Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises
This second edition of Linear Integral Equations continues the emphasis that the first edition placed on applications. Indeed, many more examples have been added throughout the text. Significant new material has been added in Chapters 6 and 8. For instance, in Chapter 8 we have included the solutions of the Cauchy type integral equations on the real line. Also, there is a section on integral equations with a logarithmic kernel. The bibliography at the end of the book has been exteded and brought up to date. I wish to thank Professor B.K. Sachdeva who has checked the revised man uscript and has suggested many improvements. Last but not least, I am grateful to the editor and staff of Birkhauser for inviting me to prepare this new edition and for their support in preparing it for publication. RamP Kanwal CHAYfERl Introduction 1.1. Definition An integral equation is an equation in which an unknown function appears under one or more integral signs Naturally, in such an equation there can occur other terms as well. For example, for a ~ s ~ b; a :( t :( b, the equations (1.1.1) f(s) = ib K(s, t)g(t)dt, g(s) = f(s) + ib K(s, t)g(t)dt, (1.1.2) g(s) = ib K(s, t)[g(t)fdt, (1.1.3) where the function g(s) is the unknown function and all the other functions are known, are integral equations. These functions may be complex-valued functions of the real variables s and t.
Cytogenetics plays an important role in understanding the chromosomal and genetic architecture of plant species. Plant Cytogenetics, Third Edition follows the tradition of its predecessors presenting theoretical and practical aspects of plant cytogenetics. Chapters describe correct handling of plant chromosomes, methods in plant cytogenetics, cell division, reproduction methods, chromosome nomenclature, karyotype analysis, chromosomal aberrations, genome analysis, transgenic crops, and cytogenetics in plant breeding. This new edition begins with a brief introduction on the historical aspect of cytogenetics and flows directly into handling of plant chromosomes by classical and modern cytological techniques, classical Mendelian Genetics, brief description of cell division, and chromosome identification by karyotype analysis. The comprehension of cytogenetics is incomplete without information on the role of aneuploidy in associating a gene on a particular chromosome, and the book covers these methodologies as a primary topic. Covering classical to modern cytogenetics, the book presents to the reader the crucial role of cytogenetics in improving crops.
Plant cytogenetics has progressed at a rapid rate since the publication of the first edition. Plant Cytogenetics, Second Edition presents an up-to-date review of cytogenetics. It covers the latest in the various classical and modern techniques in the handling of chromosomes, karyotype analysis, genetics of meiosis, genomic relationships, and chromosome manipulation. It includes new chapters on extra chromosomal inheritance and the mode of reproduction in plants, paricularly apomixis, as well as new sections on the molecular basis of heredity, genomic in situ hybridization, and the classical and molecular methods of genome analysis. The author also elaborates on the cytogenetic basis of somaclonal variation generated through cell and tissue culture.
This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.
This book presents the state of the art results on modeling and analysis of OBS networks. It provides researchers with new directions for future research and helps them gain a better understanding of modeling OBS networks. This book classifies all the literature on modeling and analysis of OBS networks and serves as a thought provoking material for the researchers working on the analysis of high-speed networks. The scope of this book however is not limited to OBS networks alone but extends to high-speed communication networks with limited or no buffers.
The book is intended to emphasize the aspects of electromagnetism which are most important for the modern student as a background both for experimental physics and for the quantum theory of matter and radiation. The emphasis is on physical theory as developed from fundamental empirical laws rather than on mathematics and internal logic. Thus, Maxwell’s equations are obtained from the experimental laws of Coulomb, Ampere and Faraday, instead of postulated initially. The physical concepts come out more clearly in this way, and the approach represents the manner in which physical theory evolves. The introduction of electrodynamic potentials and the solution of the wave equation are treated conventionally. Rationalized MKS units are used, because the majority of modern reference books and papers are now written in this system of units. I have not concentrated primarily on problem solving, the heart of the matter lies in the ideas and their development. Beautiful methods of calculus are used for the simplification of the subject matter. References for further reading are given at the end.
Computational Quantum Chemistry, Second Edition, is an extremely useful tool for teaching and research alike. It stipulates information in an accessible manner for scientific investigators, researchers and entrepreneurs. The book supplies an overview of the field and explains the fundamental underlying principles. It also gives the knowledge of numerous comparisons of different methods. The book consists of a wider range of applications in each chapter. It also provides a number of references which will be useful for academic and industrial researchers. It includes a large number of worked-out examples and unsolved problems for enhancing the computational skill of the users. Features Includes comprehensive coverage of most essential basic concepts Achieves greater clarity with improved planning of topics and is reader-friendly Deals with the mathematical techniques which will help readers to more efficient problem solving Explains a structured approach for mathematical derivations A reference book for academicians and scientific investigators Ram Yatan Prasad, PhD, DSc (India), DSc (hc) Colombo, is a Professor of Chemistry and former Vice Chancellor of S.K.M University, Jharkhand, India. Pranita, PhD, DSc (hc) Sri Lanka, FICS, is an Assistant Professor of Chemistry at Vinoba Bhave University, India.
This book introduces the finite element and boundary element methods for applications to quantum mechanical methods. It should be useful to graduate students and researchers in basic quantum theory, quantum semiconductor modeling and chemistry.
TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.
For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.
Introducing the book "Physical Pharmaceutics-I" is something that fills me with an incredible amount of joy. The content of this book has been meticulously crafted to adhere to the curriculum for Bachelor of Pharmacy students that has been outlined by the Pharmacy Council of India. An effort has been made to investigate the topic using terminology that is as straightforward as possible in order to make it more simply digestible for pupils. The book has a number of illustrations, such as flowcharts and diagrams that make it simple for students to comprehend complex ideas. It is the author's honest desire that both students and academicians would take something helpful away from reading this book.
Business Analysts and Data Scientists are in huge demand, as global companies seek to digitally transform themselves and leverage their data resources to realize competitive advantage. This book covers all the fundamentals, from statistics to programming to business applications, to equip you with the solid foundational knowledge needed to progress in business analytics. Assuming no prior knowledge of programming or statistics, this book takes a simple step-by-step approach which makes potentially intimidating topics easy to understand, by keeping Maths to a minimum and including examples of business analytics in practice. Key features: · Introduces programming fundamentals using R and Python · Covers data structures, data management and manipulation and data visualization · Includes interactive coding notebooks so that you can build up your programming skills progressively Suitable as an essential text for undergraduate and postgraduate students studying Business Analytics or as pre-reading for students studying Data Science. Ram Gopal is Pro-Dean and Professor of Information Systems at the University of Warwick. Daniel Philps is an Artificial Intelligence Researcher and Head of Rothko Investment Strategies. Tillman Weyde is Senior Lecturer at City, University of London.
The book details mathematical techniques for chemical and other engineers. Many practical examples encountered by chemical (and other) engineers, modern approach involving multiple length and time scales, use of symbolic software (such as Mathematica) and combination of analytical methods with graphics are included. It may be used by graduate chemical (and other) engineering students as well as industrial practitioners and possibly specialists.
Numerical Methods is a mathematical tool used by engineers and mathematicians to do scientific calculations. It is used to find solutions to applied problems where ordinary analytical methods fail. This book is intended to serve for the needs of co
Heterocycles are ubiquitously present in nature and occupy a unique place in organic chemistry as they are part of the DNA and haemoglobin that make life possible. The Chemistry of Heterocycles covers an introduction to the topic, followed by a chapter on the nomenclature of all classes of isolated, fused and polycyclic heterocycles. The third chapter delineates the highly strained three membered N,O and S containing aromatic and non-aromatic heterocycles with one and more than one similar and dissimilar heteroatom. The four-membered heterocycles are abundantly present in various natural and synthetic products of pharmacological importance. This chapter describes the natural abundance, synthesis, chemical reactivity, structural features and their medicinal importance. This class of compounds are present as sub-structures in penicillin and cytotoxic Taxol. Lastly, a chapter on the natural abundance, synthesis, chemical reactivity and pharmacological importance of 5-membered heterocycles with N,O,S heteroatom is covered. The chemistry of heterocycles with mixed heteroatom such as, N-S, N-O, N-S etc. is also described. - Gives in-depth, clear information about various systems of nomenclature along with widely acceptable IUPAC system for naming various classes of heterocycles - Provides complete information about natural occurrences, synthesis, chemical reactivity, pharmacological importance of heterocycles and their application in material science - Highly relevant for graduate students and researchers, providing updated information about various isolated and fused N,O and,S containing heterocycles
...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic
The subject of this book explains the social framework of consumer rights and legal framework of protecting consumer rights that has evolved in India over the last three decades. It also explains the momentous changes in Indian consumer markets over this period as a result of economic liberalisation and provides an understanding of the problems consumers face in markets and the consumer detriment there from. It analyses the buying behavior of consumers as well as the phenomena of consumer complaints and the processes and systems to address them. The development of the consumer jurisprudence in settling consumer disputes in consumer courts under the Consumers Protection Act of 1986 and 2019 is examined in detail. Leading cases are used to explain important concepts. It also addresses the role played by quality and standardization in the market place and the roles of different agencies in establishing product and service standards. The student should be able to comprehend the business firms’ interface with consumers and the consumer related regulatory and business environment for major consumer industries of India.
Asymptotic analysis is an old subject that has found applications in vari ous fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the so lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus. In view of the importance of these methods, many excellent books on this subject are available [19], [21], [27], [67], [90], [91], [102], [113]. An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a sys tematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail [15], [43], [44], [84], [92], [112]. As it turns out, generalized functions provide a very appropriate framework for asymptotic analysis, where many analytical operations can be performed, and also pro vide a systematic procedure to assign values to the divergent integrals that often appear in the literature.
This book discusses major topics in measure theory, Fourier transforms, complex analysis and algebraic topology. It presents material from a mature mathematical perspective. The text is suitable for a two-semester graduate course in analysis and will help students prepare for a research career in mathematics. After a short survey of undergraduate analysis and measure theory, the book highlights the essential theorems that have now become ubiquitous in mathematics. It studies Fourier transforms, derives the inversion theorem and gives diverse applications ranging from probability theory to mathematical physics. It reviews topics in complex analysis and gives a synthetic, rigorous development of the calculus of residues as well as applications to a wide array of problems. It also introduces algebraic topology and shows the symbiosis between algebra and analysis. Indeed, algebraic archetypes were providing foundational support from the start. Multivariable calculus is comprehended in a single glance through the algebra of differential forms. Advanced complex analysis inevitably leads one to the study of Riemann surfaces, and so the final chapter gives the student a hint of these motifs and underlying algebraic patterns.
Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuses exclusively on singular integral equations and on the distributional solutions of these equations. A large number of beautiful mathematical concepts are required to find such solutions, which in tum, can be applied to a wide variety of scientific fields - potential theory, me chanics, fluid dynamics, scattering of acoustic, electromagnetic and earth quake waves, statistics, and population dynamics, to cite just several. An integral equation is said to be singular if the kernel is singular within the range of integration, or if one or both limits of integration are infinite. The singular integral equations that we have studied extensively in this book are of the following type. In these equations f (x) is a given function and g(y) is the unknown function. 1. The Abel equation x x) = l g (y) d 0
This book is based on the lecture notes of the author delivered to the students at the Institute of Science, Banaras Hindu University, India. It covers simplex, revised simplex, two-phase method, duality, dual simplex, complementary slackness, transportation and assignment problems with good number of examples, clear proofs, MATLAB codes and homework problems. The book will be useful for both students and practitioners.
WIND ENERGY EXPLAINED Authoritative and bestselling textbook detailing the many aspects of using wind as an energy source Wind Energy Explained provides complete and comprehensive coverage on the topic of wind energy, starting with general concepts like the history of and rationale for wind energy and continuing into specific technological components and applications along with the new recent developments in the field. Divided into 16 chapters, this edition includes up-to-date data, diagrams, and illustrations, boasting an impressive 35% new material including new sections on metocean design conditions, wind turbine design, wind power plants and the electrical system, fixed and floating offshore wind turbines, project development, permitting and environmental risks and benefits, turbine installation, operation and maintenance, and high penetration wind energy systems and power-to-X. Wind Energy Explained also includes information on: Modern wind turbines, covering the design and their many components such as the rotor, drive train, and generator Aerodynamics of wind energy, covering one-dimensional momentum theory, the Betz limit, and ideal horizontal axis wind turbine with wake rotation Environmental external design conditions, such as wind, waves, currents, tides, salinity, floating ice, and many more Commonly used materials and components, such as steel, composites, copper, and concrete, plus machinery elements, such as shafts, couplings, bearings, and gears Modern design methods, including probabilistic design Environmental effects and mitigation strategies for wind project siting and the role of public engagement in the development process This book offers a complete examination of one of the most promising sources of renewable energy and is a great introduction to this cross-disciplinary field for practicing engineers. It may also be used as a textbook resource for university level courses in wind energy, both introductory and advanced.
The book covers various methods of characterization of advanced materials commonly used in engineering including understanding of the working principle and applicability of devices. It explores the techniques implemented for advanced materials like superalloys, thin films, powders, nanocomposites, polymers, shape memory alloys, high entropy alloys, and so on. Major instruments covered include X-ray diffraction, near-field scanning optical microscopy Raman, X-ray photospectroscopy, ultraviolet-visible-near-infrared spectrosphotometer, Fourier-transform infrared spectroscopy, differential scanning calorimeter, profilometer, and thermogravimetric analysis. Features: Covers material characterization techniques and the development of advanced characterization technology Includes multiple length scale characterization approaches for a large variety of materials, from nano- to micron-scale, as well as their constraints Discusses advanced material characterization technology in the microstructural and property characterization fields Reviews both practical and theoretical explanations of approaches for characterizing microstructure and properties Offers fundamentals, basic instrumentation details, experimental approaches, analyses, and applications with case studies This book is aimed at graduate students and researchers in materials science and engineering.
Discrete Mathematics will be of use to any undergraduate as well as post graduate courses in Computer Science and Mathematics. The syllabi of all these courses have been studied in depth and utmost care has been taken to ensure that all the essential topics in discrete structures are adequately emphasized. The book will enable the students to develop the requisite computational skills needed in software engineering.
1. Indefinite Integrals, 2. Definite Integrals, 3. Applications of Integrals, 4. Differential Equations, 5. Applications of Differential Equations, 6. Vectors, 7. Scalar or Dot Product of Two Vectors, 8. Vector or Cross Product of Two Vectors, 9. Angle between Two Lines, 10. Straight Line, 11. The Plane,
First published in 1983. Psychological data are segments of life histories; as such they are ordered sequences of observations and by definition time series. Yet they are often anything but well behaved; what regularities and invariances they have are buried from all but the most persistent investigator. The most common methods of representing quantitative results in psychology are frozen outside time; thus they deliberately average out much of the sequential structure that holds any sparse clues to the nature of processes within the organism. This review, whose simple aim is to bring together in an illuminating juxtaposition on basic results in both time series analysis and in experimental psychology, thus. cuts across traditions within psychology.
Multicultural Curriculum is a collection of original essays brought together to develop new theories and meaningful praxis to build a new paradigm for teaching multiculturalism in today's classroom. The impressive list of contributors shows how the current epistemological and pedagogical practices that are designed to forward multiculturalism actually serves to essentialize cultures--the antithesis of what multicultural education is designed to accomplish. The editors offer alternative theories, classroom teaching methods, and policies that are designed to promote true cultural understanding and equality.
When men of knowledge impart this knowledge, I do not mean they will convince your reason. I mean they will awaken in you the faith that it is so. - Sri Krishna, Bhagavadgita BACKGROUND The use of computers has led to significant productivity increases in the en gineering industry. Most ofthe computer-aided engineering applications were . restricted to algorithmic computations, such as finite element programs and circuit analysis programs. However, a number ofproblems encountered in en gineering are not amenable to purely algorithmic solutions. These problems are often ill-structured; the term ill-structured problems is used here to de note problems that do not have a clearly defined algorithmic solution. An experienced engineer deals with these ill-structured problems using his/her judgment and experience. The knowledge-based systems (KBS) technology, which emerged out of research in artificial intelligence (AI), offers a method ologyto solve these ill-structuredengineering problems. The emergenceofthe KBS technology can be viewed as the knowledge revolution: other important events that led to increased productivity are the industrial revolution (17th century); the invention of the transistor and associated developments (first half of the 20th century); and the world-wide web (towards the end of the 20th century). Kurzweil, in a lecture at M. LT on December 3, 1987, linked the progress of automation to two industrial revolutions: the first industrial PREFACE xxxii revolution leveraged our physical capabilities, whereas the second industrial revolution - the knowledge revolution - is expected leverage oUr mental ca pabilities.
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