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Mathematical Approaches to Liver Transplantation provides mathematical approaches to the optimization of liver graft distribution. Through mathematical and computational methods, several aspects related to organ allocation are tackled, with possible solutions presented. The book discusses topics such as patient selection for liver transplantation, transplantation procedures, dynamics of organs waiting list, improvement on grafts allocation, live donors and MELD scale. The content focuses on liver transplantation, however the mathematical approaches presented can be successfully replicated to different organs. This book is a valuable source for mathematical biologists, bioinformaticians, and several members of biomedical field who are involved in decision-making related to organs transplantation. - Provides a mathematical approach to the optimization of liver grafts distribution - Presents mathematical and computational methods for several aspects relating to organ allocations and discusses possible solutions - Encompasses optimization models for the best organ distribution strategy to support decision-makers that are responsible for liver and other organ transplantation policies

Heterogeneity of Function in Numerical Cognition presents the latest updates on ongoing research and discussions regarding numerical cognition. With great individual differences in the development or function of numerical cognition at neuroanatomical, neuropsychological, behavioral, and interactional levels, these issues are important for the achievement of a comprehensive understanding of numerical cognition, hence its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills. These functions are essential for the proper development of numerical cognition. - Provides an innovative reference on the emerging field of numerical cognition and the branches that converge on this diverse cognitive domain - Includes an overview of the multiple disciplines that comprise numerical cognition - Focuses on factors that influence numerical cognition, such as language, executive attention, memory and spatial processing - Features an innovative organization with each section providing a general overview, developmental research, and evidence from neurocognitive studies

Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological sciences (in particular, dynamic analysis and controller design of QP and polynomial systems arising from predator-prey and biochemical models). The book puts a significant emphasis on applications, focusing on quasi-polynomial (QP, or generalized Lotka-Volterra) and kinetic systems (also called biochemical reaction networks or simply CRNs) since they are universal descriptors for smooth nonlinear systems and can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems. - Describes and illustrates the relationship between the dynamical, algebraic and structural features of the quasi-polynomial (QP) and kinetic models - Shows the applicability of kinetic and QP representation in biological modeling and control through examples and case studies - Emphasizes the importance and applicability of quantitative models in understanding and influencing natural phenomena

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children's developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. - Covers innovative measures and recent methodological advances in mathematical thinking and learning - Contains contributions that improve instruction and education in these domains - Informs policy aimed at increasing the level of mathematical proficiency in the general public

Transparency Masters for Mathematics Revealed focuses on master diagrams that can be used for transparencies for an overhead projector or duplicator masters for worksheets. The book offers information on a compilation of master diagrams prepared by John R. Stafford, Jr., audiovisual supervisor at the University of Missouri at Kansas City. Some of the transparencies are designed to be shown horizontally. The initial three masters are number lines and grids that can be used in a mathematics course, while the others are adaptations of text figures which are slightly altered in some instances. The publication then shows diagrams and illustrations of a room to be fitted with an air-conditioning unit, maneuvering board, pairs of similar rectangles and triangles, dissimilar triangles and figures, surveying the height of a building, measuring of walls, family room, and church windows. The text offers graphical representations of a normal and abnormal electrocardiogram, tire pressure as a function of tire temperature, scatter diagram of ring profits, costs and sales of pens, salary, and mathematics score as a function of anxiety. The book is a helpful reference for researchers interested in the transparency masters for mathematics.

Mathematical Methods for Physicists, Third Edition provides an advanced undergraduate and beginning graduate study in physical science, focusing on the mathematics of theoretical physics. This edition includes sections on the non-Cartesian tensors, dispersion theory, first-order differential equations, numerical application of Chebyshev polynomials, the fast Fourier transform, and transfer functions. Many of the physical examples provided in this book, which are used to illustrate the applications of mathematics, are taken from the fields of electromagnetic theory and quantum mechanics. The Hermitian operators, Hilbert space, and concept of completeness are also deliberated. This book is beneficial to students studying graduate level physics, particularly theoretical physics.

Evidence-based medicine aims to apply the best available evidence gained from the scientific method to medical decision making. It is a practice that uses statistical analysis of scientific methods and outcomes to drive further experimentation and diagnosis. The profusion of evidence-based medicine in medical practice and clinical research has produced a need for life scientists and clinical researchers to assimilate biostatistics into their work to meet efficacy and practical standards. Practical Biostatistics provides researchers, medical professionals, and students with a friendly, practical guide to biostatistics. With a detailed outline of implementation steps complemented by a review of important topics, this book can be used as a quick reference or a hands-on guide to effectively incorporate biostatistics in clinical trials. - Customized presentation for biological investigators with examples taken from current clinical trials in multiple disciplines - Clear and concise definitions and examples provide a pragmatic guide to bring clarity to the applications of statistics in improving human health - Addresses the challenge of assimilation of mathematical concepts to better interpret literature, to build stronger studies, to present research effectively, and to improve communication with supporting biostatisticians

The combination of faster, more advanced computers and more quantitatively oriented biomedical researchers has recently yielded new and more precise methods for the analysis of biomedical data. These better analyses have enhanced the conclusions that can be drawn from biomedical data, and they have changed the way that experiments are designed and performed. This volume, along with the 2 previous Computer Methods volumes for the Methods in Enzymology serial, aims to inform biomedical researchers about recent applications of modern data analysis and simulation methods as applied to biomedical research. - Presents step-by-step computer methods and discusses the techniques in detail to enable their implementation in solving a wide range of problems - Informs biomedical researchers of the modern data analysis methods that have developed alongside computer hardware - Presents methods at the'nuts and bolts'level to identify and resolve a problem and analyze what the results mean

Calculations for Molecular Biology and Biotechnology: A Guide to Mathematics in the Laboratory, Second Edition, provides an introduction to the myriad of laboratory calculations used in molecular biology and biotechnology. The book begins by discussing the use of scientific notation and metric prefixes, which require the use of exponents and an understanding of significant digits. It explains the mathematics involved in making solutions; the characteristics of cell growth; the multiplicity of infection; and the quantification of nucleic acids. It includes chapters that deal with the mathematics involved in the use of radioisotopes in nucleic acid research; the synthesis of oligonucleotides; the polymerase chain reaction (PCR) method; and the development of recombinant DNA technology. Protein quantification and the assessment of protein activity are also discussed, along with the centrifugation method and applications of PCR in forensics and paternity testing. - Topics range from basic scientific notations to complex subjects like nucleic acid chemistry and recombinant DNA technology - Each chapter includes a brief explanation of the concept and covers necessary definitions, theory and rationale for each type of calculation - Recent applications of the procedures and computations in clinical, academic, industrial and basic research laboratories are cited throughout the text New to this Edition: - Updated and increased coverage of real time PCR and the mathematics used to measure gene expression - More sample problems in every chapter for readers to practice concepts

This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition. - Updates the leading graduate-level text in mathematical physics - Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering - Focuses on problem-solving skills and offers a vast array of exercises - Clearly illustrates and proves mathematical relations New in the Sixth Edition: - Updated content throughout, based on users'feedback - More advanced sections, including differential forms and the elegant forms of Maxwell's equations - A new chapter on probability and statistics - More elementary sections have been deleted

Mathematics for Multimedia explains the mathematics behind multimedia applications such as compression, signal processing, and image/video processing. This timely and thoroughly modern text is a rigorous survey of selected results from algebra and analysis, requiring only undergraduate math skills. More specifically, it focuses on when and why modern robust methods provide more accurate results. The topics are'gems'chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication. The course Mathematics for Multimedia has been offered biennially at Washington University since 1997. It has proved popular with students from sophomores to beginning graduate students who seek an innovative course of rigorous contemporary mathematics with practical applications. For the instructor, the material is divided into six chapters that may be presented in six lecture hours each. Thus, the entire text may be covered in one semester, with time left for examinations and student projects. For the student, there are more than 100 exercises with complete solutions, and numerous example programs in Standard C. Each chapter ends with suggestions for further reading. The book also describes and illustrates easy-to-use software for applying cutting-edge techniques. This book is aimed at a wide audience, including computer science and multimedia students and professors as well as those interested in employing mathematics in multimedia design and implementation. - Explains when and why modern robust methods provide more accurate results - Does not assume or require previous training in statistics - Includes many illustrations using data from actual studies - Describes and illustrates easy-to-use software for applying cutting-edge techniques

Magnetic Resonance Imaging (MRI) is among the most important medical imaging techniques available today. There is an installed base of approximately 15,000 MRI scanners worldwide. Each of these scanners is capable of running many different'pulse sequences', which are governed by physics and engineering principles, and implemented by software programs that control the MRI hardware. To utilize an MRI scanner to the fullest extent, a conceptual understanding of its pulse sequences is crucial. Handbook of MRI Pulse Sequences offers a complete guide that can help the scientists, engineers, clinicians, and technologists in the field of MRI understand and better employ their scanner. - Explains pulse sequences, their components, and the associated image reconstruction methods commonly used in MRI - Provides self-contained sections for individual techniques - Can be used as a quick reference guide or as a resource for deeper study - Includes both non-mathematical and mathematical descriptions - Contains numerous figures, tables, references, and worked example problems

This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.• Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals • Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations• Weaves numerous applications into the text• Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects• Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises• Features interesting anecdotes and biographies of 60 mathematicians and computer scientists• Instructor's Manual available for adopters• Student Solutions Manual available separately for purchase (ISBN: 0124211828)

Chemistry and physics share a common mathematical foundation. From elementary calculus to vector analysis and group theory, Mathematics for Chemistry and Physics aims to provide a comprehensive reference for students and researchers pursuing these scientific fields. The book is based on the authors many classroom experience. Designed as a reference text, Mathematics for Chemistry and Physics will prove beneficial for students at all university levels in chemistry, physics, applied mathematics, and theoretical biology. Although this book is not computer-based, many references to current applications are included, providing the background to what goes on'behind the screen'in computer experiments.

Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are'scattered off'of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium.Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering.This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research.The first interdisciplinary reference source on scattering to gather all world expertise in this techniqueCovers the major aspects of scattering in a common language, helping to widening the knowledge of researchers across disciplinesThe list of editors, associate editors and contributors reads like an international Who's Who in the interdisciplinary field of scattering

Studies in Mathematics and Mechanics is a collection of studies presented to Professor Richard von Mises as a token of reverence and appreciation on the occasion of his seventieth birthday which occurred on April 19, 1953. von Mises'thought has been a stimulus in many seemingly unconnected fields of mathematics, science, and philosophy, to which he has contributed decisive results and new formulations of fundamental concepts. The book contains 42 chapters organized into five parts. Part I contains papers on algebra, number theory and geometry. These include a study of Poincaré's representation of a hyperbolic space on an Euclidean half-space and elementary estimates for the least primitive root. Part II on analysis includes papers on a generalization of Green's Formula and its application to the Cauchy problem for a hyperbolic equation, and the fundamental solutions of a singular Beltrami operator. Part III deals with theoretical mechanics and covers topics such as turbulent flow, axially symmetric flow, and oscillating wakes. The papers in Part IV focus on applied mechanics. These include studies on plastic flow under high stresses and the problem of inelastic thermal stresses. Part V presents studies on probability and statistics, including a finite frequency theory of probability and the problem of expansion of clusters of galaxies.

Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.

Wavelets: A Tutorial in Theory and Applications is the second volume in the new series WAVELET ANALYSIS AND ITS APPLICATIONS. As a companion to the first volume in this series, this volume covers several of the most important areas in wavelets, ranging from the development of the basic theory such as construction and analysis of wavelet bases to an introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding. A fairly extensive bibliography is also included in this volume. - Covers several of the most important areas in wavelets, ranging from the development of the basic theory, such as: Construction and analysis of wavelet bases - Introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding - Extensive bibliography is also included in this volume - Companion to the first volume in this series, An Introduction to Wavelets, and can be used as supplementary instructional material for a two-semester course on wavelet analysis

Bilinear Control Processes: with Applications to Engineering, Ecology, and Medicine

Mathematical Techniques For Physiology and Medicine

Linear Algebra and Its Applications

Mathematics with Applications for the Management, Life, and Social Sciences, Second Edition presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications in management, life sciences, and social sciences. Some applications of probability, game theory, and Markov chains are given. Comprised of 16 chapters, this book begins with an introduction to set theory, followed by a discussion on Cartesian coordinate systems and graphs. Subsequent chapters focus on linear programming from a geometric point of view; matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and permutations, combinations, and counting methods. Probability for finite sample spaces and basic concepts in statistics are also considered, along with the mathematics of finance and applications of calculus. This monograph is intended for students and instructors of applied mathematics.

Quantitative Methods in the Study of Animal Behavior covers a symposium on quantitative methods in behavior. In this book, mathematics is used in two ways – statistical approaches (techniques that describe the main patterns and variability of behavior patterns) and model building. Composed of six chapters, the book opens with a discussion on the three areas of classical ethology – social dominance, behavioral taxonomy, and behavioral variability. The following chapter focuses on the information theory as an ethological tool. In Chapter 3, application of multivariate analyses to diverse ethological data is discussed. The next part of the book discusses more in detail the animal behavioral patterns, relationships, and sequences. The book is a good reference for various fields such as biological science, marine science, and zoology. Students, teachers, scientists, and researchers interested in the aspects of statistics and patterns in animal behavior can make use of this book as a valuable resource.

On the Volterra and Other Nonlinear Models of Interacting Populations explores the various models brought upon to investigate the different assemblies known to man. Assemblies include populations of various biological species, countries, and political parties among others. Because there are numerous assemblies to be measured and evaluated, it has been decided that a standard model be used to ascertain a detailed investigation. One of the models that have been brought forward is introduced by Volterra, which started as a basis for ecological processes. The book begins by establishing that Volterra's model is one of the simplest nonlinear competition models. It explores the model through the study of the population growth of a species. It also covers other theories and concepts relating to the Volterra model in the context of the study. These include equilibrium theory, diversity and stability in ecological systems, and time lags in population among others. The book is a helpful reference for students, researchers, scientists, policymakers, and other parties in search of model/s that fully investigate different assemblies.

Introductory College Mathematics: With Linear Algebra and Finite Mathematics is an introduction to college mathematics, with emphasis on linear algebra and finite mathematics. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; the fundamental ideas of linear algebra; and complex numbers, elementary combinatorics, the binomial theorem, and mathematical induction. Comprised of 15 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors and matrices, and trigonometry are also explored, together with complex numbers, linear transformations, and the geometry of space. The book concludes by considering finite mathematics, with particular reference to mathematical induction and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Mathematics Revealed focuses on the principles, processes, operations, and exercises in mathematics. The book first offers information on whole numbers, fractions, and decimals and percents. Discussions focus on measuring length, percent, decimals, numbers as products, addition and subtraction of fractions, mixed numbers and ratios, division of fractions, addition, subtraction, multiplication, and division. The text then examines positive and negative numbers and powers and computation. Topics include division and averages, multiplication, ratios, and measurements, scientific notation and estimation, signed numbers and the number line, addition and subtraction, and multiplication and division. The manuscript elaborates on angles and figures, shapes, solving equations, and functions and equation.Concerns include ratio and proportion, solving equations by multiplication, information from graphs, squares, square roots, and the Pythagorean theorem, rectangles, parallelograms, and triangles, circles and cylinders, and angles and triangles. The publication is a valuable reference for students interested in the different operations in mathematics.

Study Guide for Applied Finite Mathematics, Third Edition is a study guide that introduces beginners to the fundamentals of finite mathematics and its various realistic and relevant applications. Some applications of probability, game theory, and Markov chains are given. Each chapter includes exercises, and each set begins with basic computational'drill'problems and then progresses to problems with more substance. Comprised of 10 chapters, this book begins with exercises related to set theory and concepts such as the union and intersection of sets. Exercises on Cartesian coordinate systems and graphs as well as linear programming from a geometric and algebraic point of view are then given. Subsequent chapters deal with matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and probability and probability models for finite sample spaces as well as permutations, combinations, and counting methods. Basic concepts in statistics are also considered, along with the mathematics of finance. Some applications of probability, game theory, and Markov chains are also considered. This monograph is intended for students and instructors of applied mathematics.

Applied Finite Mathematics, Second Edition presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications. Some applications of probability, game theory, and Markov chains are given. Comprised of 10 chapters, this book begins with an introduction to set theory, followed by a discussion on Cartesian coordinate systems and graphs. Subsequent chapters focus on linear programming from a geometric and algebraic point of view; matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and probability and probability models for finite sample spaces as well as permutations, combinations, and counting methods. Basic concepts in statistics are also considered, along with the mathematics of finance. The final chapter is devoted to computers and programming languages such as BASIC. This monograph is intended for students and instructors of applied mathematics.

Applied Finite Mathematics presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications. Applications in fields such as business, biology, behavioral sciences, and social sciences are included. Comprised of nine chapters, this book begins with an introduction to set theory, explaining concepts such as sets and union and intersection of sets as well as counting elements in sets. The next chapter deals with coordinate systems and graphs, along with applications of linear equations and graphs of linear inequalities. The discussion then turns to linear programming; matrices and linear systems; probability; and statistics. Examples of applications are given, including those of game theory, Markov chains, and probability. The final chapter is devoted to computers and programming languages such as FORTRAN. This monograph is intended for students and instructors of applied mathematics.

The Theory of Splines and Their Applications

The topic with which I regularly conclude my six-term series of lectures in Munich is the partial differential equations of physics. We do not really deal with mathematical physics, but with physical mathematics; not with the mathematical formulation of physical facts, but with the physical motivation of mathematical methods. The oftmentioned'prestabilized harmony between what is mathematically interesting and what is physically important is met at each step and lends an esthetic - I should like to say metaphysical -- attraction to our subject. The problems to be treated belong mainly to the classical matherhatical literature, as shown by their connection with the names of Laplace, Fourier, Green, Gauss, Riemann, and William Thomson. In order to show that these methods are adequate to deal with actual problems, we treat the propagation of radio waves in some detail in Chapter VI.