Handbook Of Means And Their Inequalities

Author by : P.S. Bullen
Languange : en
Publisher by : Springer Science & Business Media
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Description : There seems to be two types of books on inequalities. On the one hand there are treatises that attempt to cover all or most aspects of the subject, and where an attempt is made to give all results in their best possible form, together with either a full proof or a sketch of the proof together with references to where a full proof can be found. Such books, aimed at the professional pure and applied mathematician, are rare. The first such, that brought some order to this untidy field, is the classical "Inequalities" of Hardy, Littlewood & P6lya, published in 1934. Important as this outstanding work was and still is, it made no attempt at completeness; rather it consisted of the total knowledge of three front rank mathematicians in a field in which each had made fundamental contributions. Extensive as this combined knowledge was there were inevitably certain lacunre; some important results, such as Steffensen's inequality, were not mentioned at all; the works of certain schools of mathematicians were omitted, and many important ideas were not developed, appearing as exercises at the ends of chapters. The later book "Inequalities" by Beckenbach & Bellman, published in 1961, repairs many of these omissions. However this last book is far from a complete coverage of the field, either in depth or scope.


Means And Their Inequalities

Author by : P.S. Bullen
Languange : en
Publisher by : Springer Science & Business Media
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Description : Approach your problems from the right end It isn't !hat they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal 0/ Fa/her 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuJik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fie1ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "complete1y integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing c1assification schemes. They draw upon wide1y different sections of mathematics.


Means And Their Inequalities

Author by : P.S. Bullen
Languange : en
Publisher by : Springer
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Total Read : 37
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Description : Approach your problems from the right end It isn't !hat they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal 0/ Fa/her 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuJik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fie1ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "complete1y integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing c1assification schemes. They draw upon wide1y different sections of mathematics.


Positive Definiteness Of Functions With Applications To Operator Norm Inequalities

Author by : Hideki Kosaki
Languange : en
Publisher by : American Mathematical Soc.
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Description : Positive definiteness is determined for a wide class of functions relevant in the study of operator means and their norm comparisons. Then, this information is used to obtain an abundance of new sharp (unitarily) norm inequalities comparing various operator means and sometimes other related operators.


Analytic Inequalities

Author by : Dragoslav S. Mitrinovic
Languange : en
Publisher by : Springer Science & Business Media
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Description : The Theory of Inequalities began its development from the time when C. F. GACSS, A. L. CATCHY and P. L. CEBYSEY, to mention only the most important, laid the theoretical foundation for approximative meth ods. Around the end of the 19th and the beginning of the 20th century, numerous inequalities were proyed, some of which became classic, while most remained as isolated and unconnected results. It is almost generally acknowledged that the classic work "Inequali ties" by G. H. HARDY, J. E. LITTLEWOOD and G. POLYA, which appeared in 1934, transformed the field of inequalities from a collection of isolated formulas into a systematic discipline. The modern Theory of Inequalities, as well as the continuing and growing interest in this field, undoubtedly stem from this work. The second English edition of this book, published in 1952, was unchanged except for three appendices, totalling 10 pages, added at the end of the book. Today inequalities playa significant role in all fields of mathematics, and they present a very active and attractive field of research. J. DIEUDONNE, in his book "Calcullnfinitesimal" (Paris 1968), attri buted special significance to inequalities, adopting the method of exposi tion characterized by "majorer, minorer, approcher". Since 1934 a multitude of papers devoted to inequalities have been published: in some of them new inequalities were discovered, in others classical inequalities ,vere sharpened or extended, various inequalities ,vere linked by finding their common source, while some other papers gave a large number of miscellaneous applications.


General Inequalities 7

Author by : Catherine Bandle
Languange : en
Publisher by : Springer Science & Business Media
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Description : Inequalities continue to play an essential role in mathematics. The subject is per haps the last field that is comprehended and used by mathematicians working in all the areas of the discipline of mathematics. Since the seminal work Inequalities (1934) of Hardy, Littlewood and P6lya mathematicians have laboured to extend and sharpen the earlier classical inequalities. New inequalities are discovered ev ery year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. So extensive are these developments that a new mathematical periodical devoted exclusively to inequalities will soon appear; this is the Journal of Inequalities and Applications, to be edited by R. P. Agar wal. Nowadays it is difficult to follow all these developments and because of lack of communication between different groups of specialists many results are often rediscovered several times. Surveys of the present state of the art are therefore in dispensable not only to mathematicians but to the scientific community at large. The study of inequalities reflects the many and various aspects of mathemat ics. There is on the one hand the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand the subject is a source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are many applications in a wide variety of fields from mathematical physics to biology and economics.


Proofs From The Book

Author by : Martin Aigner
Languange : en
Publisher by : Springer Science & Business Media
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Description : According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.


Mathematical Reviews

Author by : Anonim
Languange : en
Publisher by : Unknown
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Operator Inequalities Of The Jensen Eby Ev And Gr Ss Type

Author by : Silvestru Sever Dragomir
Languange : en
Publisher by : Springer Science & Business Media
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Description : The main aim of this book is to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces. In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive selfadjoint operators as well as some results for the spectrum of this class of operators are presented. This text introduces the reader to the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators as well as the step functions of selfadjoint operators. The spectral decomposition for this class of operators, which play a central role in the rest of the book and its consequences are introduced. At the end of the chapter, some classical operator inequalities are presented as well. Recent new results that deal with different aspects of the famous Jensen operator inequality are explored through the second chapter. These include but are not limited to the operator version of the Dragomir-Ionescu inequality, the Slater type inequalities for operators and its inverses, Jensen’s inequality for twice differentiable functions whose second derivatives satisfy some upper and lower bound conditions and Jensen’s type inequalities for log-convex functions. Hermite-Hadamard’s type inequalities for convex functions and the corresponding results for operator convex functions are also presented. The Čebyšev, (Chebyshev) inequality that compares the integral/discrete mean of the product with the product of the integral/discrete means is famous in the literature devoted to Mathematical Inequalities. The sister inequality due to Grüss which provides error bounds for the magnitude of the difference between the integral mean of the product and the product of the integral means has also attracted much interest since it has been discovered in 1935 with more than 200 papers published so far. The last part of the book is devoted to the operator versions of these famous results for continuous functions of selfadjoint operators on complex Hilbert spaces. Various particular cases of interest and related results are presented as well. This book is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.


Modeling Decisions For Artificial Intelligence

Author by : Yasuo Narukawa
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008, held in Sabadell, Spain, in October 2008. The 19 revised full papers presented together with 2 invited lectures were thoroughly reviewed and selected from 43 submissions; they are devoted to theory and tools for modeling decisions, as well as applications that encompass decision making processes and information fusion techniques. The papers are organized in topical sections on aggregation operators, decision making, clustering and similarity, computational intelligence and optimization, as well as data privacy.


Health Inequalities

Author by : Johan P. Mackenbach
Languange : en
Publisher by : Oxford University Press
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Description : The world we live in is hugely unequal. People in a better socioeconomic position do not only lead more comfortable lives, but also longer and healthier lives. This is true not only in the poorer parts of the world but also in the richest countries, including the advanced welfare states of Western Europe which have successfully pushed back poverty and other forms of material disadvantage. Why are health inequalities - systematically higher rates of disease, disability, and premature death among people with a lower level of education, occupation or income - so persistent? How can we expect to reduce this when it persists even in the most advanced states? Written by a leading figure in public health, this book looks to answer these questions by taking a broad, critical look at the scientific evidence surrounding the explanation of health inequalities, including recent findings from the fields of epidemiology, sociology, psychology, economics, and genetics. It concludes that a simplistic view, in which health inequalities are a direct consequence of social inequality, does not tell us the full story. Drawing upon a unique series of studies covering 30 European countries and more than three decades of observations, it shows that health inequalities are partly driven by autonomous forces that are difficult to counteract, such as educational expansion, increased social mobility, and rapid but differential health improvements. Finally, the book explores how we might use these new findings to continue our efforts to build a healthier and more equal future. Offering a truly multidisciplinary perspective and an accessible writing style, Health Inequalities is an indispensable resource for health researchers, professionals, and policy-makers, as well as for social scientists interested in inequality.


The Concept Of Justice And Equality

Author by : Eliane Saadé
Languange : en
Publisher by : Walter de Gruyter GmbH & Co KG
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Description : Unless considered on a practical level, where a precise distribution of social goods is chosen, John Rawls’s and Gerald Cohen’s approaches to social justice cannot be complementary. Their disagreement about justice and its principles calls for a choice, which opts either for the Rawlsian theory or for the Cohenian one. What is the more plausible approach to social justice? This work compares both approaches and aims to defend Cohen’s position in the light of two considerations. It answers the philosophical question about the analysis of the idea of justice, which puts the virtue of justice in its philosophical context. It, however, presents a method everyone can apply in order to arrive at the fundamental principles of justice by employing the power of reason. An analysis of the concept of justice based on the power of reason should seek to uncover the ultimate nature of justice, which is independent of facts and of other virtues. Once exposed, the understanding of justice arrived at should inform social institutions and determine people’s daily decisions. A just society is therefore a society where just persons and just institutions exhibit the virtue of justice.


Aggregation Functions In Theory And In Practise

Author by : Humberto Bustince Sola
Languange : en
Publisher by : Springer Science & Business Media
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Description : This volume collects the extended abstracts of 45 contributions of participants to the Seventh International Summer School on Aggregation Operators (AGOP 2013), held at Pamplona in July, 16-20, 2013. These contributions cover a very broad range, from the purely theoretical ones to those with a more applied focus. Moreover, the summaries of the plenary talks and tutorials given at the same workshop are included. Together they provide a good overview of recent trends in research in aggregation functions which can be of interest to both researchers in Physics or Mathematics working on the theoretical basis of aggregation functions, and to engineers who require them for applications.


An Introduction To The Theory Of Functional Equations And Inequalities

Author by : Marek Kuczma
Languange : en
Publisher by : Springer Science & Business Media
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Description : Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik)


Probabilistic Graphical Models For Computer Vision

Author by : Qiang Ji
Languange : en
Publisher by : Academic Press
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Description : Probabilistic Graphical Models for Computer Vision introduces probabilistic graphical models (PGMs) for computer vision problems and teaches how to develop the PGM model from training data. This book discusses PGMs and their significance in the context of solving computer vision problems, giving the basic concepts, definitions and properties. It also provides a comprehensive introduction to well-established theories for different types of PGMs, including both directed and undirected PGMs, such as Bayesian Networks, Markov Networks and their variants. Discusses PGM theories and techniques with computer vision examples Focuses on well-established PGM theories that are accompanied by corresponding pseudocode for computer vision Includes an extensive list of references, online resources and a list of publicly available and commercial software Covers computer vision tasks, including feature extraction and image segmentation, object and facial recognition, human activity recognition, object tracking and 3D reconstruction


A New Perspective On Thermodynamics

Author by : Bernard H. Lavenda
Languange : en
Publisher by : Springer
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Description : This book introduces a new outlook on thermodynamics. It brings the theory up to the present time and indicates areas of further development with the union of information theory and the theory of means and their inequalities.


The Khandakhadyaka Of Brahmagupta

Author by : Anonim
Languange : en
Publisher by : Motilal Banarsidass Publishe
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Critical Literacy In The Classroom

Author by : Wendy Morgan
Languange : en
Publisher by : Routledge
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Description : Critical literacy investigates how forms of knowledge, and the power they bring, are created in language and taken up by those who use texts. It asks how language might be put to different, more equitable uses, and how texts might be recreated in a way that would tell a different story. This book is a carefully documented and critically analysed example of the growing emphasis on critical literacy in syllabuses, government reports and the like. It: * bridges the gap between academics' theorizing and teachers' work * describes how secondary teachers have planned and implemented critical literacy curricula on a range of topics, from Shakespeare to the workplace * listens to teachers reflecting on their teaching and analyses classroom talk * extrapolates from present practice to a future critical literacy in a digitised, hypermedia world. Teachers and students of education, critical literacy advocates and theorists of literacy and schooling can learn much more from this book, which shows how critical literacy teachers, and their students are contributing to the ongoing reinvention of English education as critical literacy.


What Happens To People In A Competitive Society

Author by : Svein Olaf Thorbjørnsen
Languange : en
Publisher by : Springer Nature
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Description : In this book, author Svein Olaf Thorbjørnsen probes the question: What is at stake for human beings in a society dominated by competition, particularly economic competition? Is competition endemic to human nature? Does it preserve the dignity and intrinsic value of the human being? Does it secure better living conditions? In a way, the answer to these queries is a simple “yes.” It can allow for superior satisfaction of fundamental needs; legitimate self-love and self-realization; and encourage positive feelings upon mastering a skill. At the same time, however, competition can also contribute to a strong materialistic self-interest and support classicism, social ranking, and elitism: other human beings become only means to a personal success, thus jeopardizing fellowship and collaboration. In a hyper-competitive environment, some of the same positive human values mentioned above—self-love, self-realisation, individuality, and freedom—can be viewed to pose a threat to the realisation of one’s potential and to one’s true humanity. These competing, contradictory aspects of competition are presented and discussed from perspectives across varying disciplines, from social anthropology and economics to history, ethics, philosophy and theology.


Mathematics Of Computation

Author by : Anonim
Languange : en
Publisher by : Unknown
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Inequalities

Author by : G. H. Hardy
Languange : en
Publisher by : Cambridge University Press
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Description : This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and exhaustively both the statement and proof of all the standard inequalities of analysis. The authors were well known for their powers of exposition and were able here to make the subject accessible to a wide audience of mathematicians.


Inequalities And Applications 2010

Author by : Catherine Bandle
Languange : en
Publisher by : Springer Science & Business Media
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Description : Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, they constitute a challenging research field of their own. Inequalities also appear directly in mathematical models for applications in science, engineering, and economics. This edited volume covers divers aspects of this fascinating field. It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts. Within the last five decades, the late Wolfgang Walter has made great contributions to the field of inequalities. His book on differential and integral inequalities was a real breakthrough in the 1970’s and has generated a vast variety of further research in this field. He also organized six of the seven “General Inequalities” Conferences held at Oberwolfach between 1976 and 1995, and co-edited their proceedings. He participated as an honorary member of the Scientific Committee in the “General Inequalities 8” conference in Hungary. As a recognition of his great achievements, this volume is dedicated to Wolfgang Walter’s memory. The “General Inequalities” meetings found their continuation in the “Conferences on Inequalities and Applications” which, so far, have been held twice in Hungary. This volume contains selected contributions of participants of the second conference which took place in Hajdúszoboszló in September 2010, as well as additional articles written upon invitation. These contributions reflect many theoretical and practical aspects in the field of inequalities, and will be useful for researchers and lecturers, as well as for students who want to familiarize themselves with the area.


Frontiers In Time Scales And Inequalities

Author by : George A Anastassiou
Languange : en
Publisher by : World Scientific
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Description : This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional calculus in the Caputo sense. Then, it shows representation formulae of functions on time scales and presents Ostrowski type inequalities, Landau type inequalities, Grüss type and comparison of means inequalities, all these over time scales. The volume continues with integral operator inequalities and their multivariate vectorial versions using convexity of functions, again all these over time scales. It follows the Grüss and Ostrowski type inequalities involving s-convexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite–Hadamard type inequalities using m-convexity and (s, m)-convexity. Finally, it introduces the reduction method in fractional calculus and its connection to fractional Ostrowski type inequalities is studied. This book's results are expected to find applications in many areas of pure and applied mathematics, especially in difference equations and fractional differential equations. The chapters are self-contained and can be read independently, and advanced courses can be taught out of it. It is suitable for researchers, graduate students, seminars of the above subjects, and serves well as an invaluable resource for all science libraries. Contents:Foundations of Right Delta Fractional Calculus on Time ScalesPrinciples of Right Nabla Fractional Calculus on Time ScalesAbout Right Delta Discrete FractionalityAbout Right Nabla Discrete Fractional CalculusRepresentations and Ostrowski Inequalities over Time ScalesLandau Inequalities on Time ScalesGrüss and Comparison of Means Inequalities over Time ScalesAbout Integral Operator Inequalities over Time ScalesAbout Vectorial Integral Operator Inequalities Using Convexity over Time ScalesGeneral Grüss and Ostrowski Inequalities Using s-ConvexityEssential and s-Convexity Ostrowski and Grüss Inequalities Using Several FunctionsGeneral Fractional Hermite–Hadamard Inequalities Using m-Convexity and (s, m)-ConvexityAbout the Reduction Method in Fractional Calculus and Fractional Ostrowski Inequalities Readership: Advanced graduate students and researchers interested in time scales, inequalities and difference/differential equations. Key Features:Presents new research on time scales and related inequalitiesMaterials are crucially related to difference/differential equationsSelf-contained chapters that can be read independentlyAn extensive list of references is given in each chapterThe topics covered are diverseKeywords:Time Scale;Fractional Derivative;Difference Equation;Fractional Inequality


Total Liberation

Author by : David Naguib Pellow
Languange : en
Publisher by : U of Minnesota Press
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Description : When in 2001 Earth Liberation Front activists drove metal spikes into hundreds of trees in Gifford Pinchot National Forest, they were protesting the sale of a section of the old-growth forest to a timber company. But ELF’s communiqué on the action went beyond the radical group’s customary brief. Drawing connections between the harms facing the myriad animals who make their home in the trees and the struggles for social justice among ordinary human beings resisting exclusion and marginalization, the dispatch declared, “all oppression is linked, just as we are all linked,” and decried the “patriarchal nightmare” in the form of “techno-industrial global capitalism.” In Total Liberation, David Naguib Pellow takes up this claim and makes sense of the often tense and violent relationships among humans, ecosystems, and nonhuman animal species, expanding our understanding of inequality and activists’ uncompromising efforts to oppose it. Grounded in interviews with more than one hundred activists, on-the-spot fieldwork, and analyses of thousands of pages of documents, websites, journals, and zines, Total Liberation reveals the ways in which radical environmental and animal rights movements challenge inequity through a vision they call “total liberation.” In its encounters with such infamous activists as scott crow, Tre Arrow, Lauren Regan, Rod Coronado, and Gina Lynn, the book offers a close-up, insider’s view of one of the most important—and feared—social movements of our day. At the same time, it shows how and why the U.S. justice system plays to that fear, applying to these movements measures generally reserved for “jihadists”—with disturbing implications for civil liberties and constitutional freedom. How do the adherents of “total liberation” fight oppression and seek justice for humans, nonhumans, and ecosystems alike? And how is this pursuit shaped by the politics of anarchism and anticapitalism? In his answers, Pellow provides crucial in-depth insight into the origins and social significance of the earth and animal liberation movements and their increasingly common and compelling critique of inequality as a threat to life and a dream of a future characterized by social and ecological justice for all.


Inequalities In Analysis And Probability

Author by : Odile Pons
Languange : en
Publisher by : World Scientific
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Description : The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of many new results are presented in great detail. Original tools are developed for spatial point processes and stochastic integration with respect to local martingales in the plane. This second edition covers properties of random variables and time continuous local martingales with a discontinuous predictable compensator, with exponential inequalities and new inequalities for their maximum variable and their p-variations. A chapter on stochastic calculus presents the exponential sub-martingales developed for stationary processes and their properties. Another chapter devoted itself to the renewal theory of processes and to semi-Markovian processes, branching processes and shock processes. The Chapman–Kolmogorov equations for strong semi-Markovian processes provide equations for their hitting times in a functional setting which extends the exponential properties of the Markovian processes.


Advanced Inequalities

Author by : George A. Anastassiou
Languange : en
Publisher by : World Scientific
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Total Read : 67
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Description : This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end. The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and HardyOpial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as ChebyshevGruss, Gruss and Comparison of Means inequalities are studied. The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.


Negotiating Cohesion Inequality And Change

Author by : Hannah Jones
Languange : en
Publisher by : Policy Press
Format Available : PDF, ePub, Mobi
Total Read : 79
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Description : This unique study explores how local bureaucrats and politicians negotiate diversity, discrimination, migration, and class, in the midst of many other issues that affect community cohesion. Based on original empirical research, Hannah Jones contends that local government workers must often occupy “uncomfortable positions” when managing ethical, professional, and political commitments. Ultimately, she reveals the surprising extent to which governmental power affects the lives and emotions of the people who wield it.


Dimensions Of Inequality In Canada

Author by : David A. Green
Languange : en
Publisher by : UBC Press
Format Available : PDF, ePub, Mobi
Total Read : 10
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Description : Is Canada becoming a more polarized society? Or is it a kind-hearted nation that takes care of its disadvantaged? This volume closely examines these differing views through a careful analysis of the causes, trends, and dimensions of inequality to provide an overall assessment of the state of inequality in Canada. Contributors include economists, sociologists, philosophers, and political scientists, and the discussion ranges from frameworks for thinking about inequality, to original analyses using Canadian data, to assessments of significant policy issues, methodologies, and research directions. What emerges is the most detailed picture of inequality in Canada to date and, disturbingly, one that shows signs of us becoming a less just society. An invaluable source of information for policy makers, researchers, and students from a broad variety of disciplines, Dimensions of Inequality in Canada will also appeal to readers interested or involved in public debates over inequality.