This book deals with the modeling, analysis and simulation of problems arising in the life sciences, and especially in biological processes. The models and findings presented result from intensive discussions with microbiologists, doctors and medical staff, physicists, chemists and industrial engineers and are based on experimental data. They lead to a new class of degenerate density-dependent nonlinear reaction-diffusion convective equations that simultaneously comprise two kinds of degeneracy: porous-medium and fast-diffusion type degeneracy. To date, this class is still not clearly understood in the mathematical literature and thus especially interesting. The author both derives realistic life science models and their above-mentioned governing equations of the degenerate types and systematically studies these classes of equations. In each concrete case well-posedness, the dependence of solutions on boundary conditions reflecting some properties of the environment, and the large-time behavior of solutions are investigated and in some instances also studied numerically.

For more than five decades Bertram Kostant has been one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world. This is the third volume (1975-1985) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this third volume is Kostant's commentaries and summaries of his papers in his own words.

This volume provides a detailed description of the seminal theoretical construction in 1964, independently by Robert Brout and Francois Englert, and by Peter W. Higgs, of a mechanism for short-range fundamental interactions, now called the Brout-Englert-Higgs (BEH) mechanism. It accounts for the non-zero mass of elementary particles and predicts the existence of a new particle - an elementary massive scalar boson. In addition to this the book describes the experimental discovery of this fundamental missing element in the Standard Model of particle physics. The H Boson, also called the Higgs Boson, was produced and detected in the Large Hadron Collider (LHC) of CERN near Geneva by two large experimental collaborations, ATLAS and CMS, which announced its discovery on the 4th of July 2012.This new volume of the Poincare Seminar Series, The H Boson, corresponds to the nineteenth seminar, held on November 29, 2014, at Institut Henri Poincare in Paris.

Foresight is an area within Futures Studies that focuses on critical thinking concerning long term developments, whether within the public sector or in industry and management, and is something of a sub-section of complexity and network science. This book examines developments in foresight methodologies and relates in its greater part to the work done in the context of the COSTA22 network of the EU on Foresight Methodologies. Foresight is a professional practice that supports significant decisions, and as such it needs to be more assured of its claims to knowledge (methodology). Foresight is practiced across many domains and is not the preserve of specialized futurists, or indeed of foresight specialists. However, the disciplines of foresight are not well articulated or disseminated across domains, leading to re-inventions and practice that does not make best use of experience in other domains.

The methodological development of foresight is an important task that aims at strengthening the pool of the tools available for application, thereby empowering the actors involved in foresight practice. Elaborating further on methodological issues, such as those presented in the present book, enables the actors involved in foresight to begin to critique current practice from this perspective and, thirdly, to begin to design foresight practice. The present trends towards methodological concerns indicates a move from given expert-predicted futures to one in which futures are nurtured through a dialogue among stakeholders. The book has four parts, each elaborating on a set of aspects of foresight methodologies. After an introductory section, Part II considers theorizing about foresight methodologies. Part III covers system content issues, and Part IV presents foresight tools and approaches."

Features Provides a uniquely historical perspective on the mathematical underpinnings of a comprehensive list of games Suitable for a broad audience of differing mathematical levels. Anyone with a passion for games, game theory, and mathematics will enjoy this book, whether they be students, academics, or game enthusiasts Covers a wide selection of topics at a level that can be appreciated on a historical, recreational, and mathematical level.

This work presents invited contributions from the second "International Conference on Mathematics and Statistics" jointly organized by the AUS (American University of Sharjah) and the AMS (American Mathematical Society). Addressing several research fields across the mathematical sciences, all of the papers were prepared by faculty members at universities in the Gulf region or prominent international researchers. The current volume is the first of its kind in the UAE and is intended to set new standards of excellence for collaboration and scholarship in the region.

For more than five decades Bertram Kostant has been one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world. This is the fifth volume (1995-2005) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this fifth volume is Kostant's commentaries and summaries of his papers in his own words.

• Introduces the dynamics, principles and mathematics behind ten macroeconomic models allowing students to visualise the models and understand the economic intuition behind them. • Provides a step-by-step guide, and the necessary MATLAB codes, to allow readers to simulate and experiment with the models themselves.

This textbook offers an easily understandable introduction to the fundamental concepts of financial mathematics and financial engineering. The author presents and discusses the basic concepts of financial engineering and illustrates how to trade and to analyze financial products with numerous examples. Special attention is given to the valuation of basic financial derivatives. In the final section of the book, the author introduces the Wiener Stock Price Model and the basic principles of Black-Scholes theory. The book’s aim is to introduce readers to the basic techniques of modern financial mathematics in a way that is intuitive and easy to follow, and to provide financial mathematicians with insights into practical requirements when applying financial mathematical techniques in the real world. 

This thesis presents profound insights into the origins and dynamics of beam instabilities using both experimental observations and numerical simulations. When the Recycler Ring, a high-intensity proton beam accelerator at Fermi National Accelerator Laboratory, was commissioned, it became evident that the Recycler beam experiences a very fast instability of unknown nature. This instability was so fast that the existing dampers were ineffective at suppressing it. The nature of this phenomenon, alongside several other poorly understood features of the beam, became one of the biggest puzzles in the accelerator community. The author investigated a hypothesis that the instability arises from an interaction with a dense cloud of electrons accompanying the proton beam. He studied the phenomena experimentally by comparing the dynamics of stable and unstable beams, by numerically simulating the build-up of the electron cloud and its interaction with the beam, and by constructing an analytical model of an electron cloud-driven instability with the electrons trapped in combined-function dipole magnets. He has devised a method to stabilize the beam by a clearing bunch, which conclusively revealed that the instability is caused by the electron cloud, trapped in a strong magnetic field. Finally, he conducted measurements of the microwave propagation through a single dipole magnet. These measurements have confirmed the presence of the electron cloud in combined-function magnets.

Automata Theory and Formal Languages: Concepts and Practices presents the difficult concepts of automata theory in a straightforward manner, including discussions on diverse concepts and tools that play major roles in developing computing machines, algorithms and code. Automata theory includes numerous concepts such as finite automata, regular grammar, formal languages, context free and context sensitive grammar, push down automata, Turing machine, and decidability, which constitute the backbone of computing machines. This book enables readers to gain sufficient knowledge and experience to construct and solve complex machines. Each chapter begins with key concepts followed by a number of important examples that demonstrate the solution. The book explains concepts and simultaneously helps readers develop an understanding of their application with real-world examples, including application of Context Free Grammars in programming languages and Artificial Intelligence, and cellular automata in biomedical problems.

The three volumes of Interest Rate Modeling present a comprehensive and up-to-date treatment of techniques and models used in the pricing and risk management of fixed income securities. Written by two leading practitioners and seasoned industry veterans, this unique series combines finance theory, numerical methods, and approximation techniques to provide the reader with an integrated approach to the process of designing and implementing industrial-strength models for fixed income security valuation and hedging. Aiming to bridge the gap between advanced theoretical models and real-life trading applications, the pragmatic, yet rigorous, approach taken in this book will appeal to students, academics, and professionals working in quantitative finance. The first half of Volume III contains a detailed study of several classes of fixed income securities, ranging from simple vanilla options to highly exotic cancelable and path-dependent derivatives. The analysis is done in product-specific fashion covering, among other subjects, risk characterization, calibration strategies, and valuation methods. In its second half, Volume III studies the general topic of derivative portfolio risk management, with a particular emphasis on the challenging problem of computing smooth price sensitivities to market input perturbations.

This brilliant CGP book covers all the maths skills needed in AS and A-Level Physics (the use of maths is required for up to 40% of the marks in the final exams and assessments). It explains Calculations, Geometry, Trigonometry, Graph Skills and Handling Date, with clear study notes and step-by-step examples in the context of Physics. And to make sure you've really got to grips with it all, there are practice questions for each topic - with answers included at the back of the book.

This book should be of interest to statistics lecturers who want ready-made data sets complete with notes for teaching.

Basics of Ramsey Theory serves as a gentle introduction to Ramsey theory for students interested in becoming familiar with a dynamic segment of contemporary mathematics that combines ideas from number theory and combinatorics. The core of the of the book consists of discussions and proofs of the results now universally known as Ramsey's theorem, van der Waerden's theorem, Schur's theorem, Rado's theorem, the Hales-Jewett theorem, and the Happy End Problem of Erdos and Szekeres. The aim is to present these in a manner that will be challenging but enjoyable, and broadly accessible to anyone with a genuine interest in mathematics. Features Suitable for any undergraduate student who has successfully completed the standard calculus sequence of courses and a standard first (or second) year linear algebra course. Filled with visual proofs of fundamental theorems. Contains numerous exercises (with their solutions) accessible to undergraduate students. Serves as both a textbook or as a supplementary text in an elective course in combinatorics and aimed at a diverse group of students interested in mathematics.

This book presents a selection of papers based on the XXXIII Bialowieza Workshop on Geometric Methods in Physics, 2014. The Bialowieza Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Bialowieza Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Bialowieza forest in eastern Poland.The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and mathematmtics.

ThisvolumeispublishedastheproceedingsoftheRussian-GermanAdvanced Research workshop on Computational Science and High Performance C- puting in Novosibirsk Academgorodok in September 2003. The contributions of these proceedings were provided and edited by the authors, chosen after a careful selection and reviewing. The workshop was organized by the Institute of Computational Techno- gies SB RAS (Novosibirsk, Russia) and the High Performance Computing Center Stuttgart (Stuttgart, Germany). The objective was the discussion of the latest results in computational science and to develop a close coope- tion between Russian and German specialists in the above-mentioned ?eld. The main directions of the workshop are associated with the problems of computational hydrodynamics, application of mathematical methods to the development of new generation of materials, environment protection pr- lems, development of algorithms, software and hardware support for hi- performance computation, and designing modern facilities for visualization of computational modelling results. The importance of the workshop topics was con?rmed by the partici- tion of representatives of major research organizations engaged in the so- tion of the most complex problems of mathematical modelling, development of new algorithms, programs and key elements of new information techno- gies. Among the Russian participants were researchers of the Institutes of the Siberian Branch of the Russian Academy of Sciences: Institute of Com- tational Technologies, Institute of Computational Mathematics and Mat- matical Geophysics, Institute of Computational Modelling, Russian Federal Nuclear Center, All-Russian Research Institute of Experimental Physics, - merovo State University.

Using simple physical examples, this work by Erhard Scheibe presents an important and powerful approach to the reduction of physical theories. Novel to the approach is that it is not based, as usual, on a single reduction concept that is fixed once and for all, but on a series of recursively constructed reductions, with which all reductions appear as combinations of very specific elementary reductions. This leaves the general notion of theory reduction initially open and is beneficial for the treatment of the difficult cases of reduction from the fields of special and general relativity, thermodynamics, statistical mechanics,and quantum mechanics, which are treated in the second volume. The book is systematically organized and intended for readers interested in philosophy of science as well as physicists without deep philosophical knowledge.

This is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large variety of topics and procedures, ranging from a theoretical mathematical treatment of solvability to numerical procedures for practical problems. Some new and interesting problems in solid mechanics are discussed in the first section while in the last section the important new subject of solid-solid-phase transition is examined.

This book is based on the analysis of canonical commutation relations (CCRs) and their possible deformations. In light of the recent interest on PT-quantum mechanics, the author presents a special deformed version of the CCRs, and discusses the consequences of this deformation both from a mathematical side, and for its possible applications to physics. These include the analysis of several non self-adjoint Hamiltonians, a novel view to the position and momentum operators, and a general approach to compute path integrals and transition probabilities using the so-called bi-coherent states. The book is meant for researchers and is also suited for advanced students. It can be used as a gentle introduction to some delicate aspects in functional analysis and in quantum mechanics for non self-adjoint observables.

For more than five decades Bertram Kostant has been one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world. This is the second volume (1965-1975) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this second volume is Kostant's commentaries and summaries of his papers in his own words.

The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis.

In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds.

Key features:

The first book in this field
Can be used by a variety of specialists
Material is self-contained
Results can be used in the development of reliable computational algorithms
A large number of examples and graphical illustrations are given
Written by prominent specialists in the field
"

These two volumes consist of chapters written by students and colleagues of W.K. Estes. The books' contributors -- themselves eminent figures in the field -- reflect on Estes' sweeping contributions to mathematical as well as cognitive and experimental psychology. As indicated by their titles, Volume I features mathematical and theoretical essays, and Volume II presents cognitive and experimental essays. Both volumes contain insightful literature reviews as well as descriptions of exciting new theoretical and empirical advances. Many of the essays also incorporate personal reminiscences reflecting the authors' fond affection for their illustrious mentor.

In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds. Their techniques are based on an infinite dimensional generalisation of the graph transform and can be viewed as an infinite dimensional generalisation of Fenichels results. As such, they may be applied to a broad class of infinite dimensional dynamical systems.

Order stars is a recently developed technique to analyze and explain the behaviour of numerical methods. The main idea is to explore different features of numerical algorithms as properties of analytical functions in various portions of the complex plane. Thus, for example, the order of some numerical methods for ordinary differential equations can be translated to the language of approximation theory - specifically, to the question of how well a given rational function R approximates the exponential. Likewise, stability properties of the underlying method can be expressed as some other features of the function R. In this formulation, order stars establish the relationship between order and stability, helping in the search for better and more efficient computational algorithms.