Black holes present one of the most fascinating predictions of Einstein's general relativity, with strong evidence of their existence through observations of many means. The book provides a wide background to the current research on all mathematical aspects of the geometry of black hole spacetimes.
An increasing reliance on the Internet and mobile communication has deprived us of our usual means of assessing another party’s trustworthiness. This is increasingly forcing us to rely on control. Yet the notion of trust and trustworthiness is essential to the continued development of a technology-enabled society. Trust, Complexity and Control offers readers a single, consistent explanation of how the sociological concept of ‘trust’ can be applied to a broad spectrum of technology-related areas; convergent communication, automated agents, digital security, semantic web, artificial intelligence, e-commerce, e-government, privacy etc. It presents a model of confidence in which trust and control are driven and limited by complexity in one explanatory framework and demonstrates how that framework can be applied to different research and application areas. Starting with the individual’s assessment of trust, the book shows the reader how application of the framework can clarify misunderstandings and offer solutions to complex problems. The uniqueness of Trust, Complexity and Control is its interdisciplinary treatment of a variety of diverse areas using a single framework. Sections featured include: Trust and distrust in the digital world. The impact of convergent communication and networks on trust. Trust, economy and commerce. Trust-enhancing technologies. Trust, Complexity and Control is an invaluable source of reference for both researchers and practitioners within the Trust community. It will also be of benefit to students and lecturers in the fields of information technology, social sciences and computer engineering.
This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe. It introduces some of the most striking aspects of Einstein's theory of gravitation: black holes, gravitational waves, stellar models, and cosmology. It contains a self-contained introduction to tensor calculus and Riemannian geometry, using in parallel the language of modern differential geometry and the coordinate notation, more familiar to physicists. The author has strived to achieve mathematical rigour, with all notions given careful mathematical meaning, while trying to maintain the formalism to the minimum fit-for-purpose. Familiarity with special relativity is assumed. The overall aim is to convey some of the main physical and geometrical properties of Einstein's theory of gravitation, providing a solid entry point to further studies of the mathematics and physics of Einstein equations.
Contents:Nonlinear Problems in 1 + 1 and Their LinearizationClassical Field Theory ModelsHamiltonian Formulation, Action-Angle Variables, Solitons, Classical Lattice Models and Lattice Approximants of Classical FieldsQuantization on a Lattice: Relationship Classical-QuantumQuantization on a Lattice: Simple Bose ModelsSpin 1/2 Lattice Systems Related to Nonlinear Bose Problems: Lattice FermionsQuantization in Continuum: Joint Bose-Fermi Spectral Problems in 1 + 1Quantum Meaning of Classical Field Theory for Fermi SystemsOn Infinite Constituent “Elementary” Systems: Canonical (Constituent) Quantization of Soliton FieldsTowards 1 + 3: Problems and Prospects Readership: Mathematical physicists and physicists. Keywords:Nonlinear Fields;Integrability;Solvable Models;Solitons;Continuum and Lattice Models;Quantization;Fermi Fields And Their Classical Counterparts;Relationship Classical-Quantum;Boson-Fermion Reciprocity (Bosonization)
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
This book presents original problems from graduate courses in pure and applied mathematics and even small research topics, significant theorems and information on recent results. It is helpful for specialists working in differential equations.
When in 1775 the scholar Wang Xihou compiled a dictionary called Ziguan , he wrote, for illustrative purposes, the personal names of Confucius and the three emperors Kangxi, Yongzheng and Qianlong in the introduction. In oversight, he recorded their complete names. This accidental writing of a few names was condemned by Emperor Qianlong as an unprecedented crime, rebellion and high treason. Wang Xihou was executed, his property confiscated and his books were burnt. His family was arrested and his sons and grandsons were killed or sent as slaves to Heilongjiang. It is surprising what an enormous impact the tabooing of names (bihui ) had on Chinese culture. The names of sovereigns, ancestors, officials, teachers, and even friends were all considered taboo, in other words it was prohibited to pronounce them or to record them in writing. In numerous cases characters identical or similar in writing or pronunciation were often avoided as well. The tabooing of names was observed in the family and on the street, in the office and in the emperor's palace. The practice of bihui had serious consequences for the daily lives of the Chinese and for Chinese historiography. People even avoided certain places and things, and refused to accept offices. They were punished and sometimes even killed in connection with the tabooing of names. The bihui custom existed as an important element of Chinese culture and was perceived as significant by Chinese and foreigners alike. It was crucial for implementing social values and demonstrating the political hierarchy. The present work A Good Son Is Sad if He Hears the Name of His Father is a systematic study of Chinese name-tabooing customs, which until now have been relatively little explored in Western-language Sinological studies. It attempts to provide a long-term perspective on the changing dynamics of tabooing and elucidates various aspects related to the fascinating topic of tabooing of names.
The book contains a rigorous exposition of calculus of a single real variable. It covers the standard topics of an introductory analysis course, namely, functions, continuity, differentiability, sequences and series of numbers, sequences and series of functions, and integration. A direct treatment of the Lebesgue integral, based solely on the concept of absolutely convergent series, is presented, which is a unique feature of a textbook at this level. The standard material is complemented by topics usually not found in comparable textbooks, for example, elementary functions are rigorously defined and their properties are carefully derived and an introduction to Fourier series is presented as an example of application of the Lebesgue integral.The text is for a post-calculus course for students majoring in mathematics or mathematics education. It will provide students with a solid background for further studies in analysis, deepen their understanding of calculus, and provide sound training in rigorous mathematical proof.
This book offers an integrated interpretative analysis of the major thematic aspects of the English fourteenth-century romance Sir Gawain and the Green Knight. The chief aim of author Piotr Sadowski is to look at the contents of the narrative in their entirety and to take full advantage of the poem's exceptional and widely praised harmony of structure and design. Within that design, Sadowski focuses on the poem's presentation of the main protagonist and his adventures, seen first of all as a generalized metaphor of the human life understood as a spiritual quest, and, in a more historical sense, as an expression and critique of certain ideals, values, and anxieties that characterized the late medieval institutions of the court, chivalry, and the Church. Sadowski built the interpretive framework of Sir Gawain from an eclectic theoretical base that he believes is most valuable and useful in approaching medieval literature. The main focus of the study remains the literary text itself, created by an author who communicates his view of the world through the poem.
Ājīvikism was once ranked one of the most important religions in India between the 4th and 2nd centuries BCE, after Buddhism, ‘Brahmanism’ and before Jainism, but is now a forgotten Indian religion. However, Jainism has remained an integral part of the religious landscape of South Asia, despite the common beginnings shared with Ājīvikism. By rediscovering, reconstructing, and examining the Ājīvikism doctrine, its art, origins and development, this book provides new insight into Ājīvikism, and discusses how this information enables us to better understand its impact on Jainism and its role in the development of Indian religion and philosophy. This book explains how, why and when Jainism developed its strikingly unique logic and epistemology and what historical and doctrinal factors prompted the ideas which later led to the formulation of the doctrine of multiplexity of reality (anekānta-vāda). It also provides answers to difficult passages of Buddhist Sāmañña-phala-sutta that baffled both Buddhist commentators and modern researchers. Offering clearer perspectives on the origins of Jainism the book will be an invaluable contribution to Jaina Studies, Asian Religion and Religious History.
On any night in early June, if you stand on the right beaches of America’s East Coast, you can travel back in time all the way to the Jurassic. For as you watch, thousands of horseshoe crabs will emerge from the foam and scuttle up the beach to their spawning grounds, as they’ve done, nearly unchanged, for more than 440 million years. Horseshoe crabs are far from the only contemporary manifestation of Earth’s distant past, and in Relics, world-renowned zoologist and photographer Piotr Naskrecki leads readers on an unbelievable journey through those lingering traces of a lost world. With camera in hand, he travels the globe to create a words-and-pictures portrait of our planet like no other, a time-lapse tour that renders Earth’s colossal age comprehensible, visible in creatures and habitats that have persisted, nearly untouched, for hundreds of millions of years. Naskrecki begins by defining the concept of a relic—a creature or habitat that, while acted upon by evolution, remains remarkably similar to its earliest manifestations in the fossil record. Then he pulls back the Cambrian curtain to reveal relic after eye-popping relic: katydids, ancient reptiles, horsetail ferns, majestic magnolias, and more, all depicted through stunning photographs and first-person accounts of Naskrecki’s time studying them and watching their interactions in their natural habitats. Then he turns to the habitats themselves, traveling to such remote locations as the Atewa Plateau of Africa, the highlands of Papua New Guinea, and the lush forests of the Guyana Shield of South America—a group of relatively untrammeled ecosystems that are the current end point of staggeringly long, uninterrupted histories that have made them our best entryway to understanding what the prehuman world looked, felt, sounded, and even smelled like. The stories and images of Earth’s past assembled in Relics are beautiful, breathtaking, and unmooring, plunging the reader into the hitherto incomprehensible reaches of deep time. We emerge changed, astonished by the unbroken skein of life on Earth and attentive to the hidden heritage of our planet’s past that surrounds us.
Accompanying DVD-ROM contains the electronic proceedings of the summer school on mathematical general relativity and global properties of solutions of Einstein's equations held at Cargèse, Corsica, France, July 20-Aug. 10, 2002.
Rawicz extended the frontier of artistic expression, by giving the unbearable a bearable frame."--from the introduction With the publication of this paperback edition of Piotr Rawicz's prizewinning Blood from the Sky, a classic of Holocaust literature emerges from many years out of print. A novel of richness and deep originality, it tells the story of Boris D., a Jewish resident of Lvov who poses as a non-Jew to evade the Nazis. Boris survives imprisonment in a death camp and moves to Paris following the war. Yet his account of his experiences is no celebration of survival; it is rather a commemoration of the horrifying deaths of countless others. Rawicz in this work has found a possible response to the events of the Holocaust: an unforgettable cry of lyric pain that transforms the horrors of history and memory into art.
In Poland in the 1940s and '50s, a new kind of Catholic intended to remake European social and political life--not with guns, but French philosophy This collective intellectual biography examines generations of deeply religious thinkers whose faith drove them into public life, including Karol Wojtyła, future Pope John Paul II, and Tadeusz Mazowiecki, the future prime minister who would dismantle Poland's Communist regime. Seeking to change the way we understand the Catholic Church, World War II, the Cold War, and communism, this study centers on the idea of "revolution." It examines two crucial countries, France and Poland, while challenging conventional wisdom among historians and introducing innovations in periodization, geography, and methodology. Why has much of Eastern Europe gone back down the road of exclusionary nationalism and religious prejudice since the end of the Cold War? Piotr H. Kosicki helps to understand the crises of contemporary Europe by examining the intellectual world of Roman Catholicism in Poland and France between the Church's declaration of war on socialism in 1891 and the demise of Stalinism in 1956.
This book covers a diverse range of topics in Mathematical Physics, linear and nonlinear PDEs. Though the text reflects the classical theory, the main emphasis is on introducing readers to the latest developments based on the notions of weak solutions and Sobolev spaces. In numerous problems, the student is asked to prove a given statement, e.g. to show the existence of a solution to a certain PDE. Usually there is no closed-formula answer available, which is why there is no answer section, although helpful hints are often provided. This textbook offers a valuable asset for students and educators alike. As it adopts a perspective on PDEs that is neither too theoretical nor too practical, it represents the perfect companion to a broad spectrum of courses.
The last section is an interesting collection of geometry problems and their solutions from various International Mathematics Olympics … There are a sufficient number of exercises at the end of each chapter, and the answers to half of them are included at the end of the book, with an occasional full solution here and there. The book prepares the reader for a traditional introductory textbook in linear algebra.'CHOICEThe book makes a first course in linear algebra more accessible to the majority of students and it assumes no prior knowledge of the subject. It provides a careful presentation of particular cases of all core topics. Students will find that the explanations are clear and detailed in manner. It is considered as a bridge over the obstacles in linear algebra and can be used with or without the help of an instructor.While many linear algebra texts neglect geometry, this book includes numerous geometrical applications. For example, the book presents classical analytic geometry using concepts and methods from linear algebra, discusses rotations from a geometric viewpoint, gives a rigorous interpretation of the right-hand rule for the cross product using rotations and applies linear algebra to solve some nontrivial plane geometry problems.Many students studying mathematics, physics, engineering and economics find learning introductory linear algebra difficult as it has high elements of abstraction that are not easy to grasp. This book will come in handy to facilitate the understanding of linear algebra whereby it gives a comprehensive, concrete treatment of linear algebra in R² and R³. This method has been shown to improve, sometimes dramatically, a student's view of the subject.
This book represents the current (1985) state of knowledge about Zariski surfaces and related topics in differential equations in characteristic p > 0. It is aimed at research mathematicians and graduate and advanced undergraduate students of mathematics and computer science.
The first part of the book gives a general introduction to key concepts in algebraic statistics, focusing on methods that are helpful in the study of models with hidden variables. The author uses tensor geometry as a natural language to deal with multivariate probability distributions, develops new combinatorial tools to study models with hidden data, and describes the semialgebraic structure of statistical models. The second part illustrates important examples of tree models with hidden variables. The book discusses the underlying models and related combinatorial concepts of phylogenetic trees as well as the local and global geometry of latent tree models. It also extends previous results to Gaussian latent tree models. This book shows you how both combinatorics and algebraic geometry enable a better understanding of latent tree models. It contains many results on the geometry of the models, including a detailed analysis of identifiability and the defining polynomial constraints
Critical Edition and English Translation of Logical-epistemological Treatises: Nyāyâvatāra, Nyāyâvatāra-vivṛti and Nyāyâvatâra-ṭippana with Introduction and Notes
Critical Edition and English Translation of Logical-epistemological Treatises: Nyāyâvatāra, Nyāyâvatāra-vivṛti and Nyāyâvatâra-ṭippana with Introduction and Notes
The Nyayavatara, erroneously ascribed by tradition to Siddhasena Divakara, was either the first or one of the first serious Jaina treatises on epistemology. Its author enters polemics with other - mostly Buddhist - epistemological schools and endeavours to establish a Jaina epistemological tradition of its own. Despite its importance, the work is rather secondary in the sense that it relies, for the most part, on the Buddhist logical legacy. The first extant commentary is the Nyayavatara-vivrti of Siddharsigani. Its significance is often underestimated, for its author was responsible for the subsequent development of Jaina epistemological thought to a much larger degree than it has so far been recognised. He refers to major philosophical schools of his times, e.g. to Sautrantika, Yogacara, Sunya-vada, Samkhya, Mimamsa, Nyaya, Vaisesika, Advaita-vedanta, the materialists, etc. The gloss (Tippana) of Devabhadra is in addition a useful source of quotations. (Franz Steiner 2001)
This book systematically discusses the contribution of the Belt and Road Initiative (BRI) to China’s transition from an emerging to an advanced economic and financial system after more than five years. From a historical perspective, it explains to what extent the BRI plan is effective enough to help China bounce back from its economic slowdown and the financial implications in a policy trilemma context. Further, it investigates both the rationale of the BRI and its pitfalls, focusing on the various options for financing the project based on the Mundell & Fleming model. The book also analyses the impact of the BRI as well as possible policy options to deal with China’s policy trilemma in a structurally more balanced “new normal” economic growth model. Lastly, it reviews the financial stability issues concerning liberalization policies in China.
The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis
Understanding the current state and dynamics of any forest is extremely difficult - if not impossible - without recognizing its history. Białowieża Primeval Forest (BPF), located on the border between Poland and Belarus, is one of the best preserved European lowland forests and a subject of myriads of works focusing on countless aspects of its biology, ecology, management. BPF was protected for centuries (15th-18th century) as a game reserve of Polish kings and Lithuanian grand dukes. Being, at that time, a part of the Grand Duchy of Lithuania, BPF was subject to long-lasting traditional, multi-functional utilisation characteristic for this part of Europe, including haymaking on forest meadows, traditional bee-keeping and fishing in rivers flowing through forest. This traditional model of management came to an abrupt end due to political change in 1795, when Poland and Grand Duchy of Lithuania ceased to exist in effect of partitioning by neighbouring countries, and the territory of BPF was taken over by the Russian Empire. The new Russian administration, influenced by the German trends in forestry, attempted at introducing the new, science-based forestry model in the BPF throughout the 19th century. The entire 19th century in the history of BPF is a story of struggle between new trends and concepts brought and implemented by new rulers of the land, and the traditional perception of the forest and forest uses, culturally rooted in this area and originating from mediaeval (or older) practices. The book will show the historical background and the outcome of this struggle: the forest’s history in the long 19th century focusing on tracking all cultural imprints, both material (artificial landscapes, introduced alien species, human-induced processes) and immaterial (traditional knowledge of forest and use of forest resources, the political and cultural significance of the forest) that shaped the forest’s current state and picture. Our book will deliver a picture of a crucial moment in forest history, relevant not only to the Central Europe, but to the continent in general. Moment of transition between a royal hunting ground, traditional type of use widespread throughout Europe, to a modern, managed forest. Looking at main obstacles in the management shift, the essential difference in perceptions of the forest and goods it provides in both modes of management, and the implications of the management change for the state of BPF in the long 19th century could help in better understanding the changes that European forests underwent in general.
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