Publications of Our Researchers
List of selected publications in the fields of Exact Sciences and Engineering authored by our researchers. Report new publications to be added to the current page.
Aaronson J.  Aboudi, J.  Abramovich F.  Alon N.  ArtsteinAvidan, S.  Averbuch, A. Z.  BanksSills, L.  Barnea D.  BenGal I.  Benjamini Y.  Boxman R.L.  Corry L.  Dyn N.  Eidelman Y  Eppelbaum L. V.  Farkhi E.  Fibich G.  Freiman G.  Fridman E.  Fuchs C.  Fuchs M.B  Gefen A.  Gershon E.  Gilat D.  Gohberg I.  Goldberg S.  Hassin R.  Hefetz D.  HelfmanCohen, Y.  Hirschfeld J.  Hochberg Y.  Horwitz L.P.  Inselberg A.  Jarden M.  Krivelevich M.  Levanon N.  Litsyn S.  Malomed B.  Klartag B., Milman E.  Milman V. D.  Palamodov V. P.  Reich, Y.  Shaked U.  Schuss Z.  Shustin, E.  Taitel Y.  Tsirelson B.  Weiss G. H.  Yakubov Y.  Zamir R.  Zheludev, V. A.  Zwas G.
ארבל ב.  לויתן ת.  פוקס ק.  סולן א.  פרבר מ.
An introduction to infinite ergodic theory 1996 About this book
Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations.
The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behavior, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behavior" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory. 


Aboudi, J., Bednarcyk, B. A., Arnold, S. M. Micromechanics of composite materials a generalized multiscale analysis approach 2013 About this book
With composites under increasing use in industry to replace traditional materials in components and structures, the modeling of composite performance, damage and failure has never been more important.
Micromechanics of Composite Materials: A Generalized Multiscale Analysis Approach brings together comprehensive background information on the multiscale nature of the composite, constituent material behaviour, damage models and key techniques for multiscale modelling, as well as presenting the findings and methods, developed over a lifetime’s research, of three leading experts in the field. The unified approach presented in the book for conducting multiscale analysis and design of conventional and smart composite materials is also applicable for structures with complete linear and nonlinear material behavior, with numerous applications provided to illustrate use. Modeling composite behaviour is a key challenge in research and industry; when done efficiently and reliably it can save money, decrease time to market with new innovations and prevent component failure. This book provides the tools and knowledge from leading micromechanics research, allowing researchers and senior engineers within academia and industry with to improve results and streamline development workflows. 
Mechanics of composite materials : a unified micromechanical approach 1991 About this book
This book presents a unified theory for the prediction of the overall behavior of composite materials. After discussing the fundamentals of the mechanics of composites, several basic composite models are described, together with the micromechanical method of cells for the analysis of elastic composites with aligned continuous or short fibers. The cell method is used to predict the strength and the fatigue failure of composites. Also presented are an analysis of viscoelastic behavior of composite materials with thermoviscoelastic resin matrices, the determination of the nonlinear response of viscoelastic composites, and the prediction of the initial yield surfaces of a metal matrix composites under isothermal conditions and at elevated temperatures. Finally, a generalization of the method of cells for the prediction of the inelastic response of metal matrix composites are presented, and the effect of the inclusion of imperfect bonding in composites is examined.


Statistical theory : a concise introduction 2013 About this book
Designed for a onesemester advanced undergraduate or graduate course, Statistical Theory: A Concise Introduction clearly explains the underlying ideas and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, and elements of decision theory. It introduces these topics on a clear intuitive level using illustrative examples in addition to the formal definitions, theorems, and proofs.
Based on the authors’ lecture notes, this studentoriented, selfcontained book maintains a proper balance between the clarity and rigor of exposition. In a few cases, the authors present a "sketched" version of a proof, explaining its main ideas rather than giving detailed technical mathematical and probabilistic arguments. Chapters and sections marked by asterisks contain more advanced topics and may be omitted. A special chapter on linear models shows how the main theoretical concepts can be applied to the wellknown and frequently used statistical tool of linear regression. Requiring no heavy calculus, simple questions throughout the text help students check their understanding of the material. Each chapter also includes a set of exercises that range in level of difficulty. 

Alon N., Bourgain J., Connes A., Gromov M., Milman V.D. Visions in mathematics  Towards 2000 2010 About this book
"Visions in Mathematics  Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematicians worldwide. The goals of the conference were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas.
The aims of the conference are reflected in the present set of survey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the second part of a twovolume set that will serve any research mathematician or advanced student as an overview and guideline through the multifaceted body of mathematical research in the present and near future. 

The Probabilistic Method 2008 About this book
This Third Edition of The Probabilistic Method reflects the most recent developments in the field while maintaining the standard of excellence that established this book as the leading reference on probabilistic methods in combinatorics. Maintaining its clear writing style, illustrative examples, and practical exercises, this new edition emphasizes methodology, enabling readers to use probabilistic techniques for solving problems in such fields as theoretical computer science, mathematics, and statistical physics.
The book begins with a description of tools applied in probabilistic arguments, including basic techniques that use expectation and variance as well as the more recent applications of martingales and correlation inequalities. Next, the authors examine where probabilistic techniques have been applied successfully, exploring such topics as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Sections labeled "The Probabilistic Lens" offer additional insights into the application of the probabilistic approach, and the appendix has been updated to include methodologies for finding lower bounds for Large Deviations. 


ArtsteinAvidan, S., Giannopoulos, A., Milman V.D. Asymptotic Geometric Analysis, Part I 2015 About this book
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a nontrivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzkytype theorems, volume distribution in convex bodies, and more. 

Averbuch, A. Z., Neittaanmäki, P., Zheludev, V. A. Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Volume II: NonPeriodic Splines 2016 About this book
This book presents various contributions of splines to signal and image processing from a unified perspective that is based on the Zak transform (ZT). It expands the methodology from periodic splines, which were presented in the first volume, to nonperiodic splines. Together, these books provide a universal toolbox accompanied by MATLAB software for manipulating polynomial and discrete splines, splinebased wavelets, wavelet packets and wavelet frames for signal/ image processing applications. In this volume, we see that the ZT provides an integral representation of discrete and polynomial splines, which, to some extent, is similar to Fourier integral. The authors explore elements of spline theory and design, and consider different types of polynomial and discrete splines. They describe applications of splinebased wavelets to data compression. These splines are useful for realtime signal processing and, in particular, realtime wavelet and frame transforms. Further topics addressed in this volume include: "global" splines, such as interpolating, selfdual and smoothing, whose supports are infinite; the compactly supported quasiinterpolating and smoothing splines including quasiinterpolating splines on nonuniform grids; and cubic Hermite splines as a source for the design of multiwavelets and multiwavelet frames. Readers from various disciplines including engineering, computer science and mathematical information technology will find the descriptions of algorithms, applications and software in this book especially useful. 

Advances in mathematical modeling and experimental methods for materials and structures: the Jacob Aboudi volume 2010 About this book
This work presents a collection of papers, written by leading authors in honor of Professor Jacob Aboudi.
Jacob Aboudi served as Head of the Department of Solid Mechanics, Materials and Structures, as Dean of the Faculty of Engineering and as Incumbent of the Diane and Arthur Belfer Chair of Mechanics and Biomechanics at Tel Aviv University. Aboudi has published more than 200 papers, 2 books and is a leading authority in the field of composite materials. The papers in this volume cover a wide spectrum of topics in the forefront of research in experimental methods and mathematical modeling of materials and structures. Subjects treated include developments in materials science, theoretical and applied mechanics, applied mathematics, applied physics, computational methods in engineering, mechanical and civil engineering. Both theoretical and experimental approaches are presented. As this book reflects the state of the art, possible engineering applications and future research directions are suggested. 
Search and Foraging: Individual Motion and Swarm Dynamics 2015 About this book
Since the start of modern computing, the studies of living organisms have inspired the progress in developing computers and intelligent machines. In particular, the methods of search and foraging are the benchmark problems for robotics and multiagent systems. The highly developed theory of search and screening involves optimal search plans that are obtained by standard optimization techniques while the foraging theory addresses search plans that mimic the behavior of living foragers.
This book examines how to program artificial search agents so that they demonstrate the same behavior as predicted by the foraging theory for living organisms. For cybernetics, this approach yields techniques that enable the best online search planning in varying environments. For biology, it allows reasonable insights regarding the internal activity of living organisms performing foraging tasks.
The book discusses foraging theory as well as search and screening theory in the same mathematical and algorithmic framework. It presents an overview of the main ideas and methods of foraging and search theories, making the concepts of one theory accessible to specialists of the other. The book covers Brownian walks and Lévy flight models of individual foraging and corresponding diffusion models and algorithms of search and foraging in random environments both by single and multiple agents. It also describes the active Brownian motion models for swarm dynamics with corresponding Fokker–Planck equations. Numerical examples and laboratory verifications illustrate the application of both theories.


Probabilistic Search for Tracking Targets: Theory and Modern Applications 2013 About this book
This book presents a probabilistic and informationtheoretic framework for a search for static or moving targets in discrete time and space.
Probabilistic Search for Tracking Targets uses an informationtheoretic scheme to present a unified approach for known search methods to allow the development of new algorithms of search. The book addresses search methods under different constraints and assumptions, such as search uncertainty under incomplete information, probabilistic search scheme, observation errors, group testing, search games, distribution of search efforts, single and multiple targets and search agents, as well as online or offline search schemes. The proposed approach is associated with path planning techniques, optimal search algorithms, Markov decision models, decision trees, stochastic local search, artificial intelligence and heuristic informationseeking methods. Furthermore, this book presents novel methods of search for static and moving targets along with practical algorithms of partitioning and search and screening. This book includes complete material for undergraduate and graduate courses in modern applications of probabilistic search, decisionmaking and group testing, and provides several directions for further research in the search theory. 

Benjamini Y., Bretz F., Sarkar S. K. Recent developments in multiple comparison procedures 2004 About this book
Implementing Shaffer's multiple comparison procedure for a large mumber of groups / John R. Donoghue 
Approximations to multivariate t integrals with application to multiple comparison procedures / Alan Genz, Frank Bretz and Yosef Hochberg  Multiple testing in adaptive designs  a review / Martin Hellmich and Gerhard Hommel  Power and sample size comparisons of stepwise FWE and FDR controlling test procedures in the normal manyone case / Manfred Horn and Charles W. Dunnett  Multiple comparisons with the best ROC curve / Jason C. Hsu ... [et al.]  On O'Brien's OLS and GLS tests for multiple endpoints / Brent R. Logan and Ajit C. Tamhane  On two results in multiple testing / Sanat K. Sarkar, Pranab K. Sen and Helmut Finner  FDR stepdown and stepup procedures for the correlated case / Paul N. Somerville  Multiple comparisons with more than one control / John D. Spurrier and Eleanne Solorzano  Compatible confidence intervals for intersection union tests involving two hypothesis / Klaus Strassburger, Frank Bretz and Yosef Hochberg  Weighted FWEcontrolling methods in highdimensional situations / Peter H. Westfall, Siegfried Kropf and Livio Finos  Appendix : new horizons in multiple comparison procedures / Yosef Hochberg. 


Communicating science: a practical guide for engineers and physical scientists 2017 About this book
Read this book before you write your thesis or journal paper! Communicating Science is a textbook and reference on scientific writing oriented primarily at researchers in the physical sciences and engineering. It is written from the perspective of an experienced researcher. It draws on the authors' experience of teaching and working with both native English speakers and English as a Second Language (ESL) writers. For the range of topics covered, this book is relatively short and tersely written, in order to appeal to busy researchers.
Communicating Science offers comprehensive guidance on:
Mentors will find the book a useful tool for systematically guiding their students in their early writing efforts. If your students read this book first, you will save time! Communicating Science may serve as a textbook for graduate level courses in scientific writing. 

Boxman R.L., Martin, D., Sanders D. Handbook of Vacuum Arc Science and Technology 1995 About this book
This is a comprehensive text describing the basic physics and technological applications of vacuum arcs. Part I describes basic physics of the vacuum arc, beginning with a brief tutorial review of plasma and electrical discharge physics, then describes the arc ignition process, cathode and anode spots which serve as the locus for plasma generation, and resultant interelectrode plasma. Part II describes the applications of the vacuum arc for depositing thin films and coatings, refining metals, switching high power, and as sources of intense electron, ion, plasma, and xray beams.


A brief history of numbers 2015 About this book
The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? Readership: The intended readership of this book includes undergraduate students of mathematics and the sciences, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics. 
Approximation of setvalued functions : adaptation of classical approximation operators 2014 About this book
This book is aimed at the approximation of setvalued functions with compact sets in an Euclidean space as values. The interest in setvalued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D crosssections. This is reflected in the focus of this book, which is the approximation of setvalued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated setvalued functions. Specialized results are given for functions with 1D sets as values.


Ball J. A., Eidelman Y., Helton J. W., Olshevsky V., Rovnyak J. Recent Advances in Matrix and Operator Theory 2007 About this book
This book expands the lectures given at IWOTA’05 (International Workshop on Operator Theory and Applications) which was held at the University of Connecticut, Storrs, USA, July 24–27, 2005. Many developments on the cutting edge of research in operator theory, matrix theory, coding theory, system theory, control theory and numerical linear algebra are reflected in this collection of original articles.
The volume is of a crossdisciplinary nature. A number of papers are devoted to the analysis and algorithms for matrices with quasiseparable structure which is an active area of concurrent research in numerical linear algebra. 

Eidelman Y., Milman V., Tsolomitis A. Function Analysis – An Intoduction 2004 About this book
This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of selfadjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded selfadjoint operators.
The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially selfcontained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book. The text is ideal for a oneyear course. It will also provide a sound basis for further study. It is suitable for graduate students and researchers interested in operator theory and functional analysis 

Aleinikov A. A., Belikov V. T., Eppelbaum L. V. Some physical foundations of geodynamics (in Russian) 2001 

Khesin B. E., Alexeyev V. V., Eppelbaum L. V. Interpretation of Geophysical Fields in Complicated Environments 1996 About this book
Books published during recent years in the field of applied geo physics can be, in general, divided into two main types. The first type covers such multiaspect books as "Introduction to Geophysics", while the secondspecial works on fundamental theoretical prob lems with an elaborate mathematical description. The books of the first type are mainly intended for beginner students and specialists in adjacent fields. The books of the second type may be useful for teachers and theorists. However, there are also books of another (third) type. These books describe the experience in geophysical in vestigation under specific conditions or propose solutions to concrete geological problems, being a methodological guide for geophysicists and concentrating ideas both for advanced students and researchers. Authors hope to give the readers a book of this kind. Interpretation of geophysical fields is a complex consistent pro cess. Its successful realization requires: (a) knowledge of geological regularities and geological situation; (b) availability of petrophysical support; (c) mathematical methods of solving direct and inverse problems of geophysics (i.e. computation of geophysical fields from a known source and determination of source characteristics from known fields); (d) application of statistical and logicoinformational procedures to the analysis and synthesis of observation results for revealing desired objects and peculiarities of the geological structure.


The Nonlinear Schrödinger Equation  Singular Solutions and optical Collapse 2014 About this book
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blowup) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results.
The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and BoseEinstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. 

It Seems I am a Jew 1980 

Introduction to TimeDelay Systems 2014 About this book
 Leads the reader from some basic results on timedelay systems to recent developments on Lyapunovbased methods
 Covers the comprehensive LMIbased methods, starting from the simple conditions and showing the ideas that essentially improve the results  Presents a timedelay approach to the hot topics of sampleddata and networked control systems The beginning of the 21st century can be characterized as the ”timedelay boom” leading to numerous important results. The purpose of this book is twofold, to familiarize the nonexpert reader with timedelay systems and to provide a systematic treatment of modern ideas and techniques for experts. This book is based on the course ”Introduction to timedelay systems” for graduate students in Engineering and Applied Mathematics that the author taught in Tel Aviv University in 20112012 and 20122013 academic years. The sufficient background to follow most of the material are the undergraduate courses in mathematics and an introduction to control. The book leads the reader from some basic classical results on timedelay systems to recent developments on Lyapunovbased analysis and design with applications to the hot topics of sampleddata and networkbased control. The objective is to provide useful tools that will allow the reader not only to apply the existing methods, but also to develop new ones. It should be of interest for researchers working in the field, for graduate students in engineering and applied mathematics, and for practicing engineers. It may also be used as a textbook for a graduate course on timedelay systems. 

Multivariate Quality Control: Theory and Applications 1998 About this book
Provides a theoretical foundation as well as practical tools for the analysis of multivariate data, using case studies and MINITAB computer macros to illustrate basic and advanced quality control methods. This work offers an approach to quality control that relies on statistical tolerance regions, and discusses computer graphic analysis highlighting multivariate profile charts.



Structures and Their Analysis 2016 About this book
Addressing structures, this book presents a classic discipline in a modern setting by combining illustrated examples with insights into the solutions. It is the fruit of the author’s many years of teaching the subject and of just as many years of research into the design of optimal structures. Although intended for an advanced level of instruction it has an undergraduate course at its core. Further, the book was written with the advantage of having massive computer power in the background, an aspect which changes the entire approach to many engineering disciplines and in particular to structures. This paradigm shift has dislodged the force (flexibility) method from its former prominence and paved the way for the displacement (stiffness) method, despite the multitude of linear equations it spawns. In this book, however, both methods are taught: the force method offers a perfect vehicle for understanding structural behavior, bearing in mind that it is the displacement method which does the heavy number crunching. As a rule the book keeps things as simple as possible, conveying the basic ideas and refraining from lengthy calculations wherever possible. Further, it endeavors to unify the approach, showing that whatever applies to simple springs is equally valid for intricate frames. In addition to various design considerations, it also addresses several topics relating to optimal structures that will be of interest to students and teachers of structures.

The Mechanobiology of Obesity and Related Diseases 2015 About this book
This volume describes the stateofknowledge in the study of the relationships between mechanical loading states in tissues and common pathophysiologies related to increase in mass of adipose tissues and/or hyperglycemia which eventually lead to obesity, diabetes, insulin resistance, hyperlipidemia, metabolic inflammations, certain types of cancer and other related diseases.
There appears to be an interaction between the loading states in tissues and cells and these chronic conditions, as well as with factors such as age, gender and genetics of the individual. Bioengineering has made key contributions to this research field in providing technologies for cell biomechanics experimentation, microscopy and image processing, tissue engineering and multiscale, multiphysics computational modeling. Topics at the frontier of this field of study include: the continuous monitoring of cell growth, proliferation and differentiation in response to mechanical factors such as stiffness of the extracellular matrix (ECM) and mechanical loads transferred through the ECM; mechanicallyactivated signaling pathways and molecular mechanisms; effects of different loading regimes and mechanical environments on differentiation fates of mesenchymal stem cells (MSCs) into myogenic and osteogenic versus adipogenic lineages; the interactions between nutrition and mechanotransduction; cell morphology, focal adhesion patterns and cytoskeletal remodeling changes in adipogenesis; activation of receptors related to diabetes by mechanical forces; brown and white adipose plasticity and its regulation by mechanical factors. 

Multiscale Computer Modeling in Biomechanics and Biomedical Engineering 2013 About this book
This book reviews the stateoftheart in multiscale computer modeling, in terms of both accomplishments and challenges. The information in the book is particularly useful for biomedical engineers, medical physicists and researchers in systems biology, mathematical biology, microbiomechanics and biomaterials who are interested in how to bridge between traditional biomedical engineering work at the organ and tissue scales, and the newer arenas of cellular and molecular bioengineering.


PatientSpecific Modeling in Tomorrow's Medicine 2012 About this book
This book reviews the frontier of research and clinical applications of Patient Specific Modeling, and provides a stateoftheart update as well as perspectives on future directions in this exciting field. The book is useful for medical physicists, biomedical engineers and other engineers who are interested in the science and technology aspects of Patient Specific Modeling, as well as for radiologists and other medical specialists who wish to be updated about the state of implementation.


Cellular and Biomolecular Mechanics and Mechanobiology 2011 About this book
This book describes these exciting new developments, and presents experimental and computational findings that altogether describe the frontier of knowledge in cellular and biomolecular mechanics, and the biological implications, in health and disease. The book is written for bioengineers with interest in cellular mechanics, for biophysicists, biochemists, medical researchers and all other professionals with interest in how cells produce and respond to mechanical loads.


Bioengineering Research of Chronic Wounds : a multidisciplinary study approach 2009 About this book
Pressurerelated chronic wounds are an important health concern that affects millions of patients and accumulates billions in annual costs. These wounds may occur when soft tissues are mechanically compressed between bony prominences and a supporting surface. This book gives a complete and quantitative explanation of the mechanobiology which causes chronic wounds. The reviews give an overall picture on all length scales of the phenomenon, starting from musculoskeletal biomechanics to the modeling of soft tissues and their interaction with bones. At the microscopic levels, it thoroughly reviews experiments and modeling of cellular forces and molecular processes that occur during injury and healing, including the integrity of living cells subjected to sustained mechanical forces and deformations. The results allow a complete picture of the tolerance of human tissues to sustained loads, and an understanding of the risk for onset of chronic wounds. Hence, this book is also valuable for all professionals involved in the prevention and treatment of chronic wounds.



The Pathomechanics of Tissue Injury and Disease, and the Mechanophysiology of Healing 2009 About this book
Over the last decade, it became clear that mechanical factors, such as deformations, forces and stiffness properties have critical influence on a wide spectrum of diseases. Traditionally, since the 1960's, mechanics has been associated mainly with orthopaedics, trauma and rehabilitation as well as with cardiovascular problems, and so, the work of biomechanists was mostly related to these areas. This led, for example, to good understanding of the loading conditions at which bone fractures occur, and how bone fractures can be healed more quickly if their mechanical environment is adequately controlled (e.g. via compression platescrew systems). However, more recently, on the 1980's1990's, it was discovered that mechanics has much more fundamental roles and effects on biological processes, as many cell types appeared to be responsive to mechanical stimuli. This boosted biomechanical research on the effects of mechanical factors at the microscopic scale of tissues, and the fields of "mechanobiology" and "mechanotransduction" emerged. Most recently, on the 2000's, there were studies, e.g. by Dr. Valerie Weaver and colleagues (as described in this book), reporting that at the cell scale, inadequate mechanical stimuli may even provoke cancer. Hence, the role of integration between mechanics, life sciences and medicine is growing rapidly, and becomes more important by the day. What allows this integration to expand so fast is the development of sophisticated bioengineering research and analysis tools. These include highly realistic computer simulations, small animal MRI, microsensors, bioreactors and many other recent breakthroughs that allow precision measurements of the mechanical conditions that apply in tissues at different levels of architectural hierarchy, whereas at the same time, close monitoring of the biological responses to these mechanical conditions became possible. This exciting atmosphere is at the background of the present book, which contains perspectives from leading scientists worldwide on the role of mechanics in injury, disease and healing. The topics covered span from bone tumors to pressure ulcers and from osteoarthritis to breast cancer, which illustrates how mechanics is now identified as the common denominator in so many important chronic conditions, as opposed to just trauma. In view of the multidisciplinary and diverse nature of this book, I expect it to be appealing to a broad readership, obviously including biomechanists but also medical doctors, physiologists, cell biologists, physiotherapists, nurses and all those who are interested in reading on the latest developments in our journey towards understanding the complex connections between mechanics and biology.

Advanced topics in control and estimation of statemultiplicative noisy systems 2013 About this book
Advanced Topics in Control and Estimation of StateMultiplicative Noisy Systems begins with an introduction and extensive literature survey. The text proceeds to cover solutions of measurementfeedback control and state problems and the formulation of the Bounded Real Lemma for both continuous and discretetime systems. The continuoustime reducedorder and stochastictracking control problems for delayed systems are then treated.
Ideas of nonlinear stability are introduced for infinitehorizon systems, again, in both the continuous and discretetime cases. The reader is introduced to six practical examples of noisy statemultiplicative control and filtering associated with various fields of control engineering. The book is rounded out by a threepart appendix containing stochastic tools necessary for a proper appreciation of the text: a basic introduction to nonlinear stochastic differential equations and aspects of switched systems and peak to peak optimal control and filtering. Advanced Topics in Control and Estimation of StateMultiplicative Noisy Systems will be of interest to engineers engaged in control systems research and development to graduate students specializing in stochastic control theory and to applied mathematicians interested in control problems. The reader is expected to have some acquaintance with stochastic control theory and statespacebased optimal control theory and methods for linear and nonlinear systems. 

Dubins L. E., Savage L. J.; Sudderth W. D.; Gilat D. How to gamble if you must : inequalities for stochastic processes 2014 About this book
This classic of advanced statistics is geared toward graduatelevel readers and uses the concepts of gambling to develop important ideas in probability theory. The authors have distilled the essence of many years' research into a dozen concise chapters. "Strongly recommended" by the Journal of the American Statistical Association upon its initial publication, this revised and updated edition features contributions from two wellknown statisticians that include a new Preface, updated references, and findings from recent research.
Following an introductory chapter, the book formulates the gambler's problem and discusses gambling strategies. Succeeding chapters explore the properties associated with casinos and certain measures of subfairness. Concluding chapters relate the scope of the gambler's problems to more general mathematical ideas, including dynamic programming, Bayesian statistics, and stochastic processes. Revised and updated reprint of the Dover, 1976 edition. 

Holomorphic Operator Functions of One Variable and Applications : methods from complex analysis in several variables 2009 About this book
This is a book on holomorphic operator functions of a single variable and their  plications,whichisfocussedontherelationsbetweenlocalandglobaltheories.Itis based on methods and technics of Complex analysis of scalar and matrix functions of several variables. The applications concern: interpolation, holomorphic families of subspaces and frames, spectral theory of polynomials with operator coe?cients, holomorphic equivalence and diagonalization, and PlemeljMuschelishvili fact ization. The book also contains a theory of WienerHopf integral equations with operatorvalued kernels and a theory of in?nite Toplitz ¨ matrices with operator entries. We started to work on these topics long ago when one of us was a Ph.D. s dent of the other in Kishinev (now Cisinau) University. Then our main interests were in problems of factorization of operatorvalued functions and singular in gral operators. Working in this area, we realized from the beginning that di?erent methods and tools from Complex analysis of several variables and their modi? tions are very useful in obtaining results on factorization for matrix and operator functions. We have in mind di?erent methods and results concerning connections between local and global properties of holomorphic functions. The ?rst period was very fruitful and during it we obtained the basic results presented in this book.


Gohberg I., Bart H., Hempfling T.,Kaashoek M. A. Israel Gohberg and Friends: On the Occasion of his 80th Birthday 2008 About this book
This book is dedicated to Israel Gohberg on occasion of his 80th birthday on August 23, 2008. It is an expression of esteem and friendship for a great mathematician, a remarkable person and an inspiring colleague. The book contains reflections by Gohberg himself on his own mathematical activities and those of others. It also includes contributions of colleagues and coworkers, both from his time in the Soviet Union and from when he lived and worked in the West. The contributions in question are not mathematical research papers but focus on the man Israel Gohberg and are intended for a wide audience. To be found are letters, speeches, laudatios and reminiscences which, together, present an attractive picture of the way in which Israel Gohberg in the past four to five decades influenced the lives of many mathematicians. Biographical material such as a curriculum vitae, a list of publications, a list of Ph.D. students and information about honorary doctoral degrees is also included.


Gohberg I., Goldberg S., Kaashoek M. A. Classes of linear operators 1990 About this book
After the book "Basic Operator Theory" by GohbergGoldberg was pub lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications. The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics grew larger than ex pected. Consequently, we decided to divide the material into two volumes  the first volume being presented now. During the past years, courses and seminars were given at our respective in stitutions based on parts of the texts. These were well received by the audience and enabled us to make appropriate choices for the topics and presentation for the two vol umes. We would like to thank G.J. Groenewald, A.B. Kuijper and A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us with lists of remarks and corrections. We are now aware that the Basic Operator Theory book should be revised so that it may suitably fit in with our present volumes. This revision is planned to be the last step of an induction and not the first.


Ball J. A., Gohberg I., Rodman L. Interpolation of rational matrix functions 1990 

Dym H., Goldberg S., Kaashoek M.A., Lancaster P.I. The Gohberg Anniversary Collection Volume I: The Calgary Conference and Matrix Theory Papers 1989 About this book
R. S. PHILLIPS I am very gratified to have been asked to give this introductory talk for our honoured guest, Israel Gohberg. I should like to begin by spending a few minutes talking shop. One of the great tragedies of being a mathematician is that your papers are read so seldom. On the average ten people will read the introduction to a paper and perhaps two of these will actually study the paper. It's difficult to know how to deal with this problem. One strategy which will at least get you one more reader, is to collaborate with someone. I think Israel early on caught on to this, and I imagine that by this time most of the analysts in the world have collaborated with him. He continues relentlessly in this pursuit; he visits his neighbour Harry Dym at the Weizmann Institute regularly, he spends several months a year in Amsterdam working with Rien Kaashoek, several weeks in Maryland with Seymour Goldberg, a couple of weeks here in Calgary with Peter Lancaster, and on the rare occasions when he is in Tel Aviv, he takes care of his many students.



Rational queueing 2016 About this book
Understand the Strategic Behavior in Queueing Systems Rational Queueing provides one of the first unified accounts of the dynamic aspects involved in the strategic behavior in queues. It explores the performance of queueing systems where multiple agents, such as customers, servers, and central managers, all act but often in a noncooperative manner. The book first addresses observable queues and models that assume statedependent behavior. It then discusses other types of information in queueing systems and compares observable and unobservable variations and incentives for information disclosure. The next several chapters present relevant models for the maximization of individual utilities, social welfare, and profits. After covering queueing networks, from simple parallel servers to general network structures, the author describes models for planned vacations and forced vacations (such as breakdowns). Focusing on supply chain models, he then shows how agents of these models may have different goals yet they all profit when the system operates efficiently. The final chapter allows bounded rationality by lowering the assumption of fully rational agents. 
To queue or not to queue : equilibrium behavior in queueing systems 2003 About this book
The literature on equilibrium behavior of customers and servers in queuing systems is rich. However, there is no comprehensive survey of this field. Moreover, what has been published lacks continuity and leaves many issues uncovered. One of the main goals of this book is to review the existing literature under one cover. Other goals are to edit the known results in a unified manner, classify them and identify where and how they relate to each other, and fill in some gaps with new results. In some areas we explicitly mention open problems. We hope that this survey will motivate further research and enable researchers to identify important open problems. The models described in this book have numerous applications. Many examples can be found in the cited papers, but we have chosen not to include applications in the book. Many of the ideas described in this book are special cases of general principles in Economics and Game Theory. We often cite references that contain more general treatment of a subject, but we do not go into the details. we have highlighted the results For each topic covered in the book, that, in our opinion, are the most important. We also present a brief discussion of related results. The content of each chapter is briefly de scribed below. Chapter 1 is an introduction. It contains basic definitions, models and solution concepts which will be used frequently throughout the book.


Hefetz D., Krivelevich M., Stojakovic M., Szabo T. Positional Games 2014 About this book
This text serves as a thorough introduction to the rapidly developing field of positional games. This area constitutes an important branch of combinatorics, whose aim it is to systematically develop an extensive mathematical basis for a variety of twoplayer perfect information games. These range from such popular games as TicTacToe and Hex to purely abstract games played on graphs and hypergraphs. The subject of positional games is strongly related to several other branches of combinatorics such as Ramsey theory, extremal graph and set theory, and the probabilistic method.
These notes cover a variety of topics in positional games, including both classical results and recent important developments. They are presented in an accessible way and are accompanied by exercises of varying difficulty, helping the reader to better understand the theory. The text will benefit both researchers and graduate students in combinatorics and adjacent fields 


Biomimetic Design Method for Innovation and Sustainability 2016 About this book
Presenting a novel biomimetic design method for transferring design solutions from nature to technology, this book focuses on structurefunction patterns in nature and advanced modeling tools derived from TRIZ, the theory of inventive problemsolving. The book includes an extensive literature review on biomimicry as an engine of both innovation and sustainability, and discusses in detail the biomimetic design process, current biomimetic design methods and tools. The structural biomimetic design method for innovation and sustainability put forward in this text encompasses (1) the research method and rationale used to develop and validate this new design method; (2) the suggested design algorithm and tools including the Find structure database, structurefunction patterns and ideality patterns; and (3) analyses of four case studies describing how to use the proposed method. This book offers an essential resource for designers who wish to use nature as a source of inspiration and knowledge, innovators and sustainability experts, and scientists and researchers, amongst others.

Forcing, arithmetic, division rings 1975 About this book
Existentially complete structures and existentially universal structures. Modelcompletions and modelcompanions. Infinite forcing in model theory. Approximating chains for . Finite forcing in model theory. Axiomatizations. Forcing and recursion theory. Existentially complete models. Simple models and R.E. ultrapowers. Regular models. Regular models and second order models for arithmetic. Generic models and the analytic hierarchy. Applications to complete extensions of peano's arithmetic. Existentially complete division rings. Nullstellensatz. Classes of existentially complete division algebras.


Lectures on NonStandard Analysis 1969 

Multiple comparison Procedures 2008 About this book
Offering a balanced, uptodate view of multiple comparison procedures, this book refutes the belief held by some statisticians that such procedures have no place in data analysis. With equal emphasis on theory and applications, it establishes the advantages of multiple comparison techniques in reducing error rates and in ensuring the validity of statistical inferences. Provides detailed descriptions of the derivation and implementation of a variety of procedures, paying particular attention to classical approaches and confidence estimation procedures. Also discusses the benefits and drawbacks of other methods. Numerous examples and tables for implementing procedures are included, making this work both practical and informative.



Relativistic Quantum Mechanics 2015 About this book
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group ClebschGordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum LaxPhillips theory of semi group evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the StueckelbergSchroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and nonAbelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The BekensteinSanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied.

Parallel coordinates : visual multidimensional geometry and its applications 2009 About this book
This book is about visualization, systematically incorporating the fantastic human pattern recognition into the problemsolving process, and focusing on parallel coordinates. The barrier, imposed by our threedimensional habitation and perceptual experience, has been breached by this innovative and versatile methodology. The accurate visualization of multidimensional problems and multivariate data unlocks insights into the role of dimensionality.
Beginning with an introductory chapter on geometry, the mathematical foundations are intuitively developed, interlaced with applications to data mining, information visualization, computer vision, geometric modeling, collision avoidance for air traffic and processcontrol. Many results appear for the first time. Multidimensional lines, planes, proximities, surfaces and their properties are unambiguously recognized (i.e. convexity viewed in any dimension) enabling powerful construction algorithms (for intersections, interiorpoints, linearprogramming). Key features of Parallel Coordinates: * An easytoread selfcontained chapter on data mining and information visualization * Numerous exercises with solutions, from basic to advanced topics, course projects and research directions * "Fast Track" markers throughout provide a quick grasp of essential material. * Extensive bibliography, index, and a chapter containing a collection of recent results (i.e. visualizing large networks, complexvalued functions and more) Parallel Coordinates requires only an elementary knowledge of linear algebra. It is wellsuited for selfstudy and as a textbook (or companion) for courses on information visualization, data mining, mathematics, statistics, computer science, engineering, finance, management, manufacturing, in scientific disciplines and even the arts. 

Algebraic patching 2011 About this book
Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$.


Field Arithmetic 2008 About this book
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely selfcontained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.
Progress from the first edition starts by characterizing the finitefield like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being profree. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have profree absolute Galois group (includes Shafarevich's conjecture)? The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005. 

Managing the Dynamics of New Product Development Processes 2011 About this book
This book merges productbased planning, process modelling, process execution, probabilistic simulations, and simulation based decisionmaking into one framework called the Dynamic newProduct Development Process. It provides readers with a means of improving the management of product development through enhanced methods and tools that are specifically tailored to the characteristics and challenges of such processes. It calls for a new Product Lifecycle Management paradigm of utilizing the managed product data for management of the product's development process.
Within the framework, the methods used are enhanced or modified to fit the newproduct development process requirements. Each specific method is exhaustively analyzed, from the basic definition of terms through a description of the state of the art of that topic and its limitations. Then, the method enhancements are illustrated by many examples, and discussed while suggesting further research directions. Finally, the enhanced methods are integrated and demonstrated by a test case. The main two methods described are the design structure matrix (DSM) and Petri nets, which are merged into a novel concept entitled DSM nets. Managing the Dynamics of New Product Development Processes provides algorithms, proofs, and practical examples that can be used for general study of the issues concerned. The main concepts presented are applicable to systems engineering and can be used by practitioners of product development processes, such as designers, product managers, and process managers, as well as developers of process management tools for systems with dynamically changing process structures. 

Krivelevich M., Panagiotou K., Penrose M., McDiarmid C. Random Graphs, Geometry and Asymptotic Structure 2016 About this book
The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through selfstudy, covering a lot of its fundamentals but little of the more recent developments. This book provides a selfcontained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.


Radar Signals 2004 About this book
A text and general reference on the design and analysis of radar signals
As radar technology evolves to encompass a growing spectrum of applications in military, aerospace, automotive, and other sectors, innovations in digital signal processing have risen to meet the demand. Presenting a long overdue, uptodate, dedicated resource on radar signals, the authors fill a critical gap in radar technology literature. Radar Signals features indepth coverage of the most prevalent classical and modern radar signals used today, as well as new signal concepts developed in recent years. Inclusion of key MATLAB software codes throughout the book demonstrates how they dramatically simplify the process of describing and analyzing complex signals. Topics covered include: * Matched filter and ambiguity function concepts * Basic radar signals, with both analytical and numerical analysis * Frequency modulated and phasecoded pulses * Complete discussion of bandlimiting schemes * Coherent LFM pulse trainsthe most popular radar signal * Diversity in pulse trains, including stepped frequency pulses * Continuouswave signals * Multicarrier phasecoded signals Combining lucid explanation, preferred signal tables, MATLAB codes, and problem sets in each chapter, Radar Signals is an essential reference for professionalsand a systematic tutorial for any seeking to broaden their knowledge base in this dynamic field. 

Radar Principles 1988 About this book
An advanced treatment of the main concepts of radar. Systematic and organized, it nicely balances readability with mathematical rigor. Many techniques and examples have been chosen from the radar industry (Rayleigh fluctuating targets are used as they yield simple expressions for the probability of detection), and others for their pedagogical value (Costas signals lead the coded radar signals because their ambiguity function can be intuitively deduced). Ordered statistics is covered in more depth than other CFAR techniques because its performance can be obtained analytically without resorting to simulation methods. Contains many exercises.


Peak power control in multicarrier communications 2007 About this book
Peak signal power is an important factor in the implementation of multicarrier (MC) modulation schemes, like OFDM, in wireless and wireline communication systems. This 2007 book describes tools necessary for analyzing and controlling the peaktoaverage power ratio in MC systems, and how these techniques are applied in practical designs. The author starts with an overview of multicarrier signals and basic tools and algorithms, before discussing properties of MC signals in detail: discrete and continuous maxima; statistical distribution of peak power; codes with constant peaktoaverage power ratio are all covered, concluding with methods to decrease peak power in MC systems. Current knowledge, problems, methods and definitions are summarized using rigorous mathematics, with an overview of the tools for the engineer. The book is aimed at graduate students and researchers in electrical engineering, computer science and applied mathematics, and practitioners in the telecommunications industry.



Spontaneous Symmetry Breaking, SelfTrapping, and Josephson Oscillations 2013 About this book
This volume collects a number of contributions on the general theme of spontaneous symmetry breaking in nonlinear systems, and related topics.
Current studies in these areas are going ahead at a full speed. Chapters included into the book present an overview on major recent achievements. They cover a number of different physical settings, which are introduced when a nonlinearity is added to underlying symmetric configurations. The spontaneous symmetry breaking, alias selftrapping into asymmetric states, happens when the strength of the nonlinearity exceeds a certain critical value. A related generic dynamical effect appears in the form of Josephson oscillations between mutually symmetric states. Theoretical studies of these phenomena, as well as related experimental findings, are extensively discussed in the book  chiefly, in the context of BoseEinstein condensates and nonlinear optics. 
Soliton Management in Periodic Systems 2006 About this book
During the past ten years, there has been intensive development in theoretical and experimental research of solitons in periodic media. This book provides a unique and informative account of the stateoftheart in the field. The volume opens with a review of the existence of robust solitary pulses in systems built as a periodic concatenation of very different elements. Among the most famous examples of this type of systems are the dispersion management in fiberoptic telecommunication links, and (more recently) photonic crystals. A number of other systems belonging to the same broad class of spatially periodic strongly inhomogeneous media (such as the splitstep and tandem models) have recently been identified in nonlinear optics, and transmission of solitary pulses in them was investigated in detail. Similar soliton dynamics occurs in temporaldomain counterparts of such systems, where they are subject to strong timeperiodic modulation (for instance, the Feshbachresonance management in BoseEinstein condensates). Basis results obtained for all these systems are reviewed in the book. This timely work will serve as a useful resource for the soliton community.


Geometric aspects of functional analysis : Israel Seminar (GAFA) 20112013 2014 About this book
As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis. Most of the papers deal with different aspects of Asymptotic Geometric Analysis, understood in a broad sense; many continue the study of geometric and volumetric properties of convex bodies and logconcave measures in highdimensions and in particular the meannorm, meanwidth, metric entropy, spectralgap, thinshell and slicing parameters, with applications to Dvoretzky and CentralLimittype results. The study of spectral properties of various systems, matrices, operators and potentials is another central theme in this volume. As expected, probabilistic tools play a significant role and probabilistic questions regarding Gaussian noise stability, the Gaussian Free Field and First Passage Percolation are also addressed. The historical connection to the field of Classical Convexity is also well represented with new properties and applications of mixedvolumes. The interplay between the real convex and complex plurisubharmonic settings continues to manifest itself in several additional articles. All contributions are original research papers and were subject to the usual refereeing standards.



Eliashberg, Y., Milman V. D., Polterovich, L., Schoen, R. Geometries in Interaction: GAFA special issue in honor of Mikhail Gromov 2012 About this book
Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. PiatetskiShapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics.

Geometric aspects of functional analysis Israel seminar 20042005 : GAFA 20042005 2005 About this book
This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) during the years 20042005 follows the long tradition of the previous volumes that reflect the general trends of the Theory and are a source of inspiration for research.
Most of the papers deal with different aspects of the Asymptotic Geometric Analysis, ranging from classical topics in the geometry of convex bodies, to inequalities involving volumes of such bodies or, more generally, logconcave measures, to the study of sections or projections of convex bodies. In many of the papers Probability Theory plays an important role; in some limit laws for measures associated with convex bodies, resembling Central Limit Theorems, are derive and in others probabilistic tools are used extensively. There are also papers on related subjects, including a survey on the behavior of the largest eigenvalue of random matrices and some topics in Number Theory. 

Geometric aspects of functional analysis : Israel seminar 20022003 :GAFA 20022003 2003 About this book
The Israeli GAFA seminar (on Geometric Aspect of Functional Analysis) during the years 20022003 follows the long tradition of the previous volumes. It reflects the general trends of the theory. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis. In addition the volume contains papers on related aspects of Probability, classical Convexity and also Partial Differential Equations and Banach Algebras. There are also two expository papers on topics which proved to be very much related to the main topic of the seminar. One is Statistical Learning Theory and the other is Models of Statistical Physics. All the papers of this collection are original research papers.


Geometric aspects of functional analysis : Israel seminar (Gafa) 19962000 2000 About this book
This volume of original research papers from the Israeli GAFA seminar during the years 19962000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convexlike structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincarélike inequalities.



Reconstruction from Integral Data 2016 About this book
This book is used for problems arising in diagnostics, including xray, positron radiography, ultrasound, scattering, sonar, seismic, impedance, wave tomography, crystallography, photothermoacoustics, photoelastics, and strain tomography. Reconstruction from Integral Data presents both longstanding and recent mathematical results from this field in a uniform way. The book focuses on exact analytic formulas for reconstructing a function or a vector field from data of integrals over lines, rays, circles, arcs, parabolas, hyperbolas, planes, hyperplanes, spheres, and paraboloids. It also addresses range characterizations. Coverage is motivated by both applications and pure mathematics. The book first presents known facts on the classical and attenuated Radon transform. It then deals with reconstructions from data of ray (circle) integrals. The author goes on to cover reconstructions in classical and new geometries. The final chapter collects necessary definitions and elementary facts from geometry and analysis that are not always included in textbooks. 
Reconstructive Integral Geometry 2004 About this book
One hundred years ago (1904) Hermann Minkowski [58] posed a problem: to re 2 construct an even function I on the sphere 8 from knowledge of the integrals MI (C) = fc Ids over big circles C. Paul Funk found an explicit reconstruction formula for I from data of big circle integrals. Johann Radon studied a similar problem for the Eu clidean plane and space. The interest in reconstruction problems like Minkowski Funk's and Radon's has grown tremendously in the last four decades, stimulated by the spectrum of new modalities of image reconstruction. These are Xray, MRI, gamma and positron radiography, ultrasound, seismic tomography, electron mi croscopy, synthetic radar imaging and others. The physical principles of these methods are very different, however their mathematical models and solution meth ods have very much in common. The umbrella name reconstructive integral geom etryl is used to specify the variety of these problems and methods. The objective of this book is to present in a uniform way the scope of well known and recent results and methods in the reconstructive integral geometry. We do not touch here the problems arising in adaptation of analytic methods to numerical reconstruction algorithms. We refer to the books [61], [62] which are focused on these problems. Various aspects of interplay of integral geometry and differential equations are discussed in Chapters 7 and 8. The results presented here are partially new.


Brownian dynamics at boundaries and interfaces : in physics, chemistry, and biology 2013 About this book
Brownian dynamics serve as mathematical models for the diffusive motion of microscopic particles of various shapes in gaseous, liquid, or solid environments. The renewed interest in Brownian dynamics is due primarily to their key role in molecular and cellular biophysics: diffusion of ions and molecules is the driver of all life. Brownian dynamics simulations are the numerical realizations of stochastic differential equations that model the functions of biological micro devices such as protein ionic channels of biological membranes, cardiac myocytes, neuronal synapses, and many more. Stochastic differential equations are ubiquitous models in computational physics, chemistry, biophysics, computer science, communications theory, mathematical finance theory, and many other disciplines. Brownian dynamics simulations of the random motion of particles, be it molecules or stock prices, give rise to mathematical problems that neither the kinetic theory of Maxwell and Boltzmann, nor Einstein’s and Langevin’s theories of Brownian motion could predict.
This book takes the readers on a journey that starts with the rigorous definition of mathematical Brownian motion, and ends with the explicit solution of a series of complex problems that have immediate applications. It is aimed at applied mathematicians, physicists, theoretical chemists, and physiologists who are interested in modeling, analysis, and simulation of micro devices of microbiology. The book contains exercises and worked out examples throughout. 

Nonlinear filtering and optimal phase tracking 2012 About this book
This book offers an analytical rather than measuretheoretical approach to the derivation of the partial differential equations of nonlinear filtering theory. The basis for this approach is the discrete numerical scheme used in MonteCarlo simulations of stochastic differential equations and Wiener's associated path integral representation of the transition probability density. Furthermore, it presents analytical methods for constructing asymptotic approximations to their solution and for synthesizing asymptotically optimal filters. It also offers a new approach to the phase tracking problem, based on optimizing the mean time to loss of lock. The book is based on lecture notes from a onesemester special topics course on stochastic processes and their applications that the author taught many times to graduate students of mathematics, applied mathematics, physics, chemistry, computer science, electrical engineering, and other disciplines. The book contains exercises and workedout examples aimed at illustrating the methods of mathematical modeling and performance analysis of phase trackers.


Theory and applications of stochastic processes : an analytical approach 2010 About this book
This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences. Its aim is to make probability theory readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and in asymptotic methods, rather than in probability and measure theory. It shows how to derive explicit expressions for quantities of interest by solving equations. Emphasis is put on rational modeling and approximation methods.


Greuel G. M., Lossen, C., Shustin, E. Introduction to singularities and Deformations 2007 About this book
Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and technical sciences.
This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. Plane curve singularities are a classical object of study, rich of ideas and applications, which still is in the center of current research and as such provides an ideal introduction to the general theory. Deformation theory is an important technique in many branches of contemporary algebraic geometry and complex analysis. This introductory text provides the general framework of the theory while still remaining concrete. In the first part of the book the authors develop the relevant techniques, including the Weierstraß preparation theorem, the finite coherence theorem etc., and then treat isolated hypersurface singularities, notably the finite determinacy, classification of simple singularities and topological and analytic invariants. In local deformation theory, emphasis is laid on the issues of versality, obstructions, and equisingular deformations. The book moreover contains a new treatment of equisingular deformations of plane curve singularities including a proof for the smoothness of the muconstant stratum which is based on deformations of the parameterization. Computational aspects of the theory are discussed as well. Three appendices, including basic facts from sheaf theory, commutative algebra, and formal deformation theory, make the reading selfcontained. The material, which can be found partly in other books and partly in research articles, is presented from a unified point of view for the first time. It is given with complete proofs, new in many cases. The book thus can serve as source for special courses in singularity theory and local algebraic and analytic geometry. 

Itenberg I.V., Mikhalkin G., Shustin E. Tropical algebraic geometry 2007 About this book
Tropical geometry is algebraic geometry over the semifield of tropical numbers, i.e., the real numbers and negative infinity enhanced with the (max,+)arithmetics. Geometrically, tropical varieties are much simpler than their classical counterparts. Yet they carry information about complex and real varieties.
These notes present an introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for nonspecialists to make the first steps in the subject which is not yet well represented in the literature. The intended audience is graduate, postgraduate, and Ph.D. students as well as established researchers in mathematics. 

Thome J. R., Taitel Y., Barnea D. Encyclopedia of twophase heat transfer and flow I: fundamentals and methods 2016 About this book
The aim of the two set series is to present a very detailed and up to date reference for researchers and practicing engineers in the fields of mechanical, refrigeration, chemical, nuclear and electronics engineering on the important topic of twophase heat transfer and twophase flow. The scope of the first set of 4 volumes presents the fundamentals of the twophase flows and heat transfer mechanisms, and describes in detail the most important prediction methods, while the scope of the second set of 4 volumes presents numerous special topics and numerous applications, also including numerical simulation methods.
Practicing engineers will find extensive coverage to applications involving: multimicrochannel evaporator cold plates for electronics cooling, boiling on enhanced tubes and tube bundles, flow pattern based methods for predicting boiling and condensation inside horizontal tubes, pressure drop methods for singularies (Ubends and contractions), boiling in multiport tubes, and boiling and condensation in plate heat exchangers. All of these chapters include the latest methods for predicting not only local heat transfer coefficients but also pressure drops. Professors and students will find this "Encyclopediaa of TwoPhase Heat Transfer and Flow" particularly exciting, as it contains authored books and thorough stateoftheart reviews on many basic and special topics, such as numerical modeling of twophase heat tranfser and adiabatic bubbly and slug flows, the unified annular flow boiling model, flow pattern maps, condensation and boiling theories, new emerging topics, etc. Readership: Graduate students, researchers and professional in the fields of mechanical, refrigeration, chemical, nuclear and electronics engineering on the important topics of twophase heat transfer and twophase flow. 

Lectures on probability theory and statistics : Ecole d'Ete de Probabilites de SaintFlour XXXII2002 2004 About this book
This is yet another indispensable volume for all probabilists and collectors of the SaintFlour series, and is also of great interest for mathematical physicists. It contains two of the three lecture courses given at the 32nd Probability Summer School in SaintFlour (July 724, 2002). Boris Tsirelson's lectures introduce the notion of nonclassical noise produced by very nonlinear functions of many independent random variables, for instance singular stochastic flows or oriented percolation. Two examples are examined (noise made by a Poisson snake, the Brownian web). A new framework for the scaling limit is proposed, as well as old and new results about noises, stability, and spectral measures. Wendelin Werner's contribution gives a survey of results on conformal invariance, scaling limits and properties of some twodimensional random curves. It provides a definition and properties of the SchrammLoewner evolutions, computations (probabilities, critical exponents), the relation with critical exponents of planar Brownian motions, planar selfavoiding walks, critical percolation, looperased random walks and uniform spanning trees.


Observation and control for operator semigroups 2009 About this book
The evolution of the state of many systems modeled by linear partial di?erential equations (PDEs) or linear delay di?erential equations can be described by ope torsemigroups.Thestate ofsucha systemis anelementin anin?nitedimensional normed space, whence the name “in?nitedimensional linear system”. The study of operator semigroups is a mature area of functional analysis, which is still very active. The study of observation and control operators for such semigroups is relatively more recent. These operators are needed to model the  teraction of a system with the surrounding world via outputs or inputs. The main topicsofinterestaboutobservationandcontroloperatorsareadmissibility,obse ability, controllability, stabilizability and detectability. Observation and control operators are an essential ingredient of wellposed linear systems (or more gen ally system nodes). In this book we deal only with admissibility, observability and controllability. We deal only with operator semigroups acting on Hilbert spaces. This book is meant to be an elementary introduction into the topics m tioned above. By “elementary” we mean that we assume no prior knowledge of ?nitedimensional control theory, and no prior knowledge of operator semigroups or of unbounded operators. We introduce everything needed from these areas. We do assume that the reader has a basic understanding of bounded operators on Hilbert spaces, di?erential equations, Fourier and Laplace transforms, dist butions and Sobolev spaces on ndimensional domains. Much of the background needed in these areas is summarized in the appendices, often with proofs.


Application of abstract differential equations to some mechanical problems About this book
PREFACE The theory of differentialoperator equations has been described in various monographs, but the initial physical problem which leads to these equations is often hidden. When the physical problem is studied, the mathematical proofs are either not given or are quickly explained. In this book, we give a systematic treatment of the partial differential equations which arise in elastostatic problems. In particular, we study problems which are obtained from asymptotic expansion with two scales. Here the methods of operator pencils and differentialoperator equations are used. This book is intended for scientists and graduate students in Functional Analy sis, Differential Equations, Equations of Mathematical Physics, and related topics. It would undoubtedly be very useful for mechanics and theoretical physicists. We would like to thank Professors S. Yakubov and S. Kamin for helpfull dis cussions of some parts of the book. The work on the book was also partially supported by the European Community Program RTNHPRNCT200200274. xiii INTRODUCTION In first two sections of the introduction, a classical mathematical problem will be exposed: the Laplace problem. The domain of definition will be, on the first time, an infinite strip and on the second time, a sector. To solve this problem, a well known separation of variables method will be used. In this way, the structure of the solution can be explicitly found. For more details about the separation of variables method exposed in this part, the reader can refer to, for example, the book by D. Leguillon and E. SanchezPalencia [LS].
2003 

Differentialoperator equations : ordinary and partial differential equations 2000 About this book
The theory of differentialoperator equations is one of two modern theories for the study of both ordinary and partial differential equations, with numerous applications in mechanics and theoretical physics. Although a number of published works address differentialoperator equations of the first and second orders, to date none offer a treatment of the higher orders.
In DifferentialOperator Equations, the authors present a systematic treatment of the theory of differentialoperator equations of higher order, with applications to partial differential equations. They construct a theory that allows application to both regular and irregular differential problems. In particular, they study problems that cannot be solved by various known methods and irregular problems not addressed in existing monographs. These include Birkhoffirregularity, nonlocal boundary value conditions, and nonsmoothness of the boundary of the domains. 

Lattice coding for signals and networks : a structured coding approach to quantization, modulation, and multiuser information theory 2014 About this book
Unifying information theory and digital communication through the language of lattice codes, this book provides a detailed overview for students, researchers and industry practitioners. It covers classical work by leading researchers in the field of lattice codes and complementary work on dithered quantization and infinite constellations, and then introduces the more recent results on 'algebraic binning' for sideinformation problems, and linear/lattice codes for networks. It shows how high dimensional lattice codes can close the gap to the optimal information theoretic solution, including the characterisation of error exponents. The solutions presented are based on lattice codes, and are therefore close to practical implementations, with many advanced setups and techniques, such as shaping, entropycoding, sideinformation and multiterminal systems. Moreover, some of the network setups shown demonstrate how lattice codes are potentially more efficient than traditional randomcoding solutions, for instance when generalising the framework to Gaussian networks.


Numerical mathematics  a laboratory approach 1993 About this book
Numerical Mathematics is a unique textbook which presents rudimentary numerical mathematics in conjunction with computational laboratory assignments. No previous knowledge of calculus or linear algebra is presupposed, and thus the book is tailormade for undergraduate students, as well as prospective mathematics teachers. The material in the book emphasises algorithmic aspects of mathematics, which are made viable through numerical assignments, in which the traditional 'chalkandtalk' lecturer turns, in part, into a laboratory instructor. The book is not a numerical methods book, containing readymade computational recipes. Rather, it guides the student to create the algorithm required for any given assignment  expressed in whichever programming language is used  on the basis of the underlying mathematics. The computational assignments cover iterative processes, area approximations, solution of linear systems, acceleration of series summation, interpolative approximations, and construction of computerlibrary functions. Throughout the book, strong emphasis is being put upon vital concepts such as error bounds, precision control, numerical efficiency, computational complexity, as well as round off errors and numerical stability. It is the authors' belief that the material presented in this book is part and parcel of the mathematical foundations that should be acquired by a student in the microcomputer era.



מתמטיקאים ואירועים גדולים בתולדות המתמטיקה 2009 
אסטרטגיות לפתרון בעיות מתמטיות חלקים א, ב, ג 1997 

ארבל ב., קרסיקוב א., רודיטי י. בעיות עם עקרון (Dirichlet) ורעיון (הצביעה) 1995 


אסטרטגיות לפתרון בעיות מתמטיות חלקים א, ב 1990 
יסודות החשיבה המתמטית צעדים ראשונים במתמטיקה מתקדמת 2012 על הספר
הספר מיועד לקוראים המתחילים בלימודי המתמטיקה המתקדמת, למורים למתמטיקה בבתי הספר ולמעוניינים לרענן את הידע שלהם במתמטיקה מתקדמת. הספר נכתב כמורה דרך הדרגתי וידידותי במסלולה שואף להשגת היעדים הבאים: היכרות עם השפה המתמטית ועם חוקי הלוגיקה; התנסויות מגוונות בפעילויות מתמטיות מקובלות: הכללה, הסקה, הגדרה, הוכחה מתמטית וכדומה; חיזוק והעמקה של ידע קודם (שנרכש בבית הספר) במתמטיקה; הצגה פורמלית של מושגי מפתח במתמטיקה מתקדמת; פתיחת צוהר למגוון רחב של נושאים חדשים. בבסיס הספר עומדת ההחלטה להקדים ללימודי המתמטיקה המתקדמת דיון מקיף בשפה, בתרבות ובחשיבה הנדרשות מהעוסקים במתמטיקה מתקדמת. ההדגמה של המושגים ושל הרעיונות החדשים מתבססת בעיקר על תכנים מהמתמטיקה בבית הספר העליסודי – גישה שנועדה לסייע לרענן את זיכרון הקוראים בנושאים שהם נכסי צאן ברזל של כל מתמטיקאי מתחיל. כל אלה יקבלו ניסוח חדש בשפה מתמטית מדויקת ומבוססת המדגישה את הרעיונות המתמטיים הכלליים העומדים בבסיסם. הספר מורכב משלושה "צעדים": קוראים מתמטיקה (יסודות השפה המתמטית), כותבים מתמטיקה (הגדרות, טענות ומשפטים במתמטיקה) וחושבים מתמטיקה (כללי היסק, טיעונים, הוכחות מתמטיות). המאפיינים הייחודיים של "צעדים" אלו הם: שאלוני ידע מוקדם שעוזרים להתמקד בבעייתיות שבחשיבה לוגית, אינטואיטיבית ומפתחים ציפיות לקראת הדיון הקרוב; לשון הדיון שמביאה בחשבון את מגבלות הידע המתמטי של קהל היעד ועל כן אינה פורמלית יתר על המידה ועם זאת מקפידה על דיוק מתמטי; מספר רב של התנסויות, משימות וסוגיות מחיי היוםיום, מהמתמטיקה של בית הספר וגם מהמתמטיקה המתקדמת; וכן דיונים בשגיאות טיפוסיות, בתפיסות מוטעות ובכשלים לוגיים נפוצים. התקווה היא שהידע והניסיון שיירכשו בעקבות עיון בספר זה על כל רבדיו ישמשו את הקוראים בהמשך לימודי המתמטיקה, בלימוד ענפי ידע נוספים ואף בחיי היוםיום.



אמת וסקר 1998 
תורת המשחקים 2008 על הספר
תורת המשחקים היא ענף במתמטיקה העוסק במידול מצבי החלטה אינטראקטיביים ובניתוחם. במצבים אלה מעורבים כמה מקבלי החלטות שמטרותיהם שונות, וההחלטה של כל אחד מהם עשויה להשפיע על כל האחרים. ראשיתה של תורה המשחקים בשנות הארבעים של המאה העשרים, ומאז שנות החמישים היא מיושמת בכלכלה, בביולוגיה, במדעי המחשב ובמדעי המדינה.
ספר תורת המשחקים מיועד לתלמידי התואר הראשון והשני במתמטיקה, בכלכלה, במדעי המחשב, ולכל תלמיד בעל בסיס מתמטי מתאים. הספר עוסק בתורת המשחקים השיתופית והלאשיתופית, ונכללים בו נושאים בסיסיים המתאימים הן לקורס ראשון בתורת המשחקים והן לקורסים מתקדמים. בספר דוגמאות רבות ומגוונות ותרגילים בדרגות קושי שונות, המאפשרים תרגול יעיל של החומר הנלמד והטמעתו. 

מבוא לגיאומטריה דיפרנציאלית 1999 