Contents: The Possibility of Using Computer to Study the Equation of Gravitation (Q K Lu); Solving Polynomial Systems by Homotopy Continuation Methods (T Y Li); Sketch of a New Discipline of Modeling (E Engeler); The Symmetry Groups of Computer Programs and Program Equivalence (J R Gabriel); Computations with Rational Parametric Equations (S C Chou et al.); Computer Versus Paper and Pencil (M Mignotte); The Finite Basis of an Irreducible Ascending Set (H Shi); A Note on Wu Wen-Tsun's Non-Degenerate Condition (J Z Zhang et al.); Mechanical Theorem Proving in Riemann Geometry Using Wu's Method (S C Chou & X S Gao); and other papers;

Mathematical methods play a significant role in the rapidly growing field of nonlinear optical materials. This volume discusses a number of successful or promising contributions. The overall theme of this volume is twofold: (1) the challenges faced in computing and optimizing nonlinear optical material properties; and (2) the exploitation of these properties in important areas of application. These include the design of optical amplifiers and lasers, as well as novel optical switches. Research topics in this volume include how to exploit the magnetooptic effect, how to work with the nonlinear optical response of materials, how to predict laser-induced breakdown in efficient optical devices, and how to handle electron cloud distortion in femtosecond processes.

As a research subject, the biomechanics of the urinary bladder are relatively young, yet medical problems associated with them are as old as mankind. Offering an update on recent achievements in the field, the authors highlight the underlying biological, chemical and physical processes of bladder function and present the systematic development of a mathematical model of the organ as a thin, soft biological shell. The book will be a valuable resource for postgraduate students and researchers interested in the applications of computational mathematics and solid mechanics to modern problems in biomedical engineering and medicine.

A critical yet constructive description of the rich analytical techniques and substantive applications that typify how statistical thinking has been applied at the RAND Corporation over the past two decades. Case studies of public policy problems are useful for teaching because they are familiar: almost everyone knows something abut health insurance, global warming, and capital punishment, to name but a few of the applications covered in this casebook. Each case study has a common format that describes the policy questions, the statistical questions, and the successful and the unsuccessful analytic strategies. Readers should be familiar with basic statistical concepts including sampling and regression. While designed for statistics courses in areas ranging from economics to health policy to the law at both the advanced undergraduate and graduate levels, empirical researchers and policy-makers will also find this casebook informative.

In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems.

This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike. These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math. Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.

The book aims to prioritise what needs mastering and presents the content in the most understandable, concise and pedagogical way illustrated by real market examples. Given the variety and the complexity of the materials the book covers, the author sorts through a vast array of topics in a subjective way, relying upon more than twenty years of experience as a market practitioner. The book only requires the reader to be knowledgeable in the basics of algebra and statistics.

The Mathematical formulae are only fully proven when the proof brings some useful insight. These formulae are translated from algebra into plain English to aid understanding as the vast majority of practitioners involved in the financial markets are not required to compute or calculate prices or sensitivities themselves as they have access to data providers. Thus, the intention of this book is for the practitioner to gain a deeper understanding of these calculations, both for a safety reason - it is better to understand what is behind the data we manipulate - and secondly being able to appreciate the magnitude of the prices we are confronted with and being able to draft a rough calculation, aside of the market data.

The author has avoided excessive formalism where possible. Formalism is securing the outputs of research, but may, in other circumstances, burden the understanding by non-mathematicians; an example of this case is in the chapter dedicated to the basis of stochastic calculus.

The book is divided into two parts:

- First, the deterministic world, starting from the yield curve building and related calculations (spot rates, forward rates, discrete versus continuous compounding, etc.), and continuing with spot instruments valuation (short term rates, bonds, currencies and stocks) and forward instruments valuation (forward forex, FRAs and variants, swaps & futures);

- Second, the probabilistic world, starting with the basis of stochastic calculus and the alternative approach of ARMA to GARCH, and continuing with derivative pricing: options, second generation options, volatility, credit derivatives;

- This second part is completed by a chapter dedicated to market performance & risk measures, and a chapter widening the scope of quantitative models beyond the Gaussian hypothesis and evidencing the potential troubles linked to derivative pricing models.

The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.

Morphometrics is concerned with the study of variations and change in the form (size and shape) of organisms or objects adding a quantitative element to descriptions and thereby facilitating the comparison of different objects and organisms. This volume provides an introduction to morphometrics in a clear and simple way without recourse to complex mathematics and statistics. This introduction is followed by a series of case studies describing the variety of applications of morphometrics from paleontology and evolutionary ecology to archaeological artifacts analysis. This is followed by a presentation of future applications of morphometrics and state of the art software for analyzing and comparing shape.

Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincare maps, Floquet theory, the Poincare-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.

This volume presents two reviews from the cutting-edge of Russian plasma physics research. Plasma Models of Atom and Radiative-Collisional Processes, by V.A. Astapenko, L.A. Bureyeva, V.S. Lisitsa, is devoted to a unified description of the atomic core polarization effects in the free-free, free-bound and bound-bound transitions of the charged particles in the field of multielectron atom. These effects were treated independently in various applications for more than 40 years. The universal description is based on statistical plasma models of atomic processes with complex ions and atoms. This description makes it possible to extract general scaling laws for the processes above. This review is the first attempt to give the universal approach to the problem. All types of transitions are considered in the frame of both classical and quantum models for the energy scattering of the particle interacting with the atomic core. of atoms and highly charged ions, polarization phenomena in photoeffect, new polarization channel in recombination and for Bremsstrahlung of electrons, relativistic and heavy particles on complex atoms and ions. Asymptotic Theory of Charge Exchange And Mobility Processes for Atomic Ions by B.M. Smirnov reviews the process of resonant charge exchange, and also the transport processes (mobility and diffusion coefficients) for ions in parent gases which are determined by resonant electron transfer. The basis is the asymptotic theory of resonant charge exchange that allows us to evaluate cross sections for all the elements and estimate their accuracy. A simple version of the asymptotic theory is used as follows: a parameter is the ratio between an atom cross section, and the cross section of resonant charge exchange. The cross section of this process is expressed through asymptotic parameters of a transferring electron it the atom. Experimental results are also used, but their accuracy is usually lower than can be obtained by the asymptotic theory

This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.

This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.

This book focuses on mathematical theory and numerical simulation related to various aspects of continuum mechanics, such as fracture mechanics, elasticity, plasticity, pattern dynamics, inverse problems, optimal shape design, material design, and disaster estimation related to earthquakes. Because these problems have become more important in engineering and industry, further development of mathematical study of them is required for future applications. Leading researchers with profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry provide the contents of this book. They help readers to understand that mathematical theory can be applied not only to different types of industry, but also to a broad range of industrial problems including materials, processes, and products.

This book is an introduction to convolution operators with matrix-valued almost periodic or semi-almost periodic symbols.The basic tools for the treatment of the operators are Wiener-Hopf factorization and almost periodic factorization. These factorizations are systematically investigated and explicitly constructed for interesting concrete classes of matrix functions. The material covered by the book ranges from classical results through a first comprehensive presentation of the core of the theory of almost periodic factorization up to the latest achievements, such as the construction of factorizations by means of the Portuguese transformation and the solution of corona theorems.
The book is addressed to a wide audience in the mathematical and engineering sciences. It is accessible to readers with basic knowledge in functional, real, complex, and harmonic analysis, and it is of interest to everyone who has to deal with the factorization of operators or matrix functions.

Survival data or more general time-to-event data occur in many areas, including medicine, biology, engineering, economics, and demography, but previously standard methods have requested that all time variables are univariate and independent. This book extends the field by allowing for multivariate times. Applications where such data appear are survival of twins, survival of married couples and families, time to failure of right and left kidney for diabetic patients, life history data with time to outbreak of disease, complications and death, recurrent episodes of diseases and cross-over studies with time responses. As the field is rather new, the concepts and the possible types of data are described in detail and basic aspects of how dependence can appear in such data is discussed. Four different approaches to the analysis of such data are presented. The multi-state models where a life history is described as the subject moving from state to state is the most classical approach. The Markov models make up an important special case, but it is also described how easily more general models are set up and analyzed. Frailty models, which are random effects models for survival data, made a second approach, extending from the most simple shared frailty models, which are considered in detail, to models with more complicated dependence structures over individuals or over time. Marginal modelling has become a popular approach to evaluate the effect of explanatory factors in the presence of dependence, but without having specified a statistical model for the dependence. Finally, the completely non-parametric approach to bivariate censored survival data is described. This book is aimed at investigators who need to analyze multivariate survival data, but due to its focus on the concepts and the modelling aspects, it is also useful for persons interested in such data, but not having a statistical education. It can be used as a textbook for a graduate course in multivariate survival data. It is made from an applied point of view and covers all essential aspects of applying multivariate survival models. Also more theoretical evaluations, like asymptotic theory, are described, but only to the extent useful in applications and for understanding the models. For reading the book, it is useful, but not necessary, to have an understanding of univariate survival data. Philip Hougaard is a statistician at the pharmaceutical company Novo Nordisk. He has a Ph.D. in nonlinear regression models and is Doctor of Science based on a thesis on frailty models. He is associate editor of Biometrics and Lifetime Data Analysis. He has published over 80 papers in the statistical and medical literature.

Rationality - as opposed to 'ad-hoc' - and asymptotics - to emphasize the fact that perturbative methods are at the core of the theory - are the two main concepts associated with the Rational Asymptotic Modeling (RAM) approach in fluid dynamics when the goal is to specifically provide useful models accessible to numerical simulation via high-speed computing. This approach has contributed to a fresh understanding of Newtonian fluid flow problems and has opened up new avenues for tackling real fluid flow phenomena, which are known to lead to very difficult mathematical and numerical problems irrespective of turbulence. With the present scientific autobiography the author guides the reader through his somewhat non-traditional career; first discovering fluid mechanics, and then devoting more than fifty years to intense work in the field. Using both personal and general historical contexts, this account will be of benefit to anyone interested in the early and contemporary developments of an important branch of theoretical and computational fluid mechanics.

The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models," which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models," edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation."

This book is intended as an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The first part explains how to use computer algebra for applications in solid-state simulation, based on the GAP computer algebra package. Computer algebra enables us to easily obtain various group theoretical properties, such as the representations, character tables, and subgroups. Furthermore it offers a new perspective on material design, which could be executed in a mathematically rigorous and systematic way. The second part then analyzes the relation between the structural symmetry and the electronic structure in C60 (as an example of a system without periodicity). The principal object of the study was to illustrate the hierarchical change in the quantum-physical properties of the molecule, which correlates to the reduction in the symmetry (as it descends down in the ladder of subgroups). The book also presents the computation of the vibrational modes of the C60 by means of the computer algebra. In order to serve the common interests of researchers, the details of the computations (the required initial data and the small programs developed for the purpose) are explained in as much detail as possible.

The purpose of this book is to honor the fundamental contributions to many different areas of statistics made by Barry Arnold. Distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized.

The first part of this volume gathers the lecture notes of the courses of the "XVII Escuela Hispano-Francesa", held in Gijon, Spain, in June 2016. Each chapter is devoted to an advanced topic and presents state-of-the-art research in a didactic and self-contained way. Young researchers will find a complete guide to beginning advanced work in fields such as High Performance Computing, Numerical Linear Algebra, Optimal Control of Partial Differential Equations and Quantum Mechanics Simulation, while experts in these areas will find a comprehensive reference guide, including some previously unpublished results, and teachers may find these chapters useful as textbooks in graduate courses. The second part features the extended abstracts of selected research work presented by the students during the School. It highlights new results and applications in Computational Algebra, Fluid Mechanics, Chemical Kinetics and Biomedicine, among others, offering interested researchers a convenient reference guide to these latest advances.

This volume contains the invited contributions to the Spring 2012 seminar series at Virginia State University on Mathematical Sciences and Applications. It is a thematic continuation of work presented in Volume 24 of the Springer Proceedings in Mathematics & Statistics series. Contributors present their own work as leading researchers to advance their specific fields and induce a genuine interdisciplinary interaction. Thus all articles therein are selective, self-contained, and are pedagogically exposed to foster student interest in science, technology, engineering and mathematics, stimulate graduate and undergraduate research, as well as collaboration between researchers from different areas. The volume features new advances in mathematical research and its applications: anti-periodicity; almost stochastic difference equations; absolute and conditional stability in delayed equations; gamma-convergence and applications to block copolymer morphology; the dynamics of collision and near-collision in celestial mechanics; almost and pseudo-almost limit cycles; rainbows in spheres and connections to ray, wave and potential scattering theory; null-controllability of the heat equation with constraints; optimal control for systems subjected to null-controllability; the Galerkin method for heat transfer in closed channels; wavelet transforms for real-time noise cancellation; signal, image processing and machine learning in medicine and biology; methodology for research on durability, reliability, damage tolerance of aerospace materials and structures at NASA Langley Research Center. The volume is suitable and valuable for mathematicians, scientists and research students in a variety of interdisciplinary fields, namely physical and life sciences, engineering and technology including structures and materials sciences, computer science for signal, image processing and machine learning in medicine.

Semi-infinite optimization is a vivid field of active research. Recently semi infinite optimization in a general form has attracted a lot of attention, not only because of its surprising structural aspects, but also due to the large number of applications which can be formulated as general semi-infinite programs. The aim of this book is to highlight structural aspects of general semi-infinite programming, to formulate optimality conditions which take this structure into account, and to give a conceptually new solution method. In fact, under certain assumptions general semi-infinite programs can be solved efficiently when their bi-Ievel structure is exploited appropriately. After a brief introduction with some historical background in Chapter 1 we be gin our presentation by a motivation for the appearance of standard and general semi-infinite optimization problems in applications. Chapter 2 lists a number of problems from engineering and economics which give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, ro bust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming."

Given a conservative dynamical system of classical physics, how does one find a variational principle for it? Is there a canonical recipe for such a principle? The case of particle mechanics was settled by Lagrange in 1788; this text treats continuous systems. Recipes devised are algebraic in nature, and this book develops all the mathematical tools found necessary after the minute examination of the adiabatic fluid dynamics in the introduction. These tools include: Lagrangian and Hamiltonian formalisms, Legendre transforms, dual spaces of Lie algebras and associated 2-cocycles; and linearized and Z2-graded versions of all of these. The following typical physical systems, together with their Hamiltonian structures, are discussed: Classical Magnetohydro-dynamics with its Hall deformation; Multifluid Plasma; Superfluid He-4 (both irrotational and rotating) and 3He-A; Quantum fluids; Yang-Mills MHD; Spinning fluids; Spin Glass; Extended YM Plasma; A Lattice Gas. Detailed motivations, easy-to-follow arguments, open problems, and over 300 exercises help the reader.