As a survey of many technical results in probability theory and probability logic, this monograph by two widely respected scholars offers a valuable compendium of the principal aspects of the formal study of probability. Hugues Leblanc and Peter Roeper explore probability functions appropriate for propositional, quantificational, intuitionistic, and infinitary logic and investigate the connections among probability functions, semantics, and logical consequence. They offer a systematic justification of constraints for various types of probability functions, in particular, an exhaustive account of probability functions adequate for first-order quantificational logic. The relationship between absolute and relative probability functions is fully explored and the book offers a complete account of the representation of relative functions by absolute ones. The volume is designed to review familiar results, to place these results within a broad context, and to extend the discussions in new and interesting ways. Authoritative, articulate, and accessible, it will interest mathematicians and philosophers at both professional and post-graduate levels.
Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole.
Chinese proverbs are, in a sense, the DNA of Chinese culture and language. The meanings of many of these proverbs may not be obvious to Westerners. For example when Chinese say the proverb “Dog chases mouse,” they mean “Mind your own business”—that is, dogs don’t chase mice; it’s not their job. In the process of truly making a connection with Chinese language and culture, a solid understanding of these proverbs goes a long way. Learning 300 Chinese Proverbs presents a unique book of Chinese proverbs that can be used as a tool for learning spoken and written Mandarin Chinese. This helpful, practical reference is complete with a section on grammar and offers an innovative approach to learning correct pronunciation, useful to both the beginner and the advanced student. Each proverb represents a new and unique lesson in Mandarin Chinese, using Simplified Chinese and the Pinyin transliteration system. Learning 300 Chinese Proverbs is so much more than a Chinese textbook; it also offers an overview of the Chinese civilization and language that goes back thousands of years.
One fundamental premise of democratic theory is that social policy, group choice, or collective action should be based on the preferences of the individuals in the society, group, or collective. Using the tools of formal mathematical analysis, Peter C. Fishburn explores and defines the conditions for social choice and methods for synthesizing individuals' preferences. This study is unique in its emphasis on social choice functions, the general position that individual indifference may not be transitive, and the use of certain mathematics such as linear algebra. The text is divided into three main parts: social choice between two alternatives, which examines a variety of majority-like functions; simple majority social choice, which focuses on social choice among many alternatives when two-element feasible subset choices are based on simple majority; and a general study of aspects and types of social choice functions for many alternatives. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
The Voronezh Winter Mathematical School was an annual event in the scientific life of the former Soviet Union for 25 years. Articles collected here are written by prominent mathematicians and former lecturers and participants of the school, covering a range of subjects in analysis and geometry. Specific topics include global analysis, harmonic analysis, function theory, dynamical systems, operator theory, mathematical physics, spectral theory, homogenization, algebraic geometry, differential geometry, and geometric analysis. For researchers and graduate students in analysis, geometry, and mathematical physics. No index. Annotation copyrighted by Book News, Inc., Portland, OR
This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.
Honorable Mention, 2022 Sharon Harris Book Award presented by the University of Connecticut Humanities Institute Focusing on four key Chinese intellectuals of the first half of the twentieth century, Abolishing Boundaries offers new perspectives on modern Chinese political thought. These four intellectuals—Kang Youwei, Cai Yuanpei, Chen Duxiu, and Hu Shi—were deeply familiar with the Confucian and Buddhist classical texts, while also interested in the West's utopian literature of the late nineteenth century as well as Kant and the neo-Kantians, Marxists, and John Dewey and new liberalism, respectively. Although none of these four intellectuals can simply be labeled utopian thinkers, this book highlights how their thinking was intertwined with utopian ideals to produce theories of secular transcendence, liberalism, and communism, and how, in explicit and implicit ways, their ideas required some utopian impulse in order to escape the boundaries they identified as imprisoning the Chinese people and all humanity. To abolish these boundaries was to imagine alternatives to the unbearable present. This was not a matter of armchair philosophizing but of thinking through new ways to commit to action. These men did not hold a totalistic picture of some perfect society, but in distinctly different ways they all displayed a utopian impulse that fueled radical visions of change. Their work reveals much about the underlying forces shaping modern thought in China—and the world. Reacting to China's problems, they sought a better future for all humanity.
Tok Pisin is one of the most important languages of Melanesia and is used in a wide range of public and private functions in Papua New Guinea. The language has featured prominently in Pidgin and Creole linguistics and has featured in a number of debates in theoretical linguistics. With their extensive fieldwork experience and vast knowledge of the archives relating to Papua New Guinea, Peter Mühlhäusler, Thomas E. Dutton and Suzanne Romaine compiled this Tok Pisin text collection. It brings together representative samples of the largest Pidgin language of the Pacific area. These texts represent about 150 years of development of this language and will be an invaluable resource for researchers, language policy makers and individuals interested in the history of Papua New Guinea.
Mi Fu was a prominent calligrapher in 11th-century China. This analysis of his work considers content and style, and examines his calligraphy within the framework of the artist's life, the Northern Song culture in which he lived and the literati theory of art he helped to formulate.
Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.
Tori Shweet for Cameroon Pidgin English is a compendium of short stories written in Cameroon's most widely spoken lingua franca commonly called Cameroon Pidgin English (CPE). The grassfields of Cameroon serves as the nursery where these culturally enriched stories are nurtured. The collection comprises animal trickster tales, bird survival tales and human-interest stories. In conformity with the philosophy of French novelist, Stendhal, this anthology of short stories is a mirror that reflects the folklore and mores of the ethnic groups that constitute the grassland region of Cameroon. It serves as a window to the worldview, mindset and value systems of the grafi.
Now in its fifth edition, Derivatives and Internal Models provides a comprehensive and thorough introduction to derivative pricing, risk management and portfolio optimization, covering all relevant topics with enough hands-on, depth of detail to enable readers to develop their own pricing and risk tools. The book provides insight into modern market risk quantification methods such as variance-covariance, historical simulation, Monte Carlo, hedge ratios, etc., including time series analysis and statistical concepts such as GARCH Models or Chi-Square-distributions. It shows how optimal trading decisions can be deduced once risk has been quantified by introducing risk-adjusted performance measures and a complete presentation of modern quantitative portfolio optimization. Furthermore, all the important modern derivatives and their pricing methods are presented; from basic discounted cash flow methods to Black-Scholes, binomial trees, differential equations, finite difference schemes, Monte Carlo methods, Martingales and Numeraires, terms structure models, etc. The fifth edition of this classic finance book has been comprehensively reviewed. New chapters/content cover multicurve bootstrapping, the valuation and hedging of credit default risk that is inherently incorporated in every derivative—both of which are direct and permanent consequences of the financial crises with a large impact on our understanding of modern derivative valuation. The book will be accompanied by downloadable Excel spread sheets, which demonstrate how the theoretical concepts explained in the book can be turned into valuable algorithms and applications and will serve as an excellent starting point for the reader’s own bespoke solutions for valuation and risk management systems.
The emergence of the Chinese socialist realist novel can best be understood in light of the half-century long formation of the modern concept of literature in China. Globalized in the wake of modern capitalism, literary modernity configures the literary text in a relationship to both modern philosophy and literary theory. This book traces China's unique, complex, and creative articulation of literary modernity beginning with Lu Xun's “The True Story of Ah Q.” Cai Yi's aesthetic theory of the type (dianxing) and the image (xingxiang) is then explored in relation to global currents in literary thought and philosophy, making possible a fundamental rethinking of Chinese socialist realist novels like Yang Mo's Song of Youth and Luo Guangbin and Yan Yiyan's Red Crag.
Superplasticity is a state in which solid crystalline materials, such as some fine-grained metals, are deformed well beyond their usual breaking point. The phenomenon is of importance in processes such as superplastic forming which allows the manufacture of complex, high-quality components in such areas as aerospace and biomedical engineering.Superplasticity and grain boundaries in ultrafine-grained materials discusses a number of problems associated with grain boundaries in metallic polycrystalline materials. The role of grain boundaries in processes such as grain boundary diffusion, relaxation and grain growth is investigated. The authors explore the formation and evolution of the microstructure, texture and ensembles of grain boundaries in materials produced by severe plastic deformation.Written by two leading experts in the field, Superplasticity and grain boundaries in ultrafine-grained materials significantly advances our understanding of this important phenomenon and will be an important reference work for metallurgists and those involved in superplastic forming processes. - Discusses significant problems associated with grain boundaries in polycrystals incorporating structural superplasticity and grain boundary sliding - Assesses the role of grain boundaries in processes such as grain boundary diffusion, relaxation and grain growth - Explores the formation and evolution of the microstructure, texture and ensembles of grain boundaries in materials produced by severe plastic deformation
The first of four planned volumes to cover this large family, with more than 600 species known from Europe. This volume treats 150 species. It includes 14 colour plates and line drawings of male and female genitalia.
The first half of the book is aimed at quantitative research workers in biology, medicine, ecology and genetics. The book as a whole is aimed at graduate students in statistics, biostatistics, and other quantitative disciplines. Ten detailed examples show how the author approaches real-world statistical problems in a principled way that allows for adequate compromise and flexibility. The need to accommodate correlations associated with space, time and other relationships is a recurring theme, so variance-components models feature prominently. Statistical pitfalls are illustrated via examples taken from the recent scientific literature. Chapter 11 sets the scene, not just for the second half of the book, but for the book as a whole. It begins by defining fundamental concepts such as baseline, observational unit, experimental unit, covariates and relationships, randomization, treatment assignment, and the role that these play in model formulation. Compatibility of the model with the randomization scheme is crucial. The effect of treatment is invariably modelled as a group action on probability distributions. Technical matters connected with space-time covariance functions, residual likelihood, likelihood ratios, and transformations are discussed in later chapters.
English translation and appreciation by Peter Chen and Michael TanReviewed by Chan Chiu MingAn original English translation from the Chinese text: Comprises 60 poems (85 verses) and three prose compositionsOpens a window to the heart and mind of a Chinese scholar who lived from the late Qing through the 1950sReflects the life of a pioneer writer of Malayan-Singapore Chinese Literature: his personal tragedies, struggles, disappointments and the joy in his family, friends and his poetryEnglish explanations for many interesting expressions and allusions used in Chinese classical poetryEnables an English language reader to enjoy the rich and colourful heritage of Chinese culture and language A companion edition of the book in Chinese is available ? the original classical text translated into modern Chinese and profusely annotated by Associate Professor Dr Chan Chiu Ming of National Institute of Education, Singapore.
Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.
China was turned into a nation of opium addicts by the pernicious forces of imperialist trade. This study systematically questions this assertion on the basis of abundant archives from China, Europe and the US, showing that opium had few harmful effects on either health or longevity.
Since Christianity was re-introduced to China in the early nineteenth century, Chinese Christianity has undergone a holistic “transfiguration” which both truthfully restores ante-Nicene Christianity and successfully adapts to the cultural contexts of Chinese and other societies. The theoretical and theological diversity of this book is consistent with that of traditional Chinese religious writings as well as that of the ante-Nicene fathers but may be deemed un-theoretical, un-academic, or un-theological by those theologians who received Western theological training, as that tends to be too hegemonic, emotionless, and archaic in the eyes of lay believers.
The idea of heavenly ascent, while popularized in Jewish mysticism, is neither a unique nor recent one. Expertly tracing its origins back to the ancient Middle East, Levenda unearths ascent literature in Africa, India, and China, discerns a common connection in the heavens themselves, and determines that this connection has been sorely neglected in contemporary scholarship. Because scholars treat the "heavens" as metaphorical, it is necessary to recreate the physical context of the culture under discussion in order to better understand it. For the benefit of the reader, Levenda offers two useful concepts for his investigative journey: a "map," whereby he means the cosmological system to better understand the mystical technologies of each culture investigated, and a "vehicle," the method by which the individual equipped with special knowledge is able to navigate the culture's particular cosmology. With these two tools, Levenda travels from the worlds of ancient Egypt and Babylon to the Hebrew Bible, to Jewish and Christian kabbalists, to Daoists in ancient China, to Hindu Tantra and Haitian Vodoun, and, finally, to nineteenth and twentieth century European occult societies.
Author Peter Stimes’s analysis of the investment process has long been inspired by some of the best minds in the world of finance, yet some of the ways in which he approaches this discipline are truly unique. In Equity Valuation, Risk, and Investment, Stimes shares his extensive expertise with you and reveals how practitioners can integrate and apply both the theory and quantitative analysis found in finance to the day-to-day decisions they must make with regard to important investment issues.
This ground-breaking book explores the moral dimensions of sexual imagery in contemporary, general-release Asian films. It examines debates that arise over aesthetic styles and the cultural and traditional influences that determine the content and impact of these films. The social and regulatory environments for filmmakers across Asia reflect distinct national and cultural differences. In just the past decade, for instance, Indian cinema has rapidly moved from representations of coy and submissive female protagonists to highly eroticized leading ladies unafraid of flaunting their sexuality. On the other hand, the cinema emerging from the Chinese mainland has been much more circumspect in its representations of overt sexuality, at times in conflict with other Chinese cinemas from Hong Kong and Taiwan. This use of sexual imagery or morally questionable film content raises on-going debates into censorship and the use of state or industry controls to protect certain sectors of society from exposure to particular narratives or images. Film, like all forms of art, fulfils a number of aesthetic functions for local, regional and international audiences. As distribution and technological advances make Asian films more readily available across the globe, an understanding of the different aesthetics at play will enable readers of this book to recognize key cultural motifs in representations of onscreen sexuality and the surrounding controversies found in cinematic texts from Asia.
This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts. The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications. The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory.
From 1885–1924, China underwent a period of acute political struggle and cultural change, brought on by a radical change in thought: after over 2,000 years of monarchical rule, the Chinese people stopped believing in the emperor. These forty years saw the collapse of Confucian political orthodoxy and the struggle among competing definitions of modern citizenship and the state. What made it possible to suddenly imagine a world without the emperor? After Empire traces the formation of the modern Chinese idea of the state through the radical reform programs of the late Qing (1885–1911), the Revolution of 1911, and the first years of the Republic through the final expulsion of the last emperor of the Qing from the Forbidden City in 1924. It contributes to longstanding debates on modern Chinese nationalism by highlighting the evolving ideas of major political thinkers and the views reflected in the general political culture. Zarrow uses a wide range of sources to show how "statism" became a hegemonic discourse that continues to shape China today. Essential to this process were the notions of citizenship and sovereignty, which were consciously adopted and modified from Western discourses on legal theory and international state practices on the basis of Chinese needs and understandings. This text provides fresh interpretations and keen insights into China's pivotal transition from dynasty to republic.
The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
As the first intellectual history of Song, Yuan, and Ming China written from a local perspective, Localizing Learning shows how literati learning in Wuzhou came to encompass examination studies, Neo-Confucian moral philosophy, historical and Classical scholarship, encyclopedic learnedness, and literary writing, and traces how debates over the relative value of moral cultivation, cultural accomplishment, and political service unfolded locally. The book is set in one locality, Wuzhou (later Jinhua), a prefecture in China’s Zhejiang province, from the twelfth through the sixteenth century. Its main actors are literati of the Song, Yuan, and Ming, who created a local tradition of learning as a means of cementing their common identity and their claim to moral, political, and cultural leadership. Close readings of philosophical and literary texts with quantitative analysis of social and kinship networks consider why and how the local literati enterprise was built. By treating learning as the subject, it broadens our perspective, going beyond a history of ideas to investigate the social practices and networks of kinship and collegiality with which literati defined themselves in local, regional, and national contexts.
Examining the physical basis of the structure of macromolecules—proteins, nucleic acids, and their complexes—using calorimetric techniques Many scientists working in biology are unfamiliar with the basics of thermodynamics and its role in determining molecular structures. Yet measuring the heat of structural change a molecule undergoes under various conditions yields information on the energies involved and, thus, on the physical bases of the considered structures. Microcalorimetry of Macromolecules offers protein scientists unique access to this important information. Divided into thirteen chapters, the book introduces readers to the basics of thermodynamics as it applies to calorimetry, the evolution of the calorimetric technique, as well as how calorimetric techniques are used in the thermodynamic studies of macromolecules, detailing instruments for measuring the heat effects of various processes. Also provided is general information on the structure of biological macromolecules, proteins, and nucleic acids, focusing on the key thermodynamic problems relating to their structure. The book covers: The use of supersensitive calorimetric instruments, including micro and nano-calorimeters for measuring the heat of isothermal reactions (Isothermal Titration Nano-Calorimeter), the heat capacities over a broad temperature range (Scanning Nano-Calorimeter), and pressure effects (Pressure Perturbation Nano-Calorimeter) Two of the simplest but key structural elements: the α and polyproline helices and their complexes, the α-helical coiled-coil, and the pyroline coiled-coils Complicated macromolecular formations, including small globular proteins, multidomain proteins and their complexes, and nucleic acids Numerous examples of measuring the ground state of protein energetics, as well as changes seen when proteins interact The book also reveals how intertwined structure and thermodynamics are in terms of a macromolecule's organization, mechanism of formation, the stabilization of its three-dimensional structure, and ultimately, its function. The first book to describe microcalorimetric technique in detail, enough for graduate students and research scientists to successfully plumb the structural mysteries of proteins and the double helix, Microcalorimetry of Macromolecules is an essential introduction to using a microcalorimeter in biological studies.
This book examines the introduction and ongoing development of public medical care insurance in contemporary China. Based on extensive field investigations, residents’ surveys and analyses by local policy experts and practitioners it provides a comparative analysis of the marketization of public policy in China in contrast to those in other countries, such as the United Kingdom and Germany. The book highlights system-specific issues of the centrally planned economy (CPE) during economic reform, such as alienation of entitlements from funding and historically rooted obligations in the realm of public policy, and as such fills the gap in research on the Chinese government’s public financial management. Public Policy and Health Care in China will appeal to students, academics and researchers interested in public policy and health care in China, as well as Chinese society and economics more broadly.
This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved.
This volume attempts to review the historical development of Chinese Christianity from a “global-local” or “glocalization” perspective. It includes chapters on the Boxer Movement, Chinese indigenous movements, and Christian higher education and also contains seven biographical chapters. The author expounds upon the interplay of “universal” and “particular” aspects as well as the global and local forces which shaped the characteristics of Chinese Christianity in the late nineteenth and early twentieth century. This work focused on China could have wider implications for modern scholarship, both in the fields of comparative history of education and modern Chinese church history, for those scholars who are exploring the dialogical interplay between global and local Christianities.
An unexpected letter from Tokyo impels a Canadian accountant to break his resolution never to revisit the past. Hunting out an old journal, he relives his adventures on the far side of the Pacific, when he sought redemption for his sins among primitive but contented islanders. There he aided Japanese veterans in their search for a World War 2 flying boat, put an elderly English spinster in touch with her half-caste nephew and helped a tribe to preserve its age-old customs. Only now, ten years later, does he learn that, in the process, he may have forfeited the greatest opportunity of his life. In Landfall, his fourth novel, Peter Moss explores the myriad miscommunications, misunderstandings and mysteries of the human heart.
In the global world of the twenty-first century, martial arts are practised for self-defense and sporting purposes only. However, for thousands of years, they were a central feature of military practice in China and essential for the smooth functioning of society. This book, which opens with an intriguing account of the very first female martial artist, charts the history of combat and fighting techniques in China from the Bronze Age to the present. This broad panorama affords fascinating glimpses into the transformation of martial skills, techniques and weaponry against the background of Chinese history, the rise and fall of empires, their governments and their armies. Quotations from literature and poetry, and the stories of individual warriors, infuse the narrative, offering personal reflections on prowess in the battlefield and techniques of engagement. This is an engaging and readable introduction to the authentic history of Chinese martial arts.
This work includes 140 papers on pure and applied research of physics and chemistry of hydrothermal systems. It includes papers on metastable states, nucleation, super-cooled water and high temperature aqueous solutions.
This collection of 97 Cantonese love songs aims to give a wider audience the opportunity of reading these songs in English. The author investigates the language and social background of the songs and provides cross-references to Chinese and Western literature.The Chinese text of the poems is also included.
The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.
Now in four convenient volumes, Field’s Virology remains the most authoritative reference in this fast-changing field, providing definitive coverage of virology, including virus biology as well as replication and medical aspects of specific virus families. This volume of Field’s Virology: RNA Viruses, Seventh Edition covers the latest information on RNA viruses, how they cause disease, how they can cause epidemics and pandemics, new therapeutics and vaccine approaches, as provided in new or extensively revised chapters that reflect these advances in this dynamic field. Bundled with the eBook, which will be updated regularly as new information about each virus is available, this text serves as the authoritative, up-to-date reference book for virologists, infectious disease specialists, microbiologists, and physicians, as well as medical students pursuing a career in infectious diseases.
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