Applied mathematics Books

Book SynopsisThe book contains a selection of articles on special research topics on Mathematical Biology and the interdisciplinary fields of mathematical modelling of biosystems. The treatment is both pedagogical and advanced to enhance future scientific research. We include comprehensive reviews written by prominent leaders of scientific research groups, new results on Population Dynamics such as Hybrid Discrete-Continuous Models of Cell Populations and the Hopf bifurcation on Predator-Prey Models, and some state of the art research on Medical Physics such as Optimization Methods applied to Raman Spectroscopy. Other topics covered focus on evolution biology, infectious diseases, DNA structure and many more.Table of ContentsPopulation Dynamics: Application of Hybrid Discrete-Continuous Models in Cell Population Dynamics (P Kurbatova, N Eymard, A Tosenberger, V Volpert and N Bessonov); Spatially Explicit Dispersal Modelling for the Conservation of Jaguars in Colombia (A M Bernal, E Payan and J Cordovez); Sensitivity Matrix of an Ecological Network with Periodic Dynamics (F Cordova-Lepe, L Garay-Narvaez, R Ramos-Jiliberto and G Robledo); Computational Biology: Data Mining and Optimization applied to Raman Spectroscopy for Oncology Applications (M B Fenn, V Pappu, P Xanthopoulos and P M Pardalos); Exploring Triplet Entropy in HIV Sequences (L dos Santos, J L Rybarczyk Filho, G J L Gerhardt and I T S Sartor); PROTPRED-GROMACS: Evolutionary Algorithm with GROMACS for Protein Structure Prediction (R A Faccioli, I N da Silva, A C B Delbem, G T P Brancini and A Caliri); Optimal Control Techniques in Mathematical Modelling of Biological Phenomena: Transmission Dynamics of HIV/AIDS with Optimal control in the presence of Carefree susceptibles and treatment (K O Okosun, O D Makinde and G J Abiodun); Two different Approaches for Gene Expression Model Control (N A Barbosa, H Diaz and A Ramirez); Bioremediation of NaturalWater resources via Optimal Control Techniques (P Gajardo, H Ramirez, V Riquelme and A Rapaport); Theoretical Epidemiology: Change in Host Behavior and its Impact on the Transmission Dynamics of Dengue (F Sanchez, D Murillo and C Castillo-Chavez); Robust Control Approaches for Epidemiological Diseases (H Puebla, S Martinez-Delgadillo, P K Roy and E Hernandez-Martinez); Stability of Disease Free State in SIS Models. Almost Periodic Rates and Pulse Vaccination (G Robledo, M Pinto and F Cordova-Lepe); Modelling of Physiological Disorders: Sensitive Dependence on the Threshold for TAF Signaling in Solid Tumors (D I Wallace and P Winsor); Mathematical Modelling in Ecology: What can the Black Robin tell us about Population Bottlenecks? (C E M Pearce); Mathematical Modelling of Infectious Diseases: Curing by Infecting: Two-strain Competition during the Acute Phase of Chagas Disease (S P Vega, G J Sibona and C A Condat); Mathematical Modelling of the Interaction between Mycobacterium tuberculosis Infection and Cellular Immune Response (H M Yang); Biological Physics and Biophysics: Fractal Plasma: Debye-Hckel Screening on a Fractal (A Y Grosberg); Evolution Biology: Interbreeding Conditions for Explaining Neanderthal DNA in Living Humans: The Nonneutral Case (A G M Neves); Genetic Redundancy and the Origin of Chromosomes (J F Fontanari); Educational Tutorial Chapter on the Mathematical Modelling of Biological Phenomena: If Life is Analog, Why be Discrete? Middle-out Modelling in Mathematical Biology (J R Jungck); and other papers.

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Book SynopsisPAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. The programs, which are available on the internet at www.pamir-integrate.com and are free for non-profit research use, are capable of following localized peaks and valleys of the integrand. Each program comes with a Message-Passing Interface (MPI) parallel version for cluster use as well as serial versions.The first chapter presents introductory material, similar to that on the PAMIR website, and the next is a “manual” giving much more detail on the use of the programs than is on the website. They are followed by many examples of performance benchmarks and comparisons with other programs, and a discussion of the computational integration aspects of PAMIR, in comparison with other methods in the literature. The final chapter provides details of the construction of the algorithms, while the Appendices give technical details and certain mathematical derivations.Table of ContentsIntroduction; Using PAMIR; Benchmark Examples and Comparisons; Computational Integration Theory and PAMIR; Details of Construction of the PAMIR Algorithms and Programs; Appendices: Test Integrals; Derivation of the Simplex Generating Function; Derivation of the Hypercube Generating Function; Mappings Between Base Regions; Rule for Determining Where a Point Lies with Respect to a Simplex; Expansion for ∑4; Fourth Order Simplex Formula; Ninth Order Simplex Formula; Ninth Order Hypercube Formula.

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Book SynopsisPAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. The programs, which are available on the internet at www.pamir-integrate.com and are free for non-profit research use, are capable of following localized peaks and valleys of the integrand. Each program comes with a Message-Passing Interface (MPI) parallel version for cluster use as well as serial versions.The first chapter presents introductory material, similar to that on the PAMIR website, and the next is a “manual” giving much more detail on the use of the programs than is on the website. They are followed by many examples of performance benchmarks and comparisons with other programs, and a discussion of the computational integration aspects of PAMIR, in comparison with other methods in the literature. The final chapter provides details of the construction of the algorithms, while the Appendices give technical details and certain mathematical derivations.Table of ContentsIntroduction; Using PAMIR; Benchmark Examples and Comparisons; Computational Integration Theory and PAMIR; Details of Construction of the PAMIR Algorithms and Programs; Appendices: Test Integrals; Derivation of the Simplex Generating Function; Derivation of the Hypercube Generating Function; Mappings Between Base Regions; Rule for Determining Where a Point Lies with Respect to a Simplex; Expansion for ∑4; Fourth Order Simplex Formula; Ninth Order Simplex Formula; Ninth Order Hypercube Formula.

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Book SynopsisComputational finance is an interdisciplinary field which joins financial mathematics, stochastics, numerics and scientific computing. Its task is to estimate as accurately and efficiently as possible the risks that financial instruments generate. This volume consists of a series of cutting-edge surveys of recent developments in the field written by leading international experts. These make the subject accessible to a wide readership in academia and financial businesses.The book consists of 13 chapters divided into 3 parts: foundations, algorithms and applications. Besides surveys of existing results, the book contains many new previously unpublished results.Table of ContentsFoundations: Multilevel Monte Carlo Methods for Applications in Finance (Mike Giles and Lukasz Szpruch); Convergence of Numerical Methods for SDEs in Finance (Peter Kloeden and Andreas Neuenkirch); Inverse Problems in Finance (J Baumeister); Asymptotic and Non Asymptotic Approximations for Option Valuation (R Bompis and E Gobet); Algorithms: Discretization of Backward Stochastic Volterra Integral Equations (Christian Bender and Stanislav Pokalyuk); Semi-Lagrangian Schemes for Parabolic Equations (Kristian Debrabant and Espen Robstad Jakobsen); Derivative-Free Weak Approximation Methods for Stochastic Differential Equations (Kristian Debrabant and Andreas Roβler); Wavelet Solution of Degenerate Kolmogoroff Forward Equations (Oleg Reichmann and Christoph Schwab); Randomized Multilevel Quasi-Monte Carlo Path Simulation (Thomas Gerstner and Marco Noll); Applications: Drift-Free Simulation Methods for Pricing Cross-Market Derivatives with LMM (J L Fernandez, M R Nogueiras, M Pou and C Vazquez); Application of Simplest Random Walk Algorithms for Pricing Barrier Options (M Krivko and M V Tretyakov); Coupling Local Currency Libor Models to FX Libor Models (John Schoenmakers); Dimension-Wise Decompositions and Their Efficient Parallelization (Philipp Schroder, Peter Mlynczak and Gabriel Wittum).

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Book SynopsisThis book presents a concise exposition of modern mathematical concepts, models and methods with applications in computer graphics, vision and machine learning. The compendium is organized in four parts — Algebra, Geometry, Topology, and Applications. One of the features is a unique treatment of tensor and manifold topics to make them easier for the students. All proofs are omitted to give an emphasis on the exposition of the concepts. Effort is made to help students to build intuition and avoid parrot-like learning.There is minimal inter-chapter dependency. Each chapter can be used as an independent crash course and the reader can start reading from any chapter — almost. This book is intended for upper level undergraduate students, graduate students and researchers in computer graphics, geometric modeling, computer vision, pattern recognition and machine learning. It can be used as a reference book, or a textbook for a selected topics course with the instructor's choice of any of the topics.Table of ContentsAlgebra: Abstract Algebra; Linear Algebra; Tensor Algebra; Exterior Algebra; Geometric Algebra; Boolean Algebra; Geometry: Projective Geometry; Affine Geometry; Differential Geometry; Riemannian Geometry; Non-Euclidean Geometry; Topology: General Topology; Manifolds; Hilbert Spaces; Measure Spaces; Applications: Color Spaces; Projective Geometry and Photography; Tensor Product Spline Surfaces; Image Algebra; Manifold Learning; Support Vector Machines.

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Book SynopsisThis book presents a concise exposition of modern mathematical concepts, models and methods with applications in computer graphics, vision and machine learning. The compendium is organized in four parts — Algebra, Geometry, Topology, and Applications. One of the features is a unique treatment of tensor and manifold topics to make them easier for the students. All proofs are omitted to give an emphasis on the exposition of the concepts. Effort is made to help students to build intuition and avoid parrot-like learning.There is minimal inter-chapter dependency. Each chapter can be used as an independent crash course and the reader can start reading from any chapter — almost. This book is intended for upper level undergraduate students, graduate students and researchers in computer graphics, geometric modeling, computer vision, pattern recognition and machine learning. It can be used as a reference book, or a textbook for a selected topics course with the instructor's choice of any of the topics.Table of ContentsAlgebra: Abstract Algebra; Linear Algebra; Tensor Algebra; Exterior Algebra; Geometric Algebra; Boolean Algebra; Geometry: Projective Geometry; Affine Geometry; Differential Geometry; Riemannian Geometry; Non-Euclidean Geometry; Topology: General Topology; Manifolds; Hilbert Spaces; Measure Spaces; Applications: Color Spaces; Projective Geometry and Photography; Tensor Product Spline Surfaces; Image Algebra; Manifold Learning; Support Vector Machines.

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Book SynopsisDuring the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).This useful book, which is based on the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook and as a valuable resource for researchers.This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.Table of ContentsFundamental Theory; Linear Systems; Stability of Nonlinear Systems; Method of Lyapunov Functions; Two-Dimensional Systems; Second Order Linear Equations; The Index Theory and Brouwer Degree; Monotone Dynamical Systems; Introduction to Perturbation Methods.

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Book SynopsisThis is a book of a series on interdisciplinary topics of the Biological and Mathematical Sciences. The chapters correspond to selected papers on special research themes, which were presented at BIOMAT 2012 International Symposium on Mathematical and Computational Biology, in Tempe, Arizona, USA, November 6-10.This book contains state-of-the art articles on special research topics on mathematical biology, biological physics and mathematical modeling of biosystems; comprehensive reviews on interdisciplinary areas written by prominent leaders of scientific research groups. The treatment is both pedagogical and advanced in order to motivate research students as well as to fulfill the requirements of professional practitioners.Table of ContentsCompartmental Age of Infection Epidemic Models (Fred Brauer); Lyme Pathogen Transmission in Tick Populations with Multiple Host Species (Yijun Lou, Jianhong Wu and Xiaotian Wu); Quantifying the Risk of Mosquito-Borne Infection Based on the Equilibrium Prevalence in Humans (Marcos Amaku, Francisco Antonio Bezerra Coutinho and Eduardo Massad); Seasonal Fluctuation in TseTse Fly Populations and Human African Trypanosomiasis: A Mathematical Model (T Madsen, D I Wallace and N Zupan); A Mathematical Model for the Immunotherapy of Advanced Prostate Cancer (Travis Portz and Yang Kuang); Seizure Manifold of the Epileptic Brain: A State Space Reconstruction Approach (Mujahid N Syed, Pando G Georgiev and Panos M Pardalos); Synchronous Calcium Induced Calcium Release (CICR) in a Multiple Site Model of the Cardiac Myocite (D I Wallace and J E Tanenbaum); Modelling Natural Killer Cell Repertoire Development and Activation Dynamics (Michal Sternberg-Simon and Ramit Mehr); Saturation Effects on T-Cell Activation in a Model of a Multi-Stage Pathogen (Michael Shapiro and Edgar Delgado-Eckert); Advances in DE NOVO Protein Design for Monomeric, Multimeric, and Conformational Switch Proteins (James Smadbeck, George A Khoury, Meghan B Peterson, Christodoulos A Floudas); Mathematical Models and Techniques for Biomolecular Geometric Analysis (K L Xia, F Xin, Y Tong and G W Wei); Towards a New Bio-Quantum Model for Signaling and Repair of DNA Damage (Aymara Martinez Aragon, Joao Dias de Toledo Arruda Neto and Yadira Medina Guevara); Viral Evolution and Adaptation as a Multivariate Branching Process (Fernando Antoneli, Francisco Bosco, Diogo Castro and Luiz Mario Janini); Associative Learning of a Lexicon in a Noisy Cross-Situational Scenario (P F C Tilles and J F Fontanari); Relationship between Rainfall and Control Effectiveness of the Aedes aegypti Population through a Non-linear Dynamical Model - Case of Lavras City, Brazil (L B Barsante, J L Acebal, B S Carvalho, R T N Cardoso, M M Morais and A E Eiras); Spatiotemporal Dynamics of Telegraph Reaction - Diffusion Predator - Prey Models (Eliseo Hernandez Martinez, Hector Puebla, Teresa Perez Munoz, Margarita Gonzalez Brambila and Jorge X Velasco Hernandez); Population Dynamics of the Spider Monkey (Ateles hybridus) in a Fragmented Landscape of Colombia (J M Cordovez, J R Arteaga B, M Marino, A G de Luna and A Link); The Contribution of Stop Codon Frequency and Purine Bias to the Classification of Coding Sequences (N Carels and D Frias); Multiclass Classification of Tree Structured Objects: The K-NN Case (Ana Georgina Flesia); Regularity of Optimal Cost Functional Applied to the Study of Environmental Pollution (Santina Arantes and Jaime Rivera); A Sensitivity Analysis of Gene Expression Model (N A Barbosa); A Wavelet-Based Time-Varying Irregular Vector Autoregressive Model (G E Salcedo, O E Molina and R F Porto).

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Book SynopsisThe book provides some recent works in the study of some infinite-dimensional dynamical systems in atmospheric and oceanic science. It devotes itself to considering some infinite-dimensional dynamical systems in atmospheric and oceanic science, especially in geophysical fluid dynamics. The subject on geophysical fluid dynamics mainly tends to focus on the dynamics of large-scale phenomena in the atmosphere and the oceans. One of the important contents in the dynamics is to study the infinite-dimensional dynamical systems of the atmospheric and oceanic dynamics. The results in the study of some partial differential equations of geophysical fluid dynamics and their corresponding infinite-dimensional dynamical systems are also given.

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Book SynopsisThis book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming problems. The book also includes a chapter on the fast Fourier transform and a very practical introduction to the solution of linear algebra problems on modern supercomputers.The book contains the relevant theory for most of the methods employed. It also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs for solving linear algebraic problems. Highly readable FORTRAN and MATLAB codes are presented which solve all of the main problems studied.Table of ContentsReference Materials; Systems of Linear Equations; Linear Least Squares Problems; The Eigenvalue Problem; Linear Programming; The Fast Fourier Transform; Linear Algebra on Supercomputers;

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Book SynopsisThis book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming problems. The book also includes a chapter on the fast Fourier transform and a very practical introduction to the solution of linear algebra problems on modern supercomputers.The book contains the relevant theory for most of the methods employed. It also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs for solving linear algebraic problems. Highly readable FORTRAN and MATLAB codes are presented which solve all of the main problems studied.Table of ContentsReference Materials; Systems of Linear Equations; Linear Least Squares Problems; The Eigenvalue Problem; Linear Programming; The Fast Fourier Transform; Linear Algebra on Supercomputers;

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Book SynopsisThis book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided.Table of ContentsIntroduction; Geometric Fundamentals; Kinematics of Integrable Deformation; Geometry of Anholonomic Deformation; Kinematics of Anholonomic Deformation; List of Symbols; References; Index;

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Book SynopsisThis book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope.This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear Schrödinger equations, fractional Landau-Lifshitz equations and fractional Ginzburg-Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs.Table of ContentsPhysics Background; Fractional Calculus and Fractional Differential Equations; Fractional Partial Differential Equations; Numerical Approximations in Fractional Calculus; Numerical Methods for the Fractional Ordinary Differential Equations; Numerical Methods for Fractional Partial Differential Equations;

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Book SynopsisThis textbook is a short comprehensive and intuitive introduction to Lie group analysis of ordinary and partial differential equations. This practical-oriented material contains a large number of examples and problems accompanied by detailed solutions and figures. In comparison with the known beginner guides to Lie group analysis, the book is oriented toward students who are interested in financial mathematics, mathematical finance and economics.We provide the results of the Lie group analysis of actual models in Financial Mathematics using recent publications. These models are usually formulated as nonlinear partial differential equations and are rather difficult to make use of. With the help of Lie group analysis it is possible to describe some important properties of these models and to obtain interesting reductions in a clear and understandable algorithmic way.The book can serve as a short introduction for a further study of modern geometrical analysis applied to models in financial mathematics. It can also be used as textbook in a master's program, in an intensive compact course, or for self study.The textbook with a large number of examples will be useful not only for students who are interested in Financial Mathematics but also for people who are working in other areas of research that are not directly connected with Physics (for instance in such areas of Applied Mathematics like mathematical economy, bio systems, coding theory, etc.).Table of ContentsIntroduction; Point Transformations on R2; Invariants of a One-Parameter Group of Point Transformations; First Order ODEs; Prolongation Procedure; Short Overview of the Lie Algebra Properties; High Order ODEs; Lie Group Analysis of PDEs; Study of New Models in Financial Mathematics;

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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.Table of ContentsDomains, Modules and Matrices; Canonical Forms for Similarity; Functions of Matrices and Analytic Similarity; Inner Product Spaces; Elements of Multilinear Algebra; Nonnegative Matrices; Various Topics;

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Book SynopsisThis book provides the limit theorems that can be used in the development of nonlinear cointegrating regression. The topics include weak convergence to a local time process, weak convergence to a mixture of normal distributions and weak convergence to stochastic integrals. This book also investigates estimation and inference theory in nonlinear cointegrating regression.The core context of this book comes from the author and his collaborator's current researches in past years, which is wide enough to cover the knowledge bases in nonlinear cointegrating regression. It may be used as a main reference book for future researchers.Table of ContentsConvergence to a Local Time Process; Convergence to a Mixture of Normal Distributions; Convergence to Stochastic Integrals; Nonlinear Cointegrating Regression;

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Book SynopsisMatrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed. This book covers materials relevant to advanced undergraduate and graduate courses in numerical linear algebra and scientific computing. It is also well-suited for self-study. The broad content makes it convenient as a general reference to the subjects.

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Book SynopsisThis book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.Table of ContentsProbability; Random Variables; Joint Distributions; Variance and Covariance; Moment Generating Function; Analysis of Some Important Distributions; Limit Theorems; Statistical Inference: Point Estimation; Statistical Inference: Interval Estimation; Appendices: Solutions for the Problems for Weeks 1-12; Sample Problems for Final Exams; Some Bonus Challenging Problems; Statistical Tables;

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Book SynopsisThis monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss-Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries.

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Book SynopsisThis invaluable book is the first of its kind on 'selforganizology', the science of self-organization. It covers a wide range of topics, such as the theory, principle and methodology of selforganizology, agent-based modelling, intelligence basis, ant colony optimization, fish/particle swarm optimization, cellular automata, spatial diffusion models, evolutionary algorithms, self-adaptation and control systems, self-organizing neural networks, catastrophe theory and methods, and self-organization of biological communities, etc.Readers will have an in-depth and comprehensive understanding of selforganizology, with detailed background information provided for those who wish to delve deeper into the subject and explore research literature.This book is a valuable reference for research scientists, university teachers, graduate students and high-level undergraduates in the areas of computational science, artificial intelligence, applied mathematics, engineering science, social science and life sciences.Table of ContentsOrganization and Organizational Theory; Selforganizology: A Science on Self-organization; Agent-based Modeling; Intelligence Basis; Catastrophe Theory and Methods; Self-adaptation and Control Systems; Celluar Automata and Spatial Diffusion Models; Artificial Neural Networks; Ant Colony Optimization; Fish and Particle Swarm Optimization; Synergy, Coevolution and Evolutionary Algorithms; Community Succession and Assembly; Mathematical Foundations;

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Book SynopsisThis book is devoted to review two of the most relevant approaches to the study of classical field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach is also compared with others like multisymplectic formalism.It will be very useful for researchers working in classical field theories and graduate students interested in developing a scientific career in the subject.Table of ContentsA Review of Hamiltonian and Lagrangian Mechanics: Hamiltonian and Lagrangian Mechanics; k-Symplectic Formulation of Classical Field Theories: k-Symplectic Geometry; k-Symplectic Formalism; Hamiltonian Classical Field Theory; Hamilton-Jacobi Theory in k-Symplectic Field Theories; Lagrangian Classical Field Theories; Examples; k-Cosymplectic Formulation of Classical Field Theories: k-Cosymplectic Geometry; k-Cosymplectic Formalism; Hamiltonian Classical Field Theories; Hamilton-Jacobi Equation; Lagrangian Classical Field Theories; Examples; k-Symplectic Systems versus Autonomous k-Cosymplectic Systems; Relationship between k-Symplectic and k-Cosymplectic Approaches and the Multisymplectic Formalism: Multisymplectic Formalism; Appendices: Symplectic Manifolds; Cosymplectic Manifolds; Glossary of Symbols;

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Book SynopsisThe aim of this volume is to make a connection among advanced mathematical tools and application to real problems. There are many different mathematical structures analyzed in the book and all of them are in important applications, like statistics and biology, neural networks and financial markets, asymptotic methods for partial differential equations and the problem of tsunami propagation. Plasma physics has been given a new approach, using focal points in analogy to the theory of tsunami waves.

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Book SynopsisThis unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.Table of ContentsProlegomena: Exordium; Basic Working Notions; Observables and States; Connections and Differential Analysis; The Functorial Imperative; Grothendieck Topos Interpretation of the Hom-Tensor Adjunction; The Grothendieck Topology of Epimorphic Families; Unit and Counit of the Hom-Tensor Adjunction; General Theory: General Introduction; Basic Assumptions of ADG (Abstract Differential Geometry); Basic Framework; Bohr's Correspondence; Functorial, Topos-Theoretic Mechanism of ADG; Kahler Construction; Elementary Particles in the Jargon of ADG; Relational Aspect of Space, Again; Dynamical Dressing, Extension: Kahler Construction (Contn'd); Adjunction, Least Action Principle; Transformation Law of Potentials, in Terms of ADG; Characteristics of a Physical Law; Complementary Remarks; Epilogue; Applications: Fundamental Adjunctions: On Utiyama's Theme/Principle Through "A-Invariance"; "Affine Geometry" and "Quantum"; Chasing Feynman; Stone-von Neumann Adjunction; Quantized Einstein's Equation; The Essence of ADG; Peroration;

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Book SynopsisThe main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing.Table of ContentsDiscrete-Variable Real Functions; The n-th Order Backward Difference/Sum of the Discrete-Variable Function; Fractional-Order Backward Differ-Sum; The FOBD-S Graphical Interpretation; The FOBD/S Selected Properties; The FO Dynamic System Description; Linear FO System Analysis; The Linear FO Discrete-Time Fundamental Elements; FO Discrete-Time System Structures; Fractional Discrete-Time PID Controller; FOS Approximation Problems; Fractional Potential; FO Image Filtering and Edge Detection; Appendix A: Selected Linear Algebra Formulae and Discrete-Variable Special Functions;

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Book Synopsis'A wealth of examples to which solutions are given permeate the text so the reader will certainly be active.'The Mathematical GazetteThis is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a 'fein' chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a 'decision machine.' Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.

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Book SynopsisThis unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear groups and phenomena in combinatorics. The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained.

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Book SynopsisThis unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear groups and phenomena in combinatorics. The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained.

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Book SynopsisThis book digs deeper and shows not only that quantum gravity is more than just a physical theory—describing physical aspects—but also that, in fact, it covers "it all."Table of ContentsPersonal Motivation Some Fundamental Motivation Seven Days The First Day: Let There Be Nothing 1. Making Contact with Quantum Gravity The Second Day: Let There Be Photons 2. Societons and Ecotons 3. Humanitons—The Intrinsic Photons of the Human Body Understand Them and Cure Yourself 4. Social Distancing 5. Mastering Human Crises with Quantum Gravity-Based but Still Practicable Models The Third Day: Let There Be Mass and Inertia 6. Masses and the Infinity Options Principle 7. The Three Generations of Elementary Particles The Fourth Day: Let There Be Quantum Gravity 8. Toward Quantum Einstein Field Equations The Fifth Day: Let There Be a Dirac Equation 9. The Metric Dirac Equation Revisited and the Geometry of Spinors 10. The Dirac Miracle The Sixth Day: A Math for Body, Soul, and Universe 11. A Curvy Math to Salvation 12. About the Flatness Problem in Cosmology 13. Mathematical Tools for Socioeconomic and Psychological Simulations The Seventh Day: Give It Some Rest 14. About the Origin of the Minimum Principle

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Book SynopsisThis book provides a clear understanding of quantum mechanics (QM) by developing it from fundamental postulates in an axiomatic manner, as its central theme. The target audience is physics students at master’s level. It avoids historical developments, which are piecemeal, not logically well knitted, and may lead to misconceptions. Instead, in the present approach all of QM and all its rules are developed logically starting from the fundamental postulates only and no other assumptions.Specially noteworthy topics have been developed in a smooth contiguous fashion following the central theme. They provide a new approach to understanding QM. In most other texts, these are presented as disjoint separate topics. Since the reader may not be acquainted with advanced mathematical topics like linear vector space, a number of such topics have been presented as “mathematical preliminary.” Standard topics, viz. derivation of uncertainty relations, simple harmonic oscillator by operator method, bound systems in one and three dimensions, angular momentum, hydrogen-like atom, and scattering in one and three dimensions, are woven into the central theme.Advanced topics like approximation methods, spin and generalized angular momenta, addition of angular momenta, and relativistic quantum mechanics have been reserved for Volume II. ​Table of ContentsComplete manuscript is under the "Attachments" tab​​

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Book Synopsis

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Book Synopsis

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Book Synopsis

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