The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century and undoubtedly will continue to grow in importance in the future. In this monograph, the authors investigate orthogonal polynomials for exponential weights defined on a finite or infinite interval. The interval should contain 0, but need not be symmetric about 0 ; likewise, the weight need not be even. The authors establish bounds and asymptotics for orthonormal and extremal polynomials, and their associated Christoffel functions. They deduce bounds on zeros of extremal and orthogonal polynomials, and also establish Markov-Bernstein and Nikolskii inequalities. The book will be of interest to researchers in approximation theory, harmonic analysis, numerical analysis, potential theory, and all those that apply orthogonal polynomials.
This is the nineteenth edition of the book Engineering Mathematics-I. The earlier editions have received positive response from the teachers and the students. This text book has been written strictly according to the revised syllabus (R18) 2018-19 of first year (First Semester) B. Tech students of JNTU, Hyderabad. In this edition some topics have been updated. The previous question paper problems have been included at appropriate places. For the benefit of the students, previous GATE questions are included at the end of each chapter. The topics has been made as simple as possible and in some instances the detailed explanation is given, to understand content with a minimum effort.
In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''--
The subject of sterilization of food in cans has been studied both experimentally and theoretically, but limited work has been undertaken to study the sterilization of food in pouches. This book examines the interaction between fluid mechanics, heat transfer and microbial inactivation during sterilization of food in pouches. Such interaction is complex and if ignored would lead to incorrect information not only on food sterility but also on food quality.
Modelling and Simulation of Reactive Flows presents information on modeling and how to numerically solve reactive flows. The book offers a distinctive approach that combines diffusion flames and geochemical flow problems, providing users with a comprehensive resource that bridges the gap for scientists, engineers, and the industry. Specifically, the book looks at the basic concepts related to reaction rates, chemical kinetics, and the development of reduced kinetic mechanisms. It considers the most common methods used in practical situations, along with equations for reactive flows, and various techniques—including flamelet, ILDM, and Redim—for jet flames and plumes, with solutions for both. In addition, the book includes techniques to accelerate the convergence of numerical simulation, and a discussion on the analysis of uncertainties with numerical results, making this a useful reference for anyone who is interested in both combustion in free flow and in porous media. - Helps readers learn how to apply applications of numerical methods to simulate geochemical kinetics - Presents methods on how to transform the transport equations in several coordinate systems - Includes discussions of the basic concepts related to reaction rates, chemical kinetics, and the development of reduced kinetic mechanisms, including the most common methods used in practical situations - Offers a distinctive approach that combines diffusion flames and geochemical flow problems
Chapter 1: Vectors and Matrices 1.1 Vectors 1.1.1 Geometry with Vector 1.1.2 Dot Product 1.1.3 Cross Product 1.1.4 Lines and Planes 1.1.5 Vector Space 1.1.6 Coordinate Systems 1.1.7 Gram-Schmidt Orthonolization 1.2 Matrices 1.2.1 Matrix Algebra 1.2.2 Rank and Row/Column Spaces 1.2.3 Determinant and Trace 1.2.4 Eigenvalues and Eigenvectors 1.2.5 Inverse of a Matrix 1.2.6 Similarity Transformation and Diagonalization 1.2.7 Special Matrices 1.2.8 Positive Definiteness 1.2.9 Matrix Inversion Lemma 1.2.10 LU, Cholesky, QR, and Singular Value Decompositions 1.2.11 Physical Meaning of Eigenvalues/Eigenvectors 1.3 Systems of Linear Equations 1.3.1 Nonsingular Case 1.3.2 Undetermined Case - Minimum-Norm Solution 1.3.3 Overdetermined Case - Least-Squares Error Solution 1.3.4 Gauss(ian) Elimination 1.3.5 RLS (Recursive Least Squares) Algorithm Problems Chapter 2: Vector Calculus 2.1 Derivatives 2.2 Vector Functions 2.3 Velocity and Acceleration 2.4 Divergence and Curl 2.5 Line Integrals and Path Independence 2.5.1 Line Integrals 2.5.2 Path Independence 2.6 Double Integrals 2.7 Green's Theorem 2.8 Surface Integrals 2.9 Stokes' Theorem 2.10 Triple Integrals 2.11 Divergence Theorem Problems Chapter 3: Ordinary Differential Equation 3.1 First-Order Differential Equations 3.1.1 Separable Equations 3.1.2 Exact Differential Equations and Integrating Factors 3.1.3 Linear First-Order Differential Equations 3.1.4 Nonlinear First-Order Differential Equations 3.1.5 Systems of First-Order Differential Equations 3.2 Higher-Order Differential Equations 3.2.1 Undetermined Coefficients 3.2.2 Variation of Parameters 3.2.3 Cauchy-Euler Equations 3.2.4 Systems of Linear Differential Equations 3.3 Special Second-Order Linear ODEs 3.3.1 Bessel's Equation 3.3.2 Legendre's Equation 3.3.3 Chebyshev's Equation 3.3.4 Hermite's Equation 3.3.5 Laguerre's Equation 3.4 Boundary Value Problems Problems Chapter 4: Laplace Transform 4.1 Definition of the Laplace Transform 4.1.1 Laplace Transform of the Unit Step Function 4.1.2 Laplace Transform of the Unit Impulse Function 4.1.3 Laplace Transform of the Ramp Function 4.1.4 Laplace Transform of the Exponential Function 4.1.5 Laplace Transform of the Complex Exponential Function 4.2 Properties of the Laplace Transform 4.2.1 Linearity 4.2.2 Time Differentiation 4.2.3 Time Integration 4.2.4 Time Shifting - Real Translation 4.2.5 Frequency Shifting - Complex Translation 4.2.6 Real Convolution 4.2.7 Partial Differentiation 4.2.8 Complex Differentiation 4.2.9 Initial Value Theorem (IVT) 4.2.10 Final Value Theorem (FVT) 4.3 The Inverse Laplace Transform 4.4 Using of the Laplace Transform 4.5 Transfer Function of a Continuous-Time System Problems 300 Chapter 5: The Z-transform 5.1 Definition of the Z-transform 5.2 Properties of the Z-transform 5.2.1 Linearity 5.2.2 Time Shifting - Real Translation 5.2.3 Frequency Shifting - Complex Translation 5.2.4 Time Reversal 5.2.5 Real Convolution 5.2.6 Complex Convolution 5.2.7 Complex Differentiation 5.2.8 Partial Differentiation 5.2.9 Initial Value Theorem 5.2.10 Final Value Theorem 5.3 The Inverse Z-transform 5.4 Using The Z-transform 5.5 Transfer Function of a Discrete-Time System 5.6 Differential Equation and Difference Equation Problems Chapter 6: Fourier Series and Fourier Transform 6.1 Continuous-Time Fourier Series (CTFS) 6.1.1 Definition and Convergence Conditions 6.1.2 Examples of CTFS 6.2 Continuous-Time Fourier Transform (CTFT) 6.2.1 Definition and Convergence Conditions 6.2.2 (Generalized) CTFT of Periodic Signals 6.2.3 Examples of CTFT 6.2.4 Properties of CTFT 6.3 Discrete-Time Fourier Transform (DTFT) 6.3.1 Definition and Convergence Conditions 6.3.2 Examples of DTFT 6.3.3 DTFT of Periodic Sequences 6.3.4 Properties of DTFT 6.4 Discrete Fourier Transform (DFT) 6.5 Fast Fourier Transform (FFT) 6.5.1 Decimation-in-Time (DIT) FFT 6.5.2 Decimation-in-Frequency (DIF) FFT 6.5.3 Computation of IDFT Using FFT Algorithm 6.5.4 Interpretation of DFT Results 6.6 Fourier-Bessel/Legendre/Chebyshev/Cosine/Sine Series 6.6.1 Fourier-Bessel Series 6.6.2 Fourier-Legendre Series 6.6.3 Fourier-Chebyshev Series 6.6.4 Fourier-Cosine/Sine Series Problems Chapter 7: Partial Differential Equation 7.1 Elliptic PDE 7.2 Parabolic PDE 7.2.1 The Explicit Forward Euler Method 7.2.2 The Implicit Forward Euler Method 7.2.3 The Crank-Nicholson Method 7.2.4 Using the MATLAB Function 'pdepe()' 7.2.5 Two-Dimensional Parabolic PDEs 7.3 Hyperbolic PDES 7.3.1 The Explict Central Difference Method 7.3.2 Tw-Dimensional Hyperbolic PDEs 7.4 PDES in Other Coordinate Systems 7.4.1 PDEs in Polar/Cylindrical Coordinates 7.4.2 PDEs in Spherical Coordinates 7.5 Laplace/Fourier Transforms for Solving PDES 7.5.1 Using the Laplace Transform for PDEs 7.5.2 Using the Fourier Transform for PDEs Problems Chapter 8: Complex Analysis 509 8.1 Functions of a Complex Variable 8.1.1 Complex Numbers and their Powers/Roots 8.1.2 Functions of a Complex Variable 8.1.3 Cauchy-Riemann Equations 8.1.4 Exponential and Logarithmic Functions 8.1.5 Trigonometric and Hyperbolic Functions 8.1.6 Inverse Trigonometric/Hyperbolic Functions 8.2 Conformal Mapping 8.2.1 Conformal Mappings 8.2.2 Linear Fractional Transformations 8.3 Integration of Complex Functions 8.3.1 Line Integrals and Contour Integrals 8.3.2 Cauchy-Goursat Theorem 8.3.3 Cauchy's Integral Formula 8.4 Series and Residues 8.4.1 Sequences and Series 8.4.2 Taylor Series 8.4.3 Laurent Series 8.4.4 Residues and Residue Theorem 8.4.5 Real Integrals Using Residue Theorem Problems Chapter 9: Optimization 9.1 Unconstrained Optimization 9.1.1 Golden Search Method 9.1.2 Quadratic Approximation Method 9.1.3 Nelder-Mead Method 9.1.4 Steepest Descent Method 9.1.5 Newton Method 9.2 Constrained Optimization 9.2.1 Lagrange Multiplier Method 9.2.2 Penalty Function Method 9.3 MATLAB Built-in Functions for Optimization 9.3.1 Unconstrained Optimization 9.3.2 Constrained Optimization 9.3.3 Linear Programming (LP) 9.3.4 Mixed Integer Linear Programing (MILP) Problems Chapter 10: Probability 10.1 Probability 10.1.1 Definition of Probability 10.1.2 Permutations and Combinations 10.1.3 Joint Probability, Conditional Probability, and Bayes' Rule 10.2 Random Variables 10.2.1 Random Variables and Probability Distribution/Density Function 10.2.2 Joint Probability Density Function 10.2.3 Conditional Probability Density Function 10.2.4 Independence 10.2.5 Function of a Random Variable 10.2.6 Expectation, Variance, and Correlation 10.2.7 Conditional Expectation 10.2.8 Central Limit Theorem - Normal Convergence Theorem 10.3 ML Estimator and MAP Estimator 653 Problems
Evolution and Mineralization of the Arabian–Nubian Shield, Volume 3 presents the exploration for mineral resources in the Precambrian basement terrain underlying large areas of the Middle East. This book discusses the geological investigations of the tectonic evolution, structure, and metallogenesis of the Arabian–Nubian Shield. Organized into three parts encompassing 13 chapters, this volume begins with an overview of the chronologic scheme for the evolution of the southern part of the Arabian Shied and provides evidence of its genesis at a convergent plate margin between blocks of oceanic lithosphere. This text then examines the granitic crust with associated calc-alkaline volcanics of Pan-African age. Other chapters consider the isotopic ages for the rocks of the Egyptian basement complex. This book discusses as well the distribution, form, and variety of intrusive activity in the Jiddah–Rabigh–Wadi Al-Quaha area. The final chapter deals with the properties of igneous rocks from Jordan. This book is a valuable resource for geologists.
Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration. Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.
This book is a compendium of fundamental mathematical concepts, methods, models, and their wide range of applications in diverse fields of engineering. It comprises essentially a comprehensive and contemporary coverage of those areas of mathematics which provide foundation to electronic, electrical, communication, petroleum, chemical, civil, mechanical, biomedical, software, and financial engineering. It gives a fairly extensive treatment of some of the recent developments in mathematics which have found very significant applications to engineering problems.
This book provides a unified framework for various currently available mathematical models that are used to analyze progression and regression in cancer development, and to predict its dynamics with respect to therapeutic interventions. Accurate and reliable model representations of cancer dynamics are milestones in the field of cancer research. Mathematical modeling approaches are becoming increasingly common in cancer research, as these quantitative approaches can help to validate hypotheses concerning cancer dynamics and thus elucidate the complexly interlaced mechanisms involved. Even though the related conceptual and technical information is growing at an exponential rate, the application of said information and realization of useful healthcare devices are lagging behind. In order to remedy this discrepancy, more interdisciplinary research works and course curricula need to be introduced in academic, industrial, and clinical organizations alike. To that end, this book reformulates most of the existing mathematical models as special cases of a general model, allowing readers to easily get an overall idea of cancer dynamics and its modeling. Moreover, the book will help bridge the gap between biologists and engineers, as it brings together cancer dynamics, the main steps involved in mathematical modeling, and control strategies developed for cancer management. This also allows readers in both medical and engineering fields to compare and contrast all the therapy-based models developed to date using a single source, and to identify unexplored research directions.
This book offers a critical Arabic edition, annotated English translation, introductory study, and two-way glossaries of the famous dispensatory composed around the middle of the 12th century CE by the Nestorian physician Ibn at-Tilm . The dispensatory, recognized as a masterpiece already by mediaeval contemporaries, soon after its appearance became the pharmacological standard work in the hospitals and apothecs of Baghdad and the wider Arab East, replacing, after almost 300 years, the vademecum of S?b?r ibn Sahl. The dispensatory of Ibn at-Tilmi? marks the apogee and the conclusion of centuries of medico-pharmacological development in the Arab world, and it is therefore absolutely essential for a critical understanding of mediaeval Arabic medicine and pharmacy in particular, and premodern science in general.
Late-Stage Fluorination of Bioactive Molecules and Biologically-Relevant Substrates reviews how the use of these techniques on compounds with already known and relevant biological activity can provide new pharmaceutical leads with improved medicinal properties. The fluorination strategies discussed take into account both conventional and novel reagents, including nucleophilic, electrophilic, those of a radical nature, and diverse families of organic compounds, such as (hetero) aromatic rings and aliphatic substrates. Drawing on the authors' expert knowledge, this book provides researchers with a broad set of applicable methods to use in their work. - Highlights the latest developments in the field in a concise volume - Provides details of key fluorinating reagents across diverse families of organic compounds - Explores the current applications and future potential of fluorine in drug development
Al-Dawoody examines the justifications and regulations for going to war in both international and domestic armed conflicts under Islamic law. He studies the various kinds of use of force by both state and non-state actors in order to determine the nature of the Islamic law of war.
This volume presents a theoretical framework and control methodology for a class of complex dynamical systems characterised by high state space dimension, multiple inputs and outputs, significant nonlinearity, parametric uncertainty, and unmodeled dynamics. A unique feature of the authors' approach is the combination of rigorous concepts and methods of nonlinear control (invariant and attracting submanifolds, Lyapunov functions, exact linearisation, passification) with approximate decomposition results based on singular perturbations and decentralisation. Some results published previously in the Russian literature and not well known in the West are brought to light. Basic concepts of modern nonlinear control and motivating examples are given. Audience: This book will be useful for researchers, engineers, university lecturers and postgraduate students specialising in the fields of applied mathematics and engineering, such as automatic control, robotics, and control of vibrations.
I assume that you already know a good deal of microbiology. In this book, I frequently use the word "we" by which I mean "you and I". Together we are going to consider bacteriology from a broader perspective and we will think our way through the important biological problems that are frequently just skipped over in every microbiology course. My most important reason for writing this book is to make accessible the relevant thinking from fields of science other than microbiology that are important to microbiology. The book is written for people that have already have a fascination with bacteria, but can see that their background for understanding is far complete. This book consists of topics that are largely omitted from microbiology textbooks and includes some mathematics, physics, chemistry, and evolutionary biology. It contains a good deal of my own work, both experimental and theoretical, together with a lot of speculation. If ten times bigger, it would be a full text book on microbial physiology. A third of the microbial physiology is covered by the recent is no longer treated even in textbook by White (2000). Another third current specialized tests and is greatly underrepresented in text books.
This book promotes a basic understanding of the concept of solubility and miscibility between halogenated hydrocarbons and water. It points out the regularities existing between solubility and physical properties of solute and solvent. The book is valuable to chemists and chemical engineers.
The book is intended to serve as an introductory course in group theory geared towards second-year university students. It aims to provide them with the background needed to pursue more advanced courses in algebra and to provide a rich source of examples and exercises. Studying group theory began in the late eighteenth century and is still gaining importance due to its applications in physics, chemistry, geometry, and many fields in mathematics. The text is broadly divided into three parts. The first part establishes the prerequisite knowledge required to study group theory. This includes topics in set theory, geometry, and number theory. Each of the chapters ends with solved and unsolved exercises relating to the topic. By doing this, the authors hope to fill the gaps between all the branches in mathematics that are linked to group theory. The second part is the core of the book which discusses topics on semigroups, groups, symmetric groups, subgroups, homomorphisms, isomorphism, and Abelian groups. The last part of the book introduces SAGE, a mathematical software that is used to solve group theory problems. Here, most of the important commands in SAGE are explained, and many examples and exercises are provided.
This book brings together 106 papers presented at the Joint Conferences of 2015 International Conference on Computer Science and Engineering Technology (CSET2015) and 2015 International Conference on Medical Science and Biological Engineering (MSBE2015), which were held in Hong Kong on 30-31 May 2015.The joint conferences covered a wide range of research topics in new emerging technologies, ranging from computing to biomedical engineering. During the conferences, industry professionals, scholars and government agencies around the world gathered to share their latest research results and discuss the practical challenges they encountered. Their research articles were reviewed and selected by a panel of experts before being compiled into this proceedings. Combining research findings and industry applications, this proceedings should be a useful reference for researchers and engineers working in computing and biomedical science.
Humans are comprised of a body and a soul, yet most of them take care of their bodies and forget about their souls. This book wakes them up, the author hopes, and provides them with a dose of spirituality which they may never have had before. This book is written for everyone, and its stories will appeal to many, if not most, people who will find in them beauty and universality: There is One God, one human family started by Adam and Eve, one truth, one heaven, one hell, one right and one wrong... and one religion. Call any of these by any name, it does not matter, for calling a rose by any other name does not change its beauty, hue, aroma or anything else. So is the case particularly with God whom the Muslims prefer to call “All¡h” for reasons which the book explains. This Volume discusses the “99 Attributes of All¡h” or how Muslims view their Creator. Knowing a maker is done by knowing what he makes. It discusses not only prominent figures but other beings as well: jinns (or genies), angels, demons, etc. It narrates interesting tales about a number of God’s prophets and messengers such as Noah, Moses, Abraham, David, Solomon and Jesus Christ, peace with them all and many, many salutations.
This monograph is the last volume in the series 'Acoustic and Elastic Wave Fields in Geophysics'. The previous two volumes published by Elsevier (2000, 2002) dealt mostly with wave propagation in liquid media. The third volume is dedicated to propagation of plane, spherical and cylindrical elastic waves in different media including isotropic and transversely isotropic solids, liquid-solid models, and media with cylindrical inclusions (boreholes).* Prevalence of physical reasoning on formal mathematical derivations * Readers do not need to have a strong background in mathematics and mathematical physics* Detailed analysis of wave phenomena in various types of elastic and liquid-elastic media
This monograph presents in great detail a large number of both unpublished and previously published Babylonian mathematical texts in the cuneiform script. It is a continuation of the work A Remarkable Collection of Babylonian Mathematical Texts (Springer 2007) written by Jöran Friberg, the leading expert on Babylonian mathematics. Focussing on the big picture, Friberg explores in this book several Late Babylonian arithmetical and metro-mathematical table texts from the sites of Babylon, Uruk and Sippar, collections of mathematical exercises from four Old Babylonian sites, as well as a new text from Early Dynastic/Early Sargonic Umma, which is the oldest known collection of mathematical exercises. A table of reciprocals from the end of the third millennium BC, differing radically from well-documented but younger tables of reciprocals from the Neo-Sumerian and Old-Babylonian periods, as well as a fragment of a Neo-Sumerian clay tablet showing a new type of a labyrinth are also discussed. The material is presented in the form of photos, hand copies, transliterations and translations, accompanied by exhaustive explanations. The previously unpublished mathematical cuneiform texts presented in this book were discovered by Farouk Al-Rawi, who also made numerous beautiful hand copies of most of the clay tablets. Historians of mathematics and the Mesopotamian civilization, linguists and those interested in ancient labyrinths will find New Mathematical Cuneiform Texts particularly valuable. The book contains many texts of previously unknown types and material that is not available elsewhere.
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