelerating Charged Particles : A Threat to the Equivalence Principle
There has been a long debate about whether uniformly accelerated charges should radiate electromagnetic energy and how one should describe their worldline through a flat spacetime, i.e., whether the Lorentz-Dirac equation is right. There are related questions in curved spacetimes, e.g., do different varieties of equivalence principle apply to charged particles, and can a static charge in a static spacetime radiate electromagnetic energy? The problems with the LD equation in flat spacetime are spelt out in some detail here, and its extension to curved spacetime is discussed. Different equivalence principles are compared and some vindicated. The key papers are discussed in detail and many of their conclusions are significantly revised by the present solution.
Uniform Output Regulation of Nonlinear Systems : A Convergent Dynamics Approach
This book is one of the first systematic studies on the nonlinear output regulation problem that embraces both the local and global solvability analysis, covering such aspects as solvability conditions, controller design, and practical implementation issues.
Underwater Robots : Motion and Force Control of Vehicle-Manipulator Systems
Deals with the main control aspects in underwater manipulation tasks. The mathematical model with significant impact on the control strategy is discussed.
Understanding Non-equilibrium Thermodynamics : Foundations, Applications, Frontiers
Our time is characterized by an explosion of information and by an accel- ation of knowledge. A book cannot compete with the huge amount of data available on the Web. However, to assimilate all this information, it is n- essary to structure our knowledge in a useful conceptual framework. The purpose of the present work is to provide such a structure for students and researchers interested by the current state of the art of non-equilibrium th- modynamics. The main features of the book are a concise and critical pres- tation of the basic ideas, illustrated by a series of examples, selected not only for their pedagogical value but also for the perspectives o?ered by recent technological advances. This book is aimed at students and researchers in physics, chemistry, engineering, material sciences, and biology. We have been guided by two apparently antagonistic objectives: gener- ity and simplicity. To make the book accessible to a large audience of n- specialists, we have decided about a simpli?ed but rigorous presentation. Emphasis is put on the underlying physical background without sacri?cing mathematical rigour, the several formalisms being illustrated by a list of - amplesandproblems.
Understanding acoustics : An experimentalist’s view of sound and vibration
Focuses on experiments and on approximation techniques rather than mathematical rigor. The second edition has benefited from comments and corrections provided by many acousticians, in particular those who have used the first edition in undergraduate and graduate courses. For example, phasor notation has been added to clearly distinguish complex variables, and there is a new section on radiation from an unbaffled piston
Types for Proofs and Programs ; International Conference, TYPES 2007, Cividale des Friuli, Italy, May 2-5, 2007 Revised Selected Papers
The topic of this book was formal reasoning and computer programming based on type theory. Great importance was attached to languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certified software, formalization of mathematics and mathematics
Two Cultures : Essays in Honour of David Speiser
Editor Kim Williams has assembled a group of notes where scholars contribute essays inspired by their contact with Prof David Speiser. In honour of his eightieth birthday. Topics range from history of sciences to history of art, from architecture theory to music theory, from particle physics to the proliferation of nuclear weapons, to an essay on the very nature of interdisciplinary studies.
Tutorials in Mathematical Biosciences IV : Evolution and Ecology
The book offers an easy introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. The first two chapters review the concept and methodologies of phylogenetic trees; computational schemes and illustrations are given, including applications such as tracing the origin of SARS and influenza. The third chapter introduces the reader to ecological models, including predator-prey models. This chapter includes and introduction to reaction-diffusion equations, which are used to analyze the ecological models. The next chapter reviews a broad range of ongoing research in population dynamics, including evolution of dispersal models; it also features interesting mathematical theorems and lists open problems.
Tutorials in Mathematical Biosciences III : Cell Cycle, Proliferation, and Cancer
This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy.
Tutorials in Mathematical Biosciences II : Mathematical Modeling of Calcium Dynamics and Signal Transduction
This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. this book also presents much of the underlying physiology, so that readers may learn both the mathematics and the physiology at the same time, and see how the models are applied to specific biological questions.
Tutorials in Mathematical Biosciences I : Mathematical Neuroscience
Introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.
Turnpike Properties in the Calculus of Variations and Optimal Control
This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics.
Turbulence in Fluids : Fourth Revised and Enlarged ed.
This is the 4th edition of a book originally published by Kluwer Academic Publishers. It is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects, with many advanced developments using mathematical spectral methods (two-point closures like the EDQNM theory), direct-numerical simulations, and large-eddy simulations.Topics dealt with include: an introduction to turbulence in fluid mechanics; basic fluid dynamics; transition to turbulence; shear-flow turbulence; Fourier analysis for homogeneous turbulence; isotropic turbulence; phenomenology and simulations; analytical theories and stochastic models; two-dimensional turbulence; geostrophic turbulence; absolute-equilibrium ensembles; the statistical predictability theory; large-eddy simulations; and a section that explores developments towards real-world turbulence.
Turbulence and Diffusion : Scaling Versus Equations
This book is an introduction to the multidisciplinary field of anomalous diffusion in complex systems, with emphasis on the scaling approach as opposed to techniques based on the quantitative analysis of underlying transport equations. Typical examples of such systems are turbulent plasmas, convective rolls, zonal flow systems and stochastic magnetic fields. From the more methodological point of view, the approach relies on the general use of correlations estimates, quasilinear equations and continuous time random walk techniques. Yet, the mathematical descriptions are not meant to become a fixed set of recipes but rather develop and strengthen the reader's physical intuition and understanding on the underlying mechanisms involved.
