Applied mathematics Books

Book SynopsisThis book presents new computation schemes for the sensitivity of options using the binomial tree and introduces readers to the discrete Malliavin calculus. It also shows that applications of the discrete Malliavin calculus approach to the binomial tree model offer fundamental tools for computing Greeks.The binomial tree approach is one of the most popular methods in option pricing. Although it is a fairly traditional model for option pricing, it is still widely used in financial institutions since it is tractable and easy to understand. However, the book shows that the tree approach also offers a powerful tool for deriving the Greeks for options. Greeks are quantities that represent the sensitivities of the price of derivative securities with respect to changes in the underlying asset price or parameters. The Malliavin calculus, the stochastic methods of variations, is one of the most popular tools used to derive Greeks. However, it is also very difficult to understand for most students and practitioners because it is based on complex mathematics. To help readers more easily understand the Malliavin calculus, the book introduces the discrete Malliavin calculus, a theory of the functional for the Bernoulli random walk. The discrete Malliavin calculus is significantly easier to understand, because the functional space of the Bernoulli random walk is realized in a finite dimensional space. As such, it makes this valuable tool far more accessible for a broad readership.Table of ContentsIntroduction.- Single-Period Model.- Multiple Time Model.- Application to Finance.- Spectral Binomial Tree.- Short Introduction to Malliavin Calculus in Continuous Time Model.- Discrete Malliavin Greeks.

Read more less

Book SynopsisThis textbook systematically presents fundamental methods of statistical analysis: from probability and statistical distributions, through basic concepts of statistical inference, to a collection of methods of analysis useful for scientific research. It is rich in tables, diagrams, and examples, in addition to theoretical justification of the methods of analysis introduced. Each chapter has a section entitled “Exercises and Problems” to accompany the text. There are altogether about 300 exercises and problems, answers to the selected problems are given. A section entitled “Proof of the Results in This Chapter” in each chapter provides interested readers with material for further study.Trade Review"It offers a sound presentation of concepts at either the undergraduate or first-year graduate level, including a moderate amount of calculus ... A resulting strength of the text is that students are presented with a deeper understanding of analytic methods."Journal of the American Statistical Association"The main merit of this book is that the author gives for every model the corresponding method of hypothesis testing: whether the given assumption holds. The abundance of numerical examples, diagrams, tables helps the reader to analyze the problems arisen not only from biology, but from social sciences, too ... Due to the interesting applications the book can be recommended also to lecturers of theoretical statistics to demonstrate the force of the theory."Acta Scientiarum MathematicarumTable of ContentsDescriptive Statistics; Probability; Random Variables; Probability Distributions; Statistical Inference -- Interval Estimation; Hypothesis Testing -- Fundamental Concepts; Testing Hypotheses Concerning Population Means and Population Proportions; The Chi-Square Test; Linear Regression; Correlation; Multiple Regression and Correlation; One-Way Analysis of Variance; Two-Way Analysis of Variance -- Fixed Effects Model; Two-Way Analysis of Variance Random-Effects Model and Mixed Model; Design of Experiment; Analysis of Covariance; Non-Parametric Statistics.

Read more less

Book SynopsisThis is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of “the calculus of variations”) and more modern topics (under the heading of “optimal control”). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics.

Read more less

Book SynopsisThe Hilbert-Huang Transform (HHT) represents a desperate attempt to break the suffocating hold on the field of data analysis by the twin assumptions of linearity and stationarity. Unlike spectrograms, wavelet analysis, or the Wigner-Ville Distribution, HHT is truly a time-frequency analysis, but it does not require an a priori functional basis and, therefore, the convolution computation of frequency. The method provides a magnifying glass to examine the data, and also offers a different view of data from nonlinear processes, with the results no longer shackled by spurious harmonics — the artifacts of imposing a linearity property on a nonlinear system or of limiting by the uncertainty principle, and a consequence of Fourier transform pairs in data analysis. This is the first HHT book containing papers covering a wide variety of interests. The chapters are divided into mathematical aspects and applications, with the applications further grouped into geophysics, structural safety and visualization.

Read more less

Book SynopsisThis graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.Table of ContentsTechnical Preliminaries: Tensors, Actions and Functors; Applied Manifold Geometry; Applied Bundle Geometry; Applied Jet Geometry; Geometrical Path Integrals and Their Applications.

Read more less

Book SynopsisDid you like Math or Science in school? Have you played games that stimulated your thought processes for Math and Science? Trying to be creative in your Math, Science or leadership class? Can leadership be taught? Is leadership an Art or a Science or Math? Seeking to impact your training program with creative games?A primer for leadership development, this book introduces Math and Science games with a review process component that can be used for leadership instruction. The book highlights key leadership principles which show that leaders must: Ask questions; Be disciplined; Create and see things differently; Develop resources; Engage in active listening; Make priorities; Multiply leaders; Problem solve; Set an example; Sacrifice; Search and explore; Strategize; Support diversity; Work in teams and collaborate.Trade Review"I commend members of the team who have so ably crafted a compendium of games, which reflects innovation and an understanding of the role of emotional Intelligence in leadership. The book affords the reader an opportunity to delve into his own default process of problem solving in the game setting, while encouraging greater use of both the cognitive and emotional parts of the brain in concert. This may well prove to be a ground breaking milestone in the evolution of learning tools." Mark Sng, Director-Education, 6 Seconds-SEA Pte Ltd "This is a wonderful book for teachers to turn disengaged students into motivated learners and more importantly leaders. The focus is that leadership is the key to success in academic excellence. The book is filled with simple and interesting games that inspire successful leadership practices. The authors succinctly intertwines the theoretical underpinnings of key leadership actions into an accessible and practical guide for teachers in the teaching and learning of Mathematics and Science concepts and processes." Yap Meng Hong Vice Principal, Punggol Primary School "Leadership PRINCIPLES in the light of Math and Science makes the 50 Math & Science Games for Leadership unique and unorthordox. The collection of games reflects a combination of new and remaking of old Math and Science concepts that can be played competitively involving key leadership lessons. The book offers a hybrid approach to search, question and redefine the area of leadership principles in its simplest form of number and basic scientific principles. The authors lucidly reveal how LEADERSHIP actually works in the puzzle of math and science. It's also a search of the future on how leadership can be taught in the comfort arena of education. Indeed leadership is EVERYONE's business, and can be learnt and developed. Enjoy! Lily Cheng CEO, Pace Learning & Consultancy Pte Ltd "The games presented in the book are well structured and organized in such a systematic way, including graphical illustrations, that any one interested in conducting leadership training can do so without difficulty. There are also variations and opportunities for reflection after each game, which is indeed necessary for any learning to take place. The authors of the book must be congratulated for their imaginative talent in creating such entertaining games that promote both social interaction and development of leadership skills at the same time." Angeline Khoo, Associate Professor Psychological Studies Academic Group, National Institute of EducationTable of ContentsActivity Games 1-50.

Read more less

Book SynopsisDifferential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory.Beginning with elementary aspects, the author succeeds in providing a self-contained and comprehensive presentation of several advanced topics in DAE theory, such as the full characterization of linear time-varying equations via projector methods or the geometric reduction of nonlinear systems. Recent results on singularities are extensively discussed. The book also addresses in detail differential-algebraic models of electrical and electronic circuits, including index characterizations and qualitative aspects of circuit dynamics. In particular, the reader will find a thorough discussion of the state/semistate dichotomy in circuit modeling. The state formulation problem, which has attracted much attention in the engineering literature, is cleverly tackled here as a reduction problem on semistate models.Table of ContentsIntroduction to Differential-Algebraic Equations; Linear DAEs and Projector-Based Methods; Nonlinear DAEs and Reduction Methods; Singularities; Semistate Models of Electrical Circuits; Nodal Analysis; Branch-Oriented Methods.

Read more less

Book SynopsisThis book aims to provide the readers with a wide panorama of different aspects related to Chaos, Complexity and Transport. It consists of a collection of contributions ranging from applied mathematics to experiments, presented during the CCT'07 conference (Marseilles, June 4-8, 2007). The book encompasses different traditional fields of physics and mathematics while trying to keep a common language among the fields, and targets a nonspecialized audience.Table of ContentsTheory: Out of Equilibrium Phase Transitions in Mean-Field Hamiltonian Dynamics (S Ruffo); Chaotic Geodesics (J-L Thiffeault); Wave Condensation (S Rica); Applications: Plasmas and Fluids: Experimental Studies of Advection-Reaction Diffusion Systems (T H Solomon); Intermittency Scenario of Transition to Chaos in Plasma (D G Dimitriu); On the Complexity of the Neutral Curve of Oscillatory Flows (M Wadih); Others: The Formation of Spiral Arms and Rings in Barred Galaxies (M Romero-Gomez); Wave Chaos and Ghost Orbits in an Underwater Sound-Channel (D V Makarov); Nodal Pattern Analysis for Conductivity of Quantum Ring in Magnetic Field (M Tomiya); and other papers.

Read more less

Book SynopsisThis volume contains recent results in quantum probability and related topics. The contributions include peer-reviewed papers on interacting Fock space and orthogonal polynomials, quantum Markov semigroups, infinitely divisible processes, free probability, white noise, quantum filtering and control, quantum information, dilations, applications of quantum probability in physics, and quantum and classical models in biology. This diversity reflects the strong and constructive relations between quantum probability and different sectors of mathematics, physics, and other sciences and technologies.Table of ContentsLinear Independence of the Renormalized Higher Powers of White Noise (L Accardi & A Boukas); Brownian Dynamics Simulation for Protein Holding and Binding (T Ando); Quantum Fokker-Planck Models: the Lindblad and the Wigner Approaches (A Arnold et al.); Free Martingale Polynomials for Stationary Jacobi Processes (N Demni); Accardi Complementarity for -1/2 < A < 0 and Related Results (L A Echavarria et al.); Quantum Models of Brain Activity I. Recognition of Signals (K H Fichtner & L Fichtner); Central Decompositions of Endomorphisms of von Neumann Algebras (R Floricel); Schrodinger Equation, Lp-Duality and the Geometry of Wigner-Yanase-Dyson Information (P Gibilisco et al.); Multiplicative Renormalization Method for Orthogonal Polynomials (H H Kuo); Quantum Lp and Orlicz Spaces (L E Labuschagne & W Majewski); Vicious Random Walkers and Truncated Haar Unitaries (J I Novak); Incoherent Quantum Control (A Pechen & H Rabitz); Compromising Non-demolition and Information Gaining for Qubit State Estimation (L Rupper et al.); Positivity of Free Convolution Semigroups (M Schurman & S VoA ); Quasi-Free Stochastic Integrals and Martingale Representation (W J Spring); A Method of Recovering the Moments of a Probability Measure from Commutators (A I Stan & J J Whitaker); Description of Decoherence by Means of Translation Covariant Master Equation and Levy Processes (B Vachinni); and other papers

Read more less

Book SynopsisAlthough more than 60 years have passed since their first appearance, Feynman path integrals have yet to lose their fascination and luster. They are not only a formidable instrument of theoretical physics, but also a mathematical challenge; in fact, several mathematicians in the last 40 years have devoted their efforts to the rigorous mathematical definition of Feynman's ideas.This volume provides a detailed, self-contained description of the mathematical difficulties as well as the possible techniques used to solve these difficulties. In particular, it gives a complete overview of the mathematical realization of Feynman path integrals in terms of well-defined functional integrals, that is, the infinite dimensional oscillatory integrals. It contains the traditional results on the topic as well as the more recent developments obtained by the author.Mathematical Feynman Path Integrals and Their Applications is devoted to both mathematicians and physicists, graduate students and researchers who are interested in the problem of mathematical foundations of Feynman path integrals.Table of ContentsInfinite Dimensional Oscillatory Integrals; Feynman Path Integrals and The Schroedinger Equation; The Stationary Phase Method and the Semiclassical Limit of Quantum Mechanics; Quantum Open Systems; Alternative Approaches and Further Results.

Read more less

Book SynopsisThis book presents a systematic approach to problems in economic equilibrium based on fixed-point arguments and rigorous set-theoretical (axiomatic) methods. It describes the highest-level research on the classical theme, fixed points and economic equilibria, in the theory of mathematical economics, and also presents basic results in this area, especially in the general equilibrium theory and non-co-operative game theory. The arguments also contain distinguishable developments of the main theme in the homology theory for general topological spaces, in the model theory and mathematical logic, and in the methodology and philosophy of social sciences. It can thus serve as a graduate-level textbook on mathematical economics as well as an advanced monograph for students and researchers who are concerned about rigorous mathematical treatment in the social sciences.Table of ContentsFixed-Point Theorems; Nash Equilibrium and Abstract Economy; Gale-Nikaido-Debreu's Theorem; General Economic Equilibrium; The Čech-Type Homology Theory and Fixed Points; Dual-System Structure and Fixed-Point Index; Applications to Related Topics; Mathematics and Social Sciences.

Read more less

Book SynopsisThis volume contains pedagogical and elementary introductions to genetics for mathematicians and physicists as well as to mathematical models and techniques of population dynamics. It also offers a physicist's perspective on modeling biological processes.Each chapter starts with an overview followed by the recent results obtained by authors. Lectures are self-contained and are devoted to various phenomena such as the evolution of the genetic code and genomes, age-structured populations, demography, sympatric speciation, the Penna model, Lotka-Volterra and other predator-prey models, evolutionary models of ecosystems, extinctions of species, and the origin and development of language. Authors analyze their models from the computational and mathematical points of view.Table of ContentsPreface; To Understand Nature - Computer Modeling Between Genetics and Evolution; Evolution of the Age-Structured Populations and Demography; Darwinian Purifying Selection versus Complementing Strategy in Monte-Carlo Simulations; Models of Population Dynamics and Their Applications in Genetics; Computational Modeling of Evolution: Ecosystems and Language; Age-Structured Population Models with Genetics.

Read more less

Book SynopsisThis new volume introduces readers to the current topics of industrial and applied mathematics in China, with applications to material science, information science, mathematical finance and engineering. The authors utilize mathematics for the solution of problems. The purposes of the volume are to promote research in applied mathematics and computational science; further the application of mathematics to new methods and techniques useful in industry and science; and provide for the exchange of information between the mathematical, industrial, and scientific communities.Table of ContentsMechanized Methods for Differential and Difference Equations (X Gao & Z Li); Recent Computational Methods for High-Frequency Waves in Heterogeneous Media (S Jin); Some Recent Results on Ranking Webpages and Websites (Y Bao et al.); Report on Testing and Finding the Generating Functions g of an Option Pricing Mechanism Through Market Data (L Chen & S Peng); and other papers.

Read more less

Book SynopsisThe aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in calculus to complex analysis in two different levels.If the reader is in a hurry, he can browse the quickest introduction to complex analysis at the beginning of Chapter 1, which explains the very basics of the theory in an extremely user-friendly way. Those who want to do self-study on complex analysis can concentrate on Chapter 1 in which the two mainstreams of the theory — the power series method due to Weierstrass and the integration method due to Cauchy — are presented in a very concrete way with rich examples. Readers who want to learn more about applied calculus can refer to Chapter 2, where numerous practical applications are provided. They will master the art of problem solving by following the step by step guidance given in the worked-out examples.This book helps the reader to acquire fundamental skills of understanding complex analysis and its applications. It also gives a smooth introduction to Fourier analysis as well as a quick prelude to thermodynamics and fluid mechanics, information theory, and control theory. One of the main features of the book is that it presents different approaches to the same topic that aids the reader to gain a deeper understanding of the subject.

Read more less

Book SynopsisThe aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in calculus to complex analysis in two different levels.If the reader is in a hurry, he can browse the quickest introduction to complex analysis at the beginning of Chapter 1, which explains the very basics of the theory in an extremely user-friendly way. Those who want to do self-study on complex analysis can concentrate on Chapter 1 in which the two mainstreams of the theory — the power series method due to Weierstrass and the integration method due to Cauchy — are presented in a very concrete way with rich examples. Readers who want to learn more about applied calculus can refer to Chapter 2, where numerous practical applications are provided. They will master the art of problem solving by following the step by step guidance given in the worked-out examples.This book helps the reader to acquire fundamental skills of understanding complex analysis and its applications. It also gives a smooth introduction to Fourier analysis as well as a quick prelude to thermodynamics and fluid mechanics, information theory, and control theory. One of the main features of the book is that it presents different approaches to the same topic that aids the reader to gain a deeper understanding of the subject.

Read more less

Book SynopsisThis volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected and interdependent. The choice of the topics is very personal and reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of non-negative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics.

Read more less

Book SynopsisProceedings of the International School of Subnuclear Physics, ISSP 2014, 52nd Course, ERICE, Erice, 24 June - 3 July 2014.

Read more less

Book Synopsis'This is a book to be read and worked with. For a beginning graduate student, this can be a valuable experience which at some points in fact leads up to recent research. For such a reader there is also historical information included and many comments aiming at an overview. It is inspiring and original how old material is combined and mixed with new material. There is always something unexpected included in each chapter, which one is thankful to see explained in this context and not only in research papers which are more difficult to access.'Mathematical Reviews ClippingsThe book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.Table of ContentsForeword; Preface; Acknowledgment; Abbreviations, Notation, Some Core Theorems; Introduction and Motivation; Topics from Functional Analysis and Operators in Hilbert Space: A Selection: Elementary Facts; Unbounded Operators in Hilbert Space; Spectral Theory; Applications: GNS and Representations; Completely Positive Maps; Brownian Motion; Lie Groups, and their Unitary Representations; The Kadison-Singer Problem; Extension of Operators: Selfadjoint Extensions; Unbounded Graph-Laplacians; Reproducing Kernel Hilbert Space; Appendices: An Overview of Functional Analysis Books (Cast of Characters); Terminology from Neighboring Areas; Often Cited; Prizes and Fame; List of Exercises; Definitions of Frequently Occurring Terms; List of Figures; List of Tables; Bibliography; Index;

Read more less

Book Synopsis'This is a book to be read and worked with. For a beginning graduate student, this can be a valuable experience which at some points in fact leads up to recent research. For such a reader there is also historical information included and many comments aiming at an overview. It is inspiring and original how old material is combined and mixed with new material. There is always something unexpected included in each chapter, which one is thankful to see explained in this context and not only in research papers which are more difficult to access.'Mathematical Reviews ClippingsThe book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

Read more less

Book SynopsisThis book provides a thorough, intermediate-level yet concise course in Trigonometry for use in colleges. There are 37 short chapters, each treating one specific theme and containing worked examples and easy exercises. Central to the work are the trigonometric properties of triangle ABC and its associated points. A small appendix contains some Spherical Trigonometry with interesting problems related to the earth; a larger one for enthusiastic students provides further lengthier exercises for extra practice, and full solutions are supplied in the conclusion.Compared with other books on Trigonometry, this book covers the vast spread of topics. Especially, the author reminds readers of the historical importance of theorems enunciated by such contributors as Ptolemy, Euler, Morley, etc. Their names not only invite the readers to appreciate the beauty of these results, but also direct readers to mystery unknown.

Read more less

Book SynopsisThis book provides a thorough, intermediate-level yet concise course in Trigonometry for use in colleges. There are 37 short chapters, each treating one specific theme and containing worked examples and easy exercises. Central to the work are the trigonometric properties of triangle ABC and its associated points. A small appendix contains some Spherical Trigonometry with interesting problems related to the earth; a larger one for enthusiastic students provides further lengthier exercises for extra practice, and full solutions are supplied in the conclusion.Compared with other books on Trigonometry, this book covers the vast spread of topics. Especially, the author reminds readers of the historical importance of theorems enunciated by such contributors as Ptolemy, Euler, Morley, etc. Their names not only invite the readers to appreciate the beauty of these results, but also direct readers to mystery unknown.

Read more less

Book SynopsisThis unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1,000 examples. The initial draft was used to teach more than 10,000 advanced undergraduate students in engineering, physics, economics, as well as applied mathematics. It is a good source for students to learn problem-solving skills and for educators to find problems for homework assignments and tests. The 2nd edition, with at least 100 more examples and five added subsections, has been restructured to flow more pedagogically.

Read more less

Book SynopsisThis unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1,000 examples. The initial draft was used to teach more than 10,000 advanced undergraduate students in engineering, physics, economics, as well as applied mathematics. It is a good source for students to learn problem-solving skills and for educators to find problems for homework assignments and tests. The 2nd edition, with at least 100 more examples and five added subsections, has been restructured to flow more pedagogically.

Read more less

Book SynopsisThis volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10–12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday. The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.Table of ContentsPreface; My Thanks to Mourad Ismail for His Work (Richard Askey); Binomial Andrews–Gordon–Bressoud Identities (Dennis Stanton); Symmetric Expansions of Very Well Poised Basic Hypergeometric Series (George E Andrews); A Sturm–Liouville Theory for Hahn Difference Operator (A H Annaby, A E Hamza and S D Makharesh); Solvability of the Hankel Determinant Problem for Real Sequences (Andrew Bakan and Christian Berg); Convolution and Product Theorems for the Special Affine Fourier Transform (Ayush Bhandari and Ahmed I Zayed); A Further Look at Time-and-Band Limiting for Matrix Orthogonal Polynomials (M Castro, F A Grünbaum, I Pacharoni and I Zurrián); The Orthogonality of Al–Salam–Carlitz Polynomials for Complex Parameters (Howard S Cohl, Roberto S Costas-Santos and Wenqing Xu); Crouching AGM, Hidden Modularity (Shaun Cooper, Jesús Guillera, Armin Straub and Wadim Zudilin); Asymptotics of Orthogonal Polynomials and the Painlevé Transcendents (Dan Dai); From Gaussian Circle Problem to Multivariate Shannon Sampling (W Freeden, M Z Nashed); Weighted Partition Identities and Divisor Sums (F G Garvan); On the Ismail–Letessier–Askey Monotonicity Conjecture for Zeros of Ultraspherical Polynomials (Walter Gautschi); A Discrete Top-Down Markov Problem in Approximation Theory (Walter Gautschi); Supersymmetry of the Quantum Rotor (Vincent X Genest, Luc Vinet, Guo-Fu Yu and Alexei Zhedanov); The Method of Brackets in Experimental Mathematics (Ivan Gonzalez, Karen Kohl, Lin Jiu and Victor H Moll); Balanced Modular Parameterizations (Tim Huber, Danny Lara and Esteban Melendez); Some Smallest Parts Functions from Variations of Bailey's Lemma (Chris Jennings-Shaffer); Dual Addition Formulas Associated with Dual Product Formulas (Tom H Koornwinder); Holonomic Tools for Basic Hypergeometric Functions (Christoph Koutschan and Peter Paule); A Direct Evaluation of an Integral of Ismail and Valent (Alexey Kuznetsov); Algebraic Generating Functions for Gegenbauer Polynomials (Robert S Maier); q-Analogues of Two Product Formulas of Hypergeometric Functions by Bailey (Michael J Schlosser); Asymptotics of Generalized Hypergeometric Functions (Y Lin and R Wong); Mock Theta-Functions of the Third Order of Ramanujan in Terms of Appell–Lerch Series (Changgui Zhang); On Certain Positive Semidefinite Matrices of Special Functions (Ruiming Zhang);

Read more less

Book SynopsisThis book is devoted to the Einstein's field equations of general relativity for self-gravitating massive scalar fields. We formulate the initial value problem when the initial data set is a perturbation of an asymptotically flat, spacelike hypersurface in Minkowski spacetime. We then establish the existence of an Einstein development associated with this initial data set, which is proven to be an asymptotically flat and future geodesically complete spacetime.

Read more less

Book SynopsisThis book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory — or the flow — may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.Table of ContentsDifferential Equations; Hartman-Grobman Theorem; Liapounoff Stability Theorem; Phase Portraits; Poincare-Bendixson Theorem; Attractors; Strange Attractors; Hamiltonian and Integrable Systems; K A M Theorem; Invariant Sets; Global/Local Invariance; Center Manifold Theorem; Normal Form Theorem; Local Bifurcations of Codimension 1; Hopf Bifurcation, Slow-Fast Dynamical Systems; Geometric Singular Perturbation Theory; Darboux Theory of Integrability; Differential Geometry; Generalized Frenet Moving Frame; Curvatures of Trajectory Curves; Flow Curvature Manifold; Flow Curvature Method; Van der Pol Model; FitzHugh-Nagumo Model; Pikovskii-Rabinovich-Trakhtengerts Model; Rikitake Model; Chua's Model; Lorenz Model.

Read more less

Book SynopsisThis book provides an up-to-date overview of research articles in applied and industrial mathematics in Italy. This is done through the presentation of a number of investigations focusing on subjects as nonlinear optimization, life science, semiconductor industry, cultural heritage, scientific computing and others.This volume is important as it gives a report on modern applied and industrial mathematics, and will be of specific interest to the community of applied mathematicians.This book collects selected papers presented at the 9th Conference of SIMAI. The subjects discussed include image analysis methods, optimization problems, mathematics in the life sciences, differential models in applied mathematics, inverse problems, complex systems, innovative numerical methods and others.

Read more less

Book SynopsisThis book captures the state-of-the-art in the field of Strong Stability Preserving (SSP) time stepping methods, which have significant advantages for the time evolution of partial differential equations describing a wide range of physical phenomena. This comprehensive book describes the development of SSP methods, explains the types of problems which require the use of these methods and demonstrates the efficiency of these methods using a variety of numerical examples. Another valuable feature of this book is that it collects the most useful SSP methods, both explicit and implicit, and presents the other properties of these methods which make them desirable (such as low storage, small error coefficients, large linear stability domains). This book is valuable for both researchers studying the field of time-discretizations for PDEs, and the users of such methods.Table of ContentsThe Development of SSP Methods; The Need for SSP Methods; Bounds on the SSP Coefficient for Runge-Kutta, Linear Multistep, and General Linear Methods; Explicit Strong Stability Preserving Runge-Kutta Methods; Low Storage Explicit SSP Runge-Kutta Methods; Optimal SSP Runge-Kutta Methods for Linear Constant Coefficient Problems; Optimal Implicit SSP Runge-Kutta Methods; Explicit and Implicit SSP Linear Multistep Methods; The SSP Properties of Other Methods; Optimal Multistep Multistage Methods; Applications of SSP Methods.

Read more less

Book SynopsisOlympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics.In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate number of test questions is available for reader's practice and testing purpose. Their detailed solutions are also conveniently provided.The examples are not very complicated so that readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions are from many countries, e.g. China, Russia, USA, Singapore, etc. In particular, the reader can find many questions from China, if he is interested in understanding mathematical Olympiad in China. This book serves as a useful textbook of mathematical Olympiad courses, or as a reference book for related teachers and researchers.Table of ContentsVolume 1: Operations on Rational Numbers; Linear Equations of Single Variable; Multiplication Formulae; Absolute Value and Its Applications; Congruence of Triangles; Similarity of Triangles; Divisions of Polynomials; Solutions to Testing Questions; Volume 2: Congruence of Integers; Decimal Representation of Integers; Pigeonhole Principle; Viete's Theorem and Its Applications; Linear Inequalities and System of Linear Inequalities; Inequalities with Absolute Values; Geometric Inequalities; Fundamental Properties of Circles; Solutions to Testing Questions; and other chapters.

Read more less

Book SynopsisThis volume contains the selected contributed papers from the BIOMAT 2009 — Ninth International Symposium on Mathematical and Computational Biology and the contributions of the Keynote Speakers which present the state of the art of fundamental topics of interdisciplinary science to research groups and interested individuals on the mathematical modelling of biological phenomena. New results are presented on cells, particularly their growth rate and fractal behavior of colony contours; on control mechanisms of molecular systems; the Monte-Carlo simulation of protein models; and on fractal and nonlinear analysis of biochemical time series. There are also new results on population dynamics, such as the paleodemography of New Zealand and a comprehensive review on complex food webs. Contributions on computational biology include the use of graph partitioning to analyse biological networks and graph theory in chemosystematics. The studies of infectious diseases include the dynamics of reinfection of Tuberculosis; the spread of HIV infection in the immune system and the real-time forecasting of an Influenza pandemic in the UK. New contributions to the field of modelling of physiological disorders include the study of macrophages and tumours and the influence of microenvironment on tumour cells proliferation and migration.Table of ContentsModeling Physiological Disorders: Macrophages and Tumours: Friends or Foe? (H M Byrne & M R Owen); Evidence of Deterministic Evolution in the Immunological Memory Process (A de Castro et al.); Modeling of Biosystems Structure and Biological Physics: Stochastic Matrices as a Tool for Biological Evolution Models (R Kerner & R ldrovandi); Fractal and Nonlinear Analysis of Biochemical Time Series (H Puebla et al.); Protein Structure: A Correlation between Steiner Atom Sites and Amide Planes in Protein Structures (R P Mondaini); Ecological Modeling: Mathematical Modeling of Sustainable Development: An Application to the Case of the Rain-Forest of Madagascar (C Bernard); Population Dynamics: Population Dynamics on Complex Food Webs (L Berec); Effect of Mass Media on the Cultural Diversity of Axelrod Model of Social Influence (J F Fontanari); Computational Biology: Graph Partitioning Approaches for Analyzing Biological Networks (N Fan et al.); Natural Clustering using Python (D E Razera et al.); Modeling Infectious Diseases: On the Dynamics of Reinfection: The case of Tuberculosis (X-H Wang et al.); Real-Time Forecasting for an Influenza Pandemic in the UK from Prior Information and Multiple Surveillance Datasets (G Ketsetzis et al.); and other papers.

Read more less

Book SynopsisThis book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a state-of-the-art in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective.The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented. Applications range for the reconstruction of noisy or blurred images, pattern and face recognition, to nonlinear approximation in strongly anisotropic contexts, and to the classification tools based on multifractal analysis.Table of ContentsTight Frame based Method for High-Resolution Image Reconstruction (J-F Cai et al.); Greedy Algorithms for Adaptive Triangulations and Approximations (A Cohen); The Contribution of Wavelets in Multifractal Analysis (S Jaffard et al.); Image-Based Face Recognition: A Survey (C-C Liu & D-Q Dai); Hilbert-Huang Transform: Its Background, Algorithms and Applications (L-H Yang).

Read more less

Book SynopsisThis unique volume provides self-contained accounts of some recent trends in Biostatistics methodology and their applications. It includes state-of-the-art reviews and original contributions.The articles included in this volume are based on a careful selection of peer-reviewed papers, authored by eminent experts in the field, representing a well balanced mix of researchers from the academia, R&D sectors of government and the pharmaceutical industry.The book is also intended to give advanced graduate students and new researchers a scholarly overview of several research frontiers in biostatistics, which they can use to further advance the field through development of new techniques and results.Table of ContentsA New Adaptive Method to Control the False Discovery Rate; Adaptive Multiple Testing Procedures Under Positive Dependence; A False Discovery Rate Procedure for Categorical Data; A Distribution for P-Values; Conditional Nelson-Aalen and Kaplan-Meier Estimators with the Muller-Wang Boundary Kernel; The Inverse Censoring Weighted Approach for Estimation of Survival Functions from Left and Right Censored Data; Modeling Survival Data Using the Piecewise Exponential Model with Random Time Grid; Analysis of Recurrent Time-to-Event Data Under Dependent Censoring; Efficient Algorithms in Bayesian Binary Regression with Skew-Probit Link; M-Estimation Methods in Heteroscedastic Nonlinear Regression Model; Regression Analysis in Failure Time Mixture Models with Change Points According to Thresholds in a Covariate; Competing Risks Data: Design and Analysis; Comparative Genomic Analysis Using Information Theory; Statistical Modeling for Positron Emission Tomography; Subset Selection in Comparative Selection Trials; Using Latent Class Analysis in Medical Diagnosis.

Read more less

Book SynopsisThe Pacific Symposium on Biocomputing (PSB) 2011 is an international, multidisciplinary conference for the presentation and discussion of current research in the theory and application of computational methods in problems of biological significance. Presentations are rigorously peer reviewed and are published in an archival proceedings volume. PSB 2011 will be held on January 3 - 7, 2011 in Kohala Coast, Hawaii. Tutorials and workshops will be offered prior to the start of the conference.PSB 2011 will bring together top researchers from the US, Asia Pacific, and around the world to exchange research results and address pertinent issues in all aspects of computational biology. It is a forum for the presentation of work in databases, algorithms, interfaces, visualization, modeling, and other computational methods, as applied to biological problems, with emphasis on applications in data-rich areas of molecular biology.The PSB has been designed to be responsive to the need for critical mass in sub-disciplines within biocomputing. For that reason, it is the only meeting whose sessions are defined dynamically each year in response to specific proposals. PSB sessions are organized by leaders of research in biocomputing's “hot topics”. In this way, the meeting provides an early forum for serious examination of emerging methods and approaches in this rapidly evolving field.Table of ContentsComputational Challenges in Comparative Genomics; Computational Studies of Non-Coding RNAs; Dynamics of Biological Networks; Multi-Resolution Modeling of Biological Macromolecules; Personal Genomics; Reverse Engineering and Synthesis of Biomolecular Systems.

Read more less

Book SynopsisAlgebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.Table of ContentsSage: A Basic Overview for Coding Theory and Cryptography (D Joyner); Aspects of Random Network Coding (O Geil and C Thomsen); Steganography from a Coding Theory Point of View (C Munuera); An Introduction to LDPC Codes (I Marquez-Corbella & E Martinez-Moro); Numerical Semigroups and Codes (M Bras-Amoros); Codes, Arrangements and Matroids (R Jurrius & R Pellikaan).

Read more less

Book SynopsisThis unique volume presents reviews of research in several important areas of applications of mathematical concepts to science and technology, for example applications of inverse problems and wavelets to real world systems. The book provides a comprehensive overview of current research of several outstanding scholars engaged in diverse fields such as complexity theory, vertex coupling in quantum graphs, mixing of substances by turbulence, network dynamics and architecture, processes with rate — independent hysteresis, numerical analysis of Hamilton Jacobi — Bellman equations, simulations of complex stochastic differential equations, optimal flow control, shape optimal flow control, shape optimization and aircraft designing, mathematics of brain, nanotechnology and DNA structure and mathematical models of environmental problems. The volume also contains contributory talks based on current researches of comparatively young researchers participating in the conference.

Read more less

Book SynopsisThe book reviews recent research activities in applied mechanics and applied mathematics such as the fields of solid & fluid constitutive modeling for coupled fields, applications of geophysical & environmental context in judicious numerical-computational implementations. The book aims to merge foundation aspects of continuum mechanics with modern technological applications, notably on reviewing recent advances in the treated subjects in an attractive presentation accessible to a wide readership of engineering and applied sciences.Table of ContentsWaves: Lamb Waves in Phononic Band Gap Structures (T T Wu); On Generalization of the Phase Relations in the Method of Reverberation-Ray Matrix (W Q Chen); Surface-Wave Nonlinearity Measured with Emat for Fatigued Steels (M Hirao); Acoustoelastic Lamb Waves and Implications for Structural Health Monitoring (J E Michaels); Source Synthesis for Inverse Problems in Wave Propagation (W W Symes); Numerical Mathematics/Time Series Analysis: An Introduction to an Adaptive Data Analysis Method (N E Huang); Computational Fluid Dynamics Based on the Unified Coordinates - A Brief Review (W H Hui); Towards Green's Function Retrieval from Imperfectly Partitioned Ambient Wave Fields: Travel Times, Attenuations, Specific Intensities, and Scattering (R L Weaver); Study on Two Scale Design Optimization for Structure and Material with Periodic Microstructure (G D Cheng); Continuum Mechanical Theories: A Continuum Formulation of Lava Flows - From Fluid Ejection to Solid Deposition (K Hutter); Rigorous Mechanics and Elegant Mathematics on the Formulation of Constitutive Laws for Complex Materials: An Example from Biomechanics (V Mow); Professor Pao's Influence on Research in Coupled Field Problems, Chirality and Acoustic and Electromagnetic and their Applications (V V Varadan); Magnetic Force Model for Magnetizable Elastic Body in the Magnetic Field (Z J Zheng); Wind Energy: Principles of Nonlinear Vibro-Wind Energy Conversion (F Moon); and other papers.

Read more less

Book SynopsisThe Proceedings describe the current state of research dealing with biological shape analysis. The quantitative analysis of the shape of biological organisms represents a challenge that has now seen breakthroughs with new methodologies such as elliptical Fourier analysis, quantitative trait loci analysis (QTLs), chromosome segment substitution lines (CSSLs), thin plate splines, etc. The Proceedings also illustrate the diversity of disciplines that are actively involved in the characterization and analysis of biological shape. Moreover, many of the papers focus on the relationship of the shape to the processes that determine the biological form, an issue of major continuing concern in biology.Table of ContentsA New Behavioral Experiment using Computerized Shape Analysis of Actual Flowers (Y Yoshioka); Quantitative Evaluation of Blade Shape of Citrus Varieties (Z Zheng et al.); Quantitative Assessment of Soybean Plant Shape during Growth based on Sequential Image Analysis (R Ohsawa & S Minagawa); Shape Analysis and Its Potential in Varietal Identification (S. G. Bhagwat et al.); Three-dimensional Facial Shape Archetypes for Identification and Diagnosis (C D L Thomas et al.); Dissecting the Genetic Architecture of Craniofacial Shape (R J Sherwood & K P McNulty); Computational Shape Analysis: Based on a Fourier-Wavelet Representation of the Fossil Human Cranial Vault (P E Lestrel et al.); The Use of Elliptical Fourier Analysis on Orbit Shape in Human Skeletal Remains (T Gore et al.); The Geometry of Universal Natural Shapes (J Gielis); and other papers.

Read more less

Book SynopsisThe Institute for Mathematical Sciences at the National University of Singapore hosted a two-month research program on “Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design” from 1 July to 31 August 2009. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers.This invaluable volume collects four expanded lecture notes with self-contained tutorials. They cover a number of aspects on multiscale modeling, analysis and simulations for problems arising from materials science including some critical components in computational prediction of materials properties such as the multiscale properties of complex materials, properties of defects, interfaces and material microstructures under different conditions, critical issues in developing efficient numerical methods and analytic frameworks for complex and multiscale materials models.This volume serves to inspire graduate students and researchers who choose to embark into original research work in these fields.Table of ContentsDislocation Dynamics in 2 + ε Dimensions: Slip Planes, Thin Films, and Grain Boundaries (Y Xiang et al.); Introduction to Molecular Dynamics Simulations (X-T Li); Modeling and Numerical Approximation of Two-Phase Incompressible Flows by a Phase-Field Approach (J Shen); Introduction to Numerical Stochastic Homogenization and the Related Computational Challenges: Some Recent Developments (A Anantharaman et al.).

Read more less

Book SynopsisKarl Gustafson is the creator of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance.Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to a wide range of specialists.Table of ContentsThe Essentials of Antieigenvalue Theory; Convexity in Norm Geometry; The Min-Max Theorem; The Euler Equation; Higher Antieigenvalues; Applications in Numerical Analysis; Applications in Wavelets, Control, and Scattering; The Trigonometry of Matrix Statistics; Bell's Inequalities, Penrose Twistors, and Quantum Trigonometry; Trigonometry of Financial Instruments.

Read more less

Book SynopsisA generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations.This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.Table of ContentsMulti-Dimensional Data; Semi-Tensor Product of Matrices; Multilinear Mappings Among Vector Spaces; Right and General Semi-Tensor Products; Rank, Pseudo-Inverse, and Positivity of STP; Matrix Expression of Logic; Mix-Valued Logic; Logical Matrix, Fuzzy Set and Fuzzy Logic; Fuzzy Relational Equation; Fuzzy Control with Coupled Fuzzy Relations; Boolean Function with Galois Field Structure; Decomposition of Logical Functions; Boolean Calculus; Lattice, Graph, and Universal Algebra; Boolean Network; Boolean Control System; Game Theory; Multi-Variable Polynomials; Some Applications to Differential Geometry and Algebra; Morgan's Problem; Linearization of Nonlinear Control Systems; Stability Region of Dynamic System.

Read more less

Book SynopsisThis monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.Table of ContentsShort Introduction to Pattern Theory; Purpose of Book; Criterion for Judging the Model; Thoughts in Goethe; Idea of Personality; Thought Dynamics; Calculus of Thinking; Building a GOLEM; Software Architecture; Application to Legacy; Development of GOLEM; Multi-Level Networks; Conclusions; Looking Forward.

Read more less