Complex Analysis for Math

The recent financial crisis has heightened the need for appropriate methodologies for managing and monitoring complex risks in financial markets. The measurement, management, and regulation of risks in portfolios composed of credits, credit derivatives, or life insurance contracts is difficult because of the nonlinearities of risk models, dependencies between individual risks, and the several thousands of contracts in large portfolios. The granularity principle was introduced in the Basel regulations for credit risk to solve these difficulties in computing capital reserves. In this book, authors Patrick Gagliardini and Christian Gouriéroux provide the first comprehensive overview of the granularity theory and illustrate its usefulness for a variety of problems related to risk analysis, statistical estimation, and derivative pricing in finance and insurance. They show how the granularity principle leads to analytical formulas for risk analysis that are simple to implement and accurate e

In the structural design of airframes and buildings, probability-based procedures are used to mitigate the risk of failure as well as produce cost-effective designs. This book introduces the subject of probabilistic analysis to structural and fire protection engineers and can also be used as a reference to guide those applying this technology. In addition to providing an understanding of how fire affects structures and how to optimize the performance of structural framing systems, Probability-Based Structural Fire Load provides guidance for design professionals and is a resource for educators. The goal of this book is to bridge the gap between prescriptive and probability-based performance design methods and to simplify very complex and comprehensive computer analyses to the point that stochastic structural fire loads have a simple, approximate analytical expression that can be used in structural analysis and design on a day-to-day basis. Numerous practical examples are presented in st

Dependability metrics are omnipresent in every engineering field, from simple ones through to more complex measures combining performance and dependability aspects of systems. This book presents the mathematical basis of the analysis of these metrics in the most used framework, Markov models, describing both basic results and specialised techniques. The authors first present both discrete and continuous time Markov chains before focusing on dependability measures, which necessitate the study of Markov chains on a subset of states representing different user satisfaction levels for the modelled system. Topics covered include Markovian state lumping, analysis of sojourns on subset of states of Markov chains, analysis of most dependability metrics, fundamentals of performability analysis, and bounding and simulation techniques designed to evaluate dependability measures. The book is of interest to graduate students and researchers in all areas of engineering where the concepts of lifetime

This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive biblio

Simulation of ODE/PDE Models with MATLABR, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is

The law and policy applicable to the not-for-profit sector is of growing importance around the world. In this book, legal experts address fundamental questions about not-for-profit law from a range of theoretical and comparative perspectives. The essays provide scholarly analysis of not-for-profit law, organised around four themes: (1) Politics, in the broader sense of living as a community, and the narrower sense of political power; (2) Charity, how it is defined and changes in its meaning over time; (3) Taxation, including the rationale for government support of the sector through the tax system; (4) Regulation, which is of increasing significance as governments establish increasingly complex forms of regulation of not-for-profit activity. The fundamental aim of the book is to deepen our understanding of not-for-profit law and of the rationales and modes of government support for the not-for-profit sector.

The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical electrodynamics to current approaches to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics research, are presented and defended in an accessible format that avoids complex mathematics. Blending history, philosophy, and theoretical physics, this refreshing outlook on the nature of spacetime sheds light on one of the most thought-provoking topics in modern p

Does the WTO leave appropriate policy space to its Members to pursue legitimate objectives, such as the economic development of developing countries, the conversion to a greener economy, or recovery in times of a global economic downturn? This legal and normative analysis of the WTO rules on subsidies and countervailing measures sheds light on why governments resort to subsidization and, by tracing the historical origins of the SCM Agreement and the Agreement on Agriculture, on why they have been willing to gradually confine their policy space. This sets the stage for a systematic and comprehensive legal analysis of both agreements, which integrates the vast amount of case law and proposals tabled in the Doha round. A separate case study explores the complex rules on export credit support, and the book closes with an in-depth normative assessment of these WTO rules on subsidies and countervailing measures.

Nietzsche's Ecce Homo was published posthumously in 1908, eight years after his death, and has been variously described ever since as useless, mad, or merely inscrutable. Against this backdrop, Nicholas D. More provides the first complete and compelling analysis of the work, and argues that this so-called autobiography is instead a satire. This form enables Nietzsche to belittle bad philosophy by comic means, attempt reconciliation with his painful past, review and unify his disparate works, insulate himself with humor from the danger of 'looking into abysses', and establish wisdom as a special kind of 'good taste'. After showing how to read this much-maligned book, More argues that Ecce Homo presents the best example of Nietzsche making sense of his own intellectual life, and that its unique and complex parody of traditional philosophy makes a powerful case for reading Nietzsche as a philosophical satirist across his corpus.

Oil, Democracy, and Development in Africa presents an optimistic analysis of the continent's oil-producing states. With attention to the complex histories, the interactions of key industry actors and policy makers, and the goals of diverse groups in society, this contribution fills a gap in the literature on resource-abundant countries. John R. Heilbrunn presents a positive assessment of circumstances in contemporary African oil exporters. The book demonstrates that even those leaders who are among the least accountable use oil revenues to improve their citizens' living standards, if only a little bit. As a consequence, African oil producers are growing economically and their people are living under increasingly democratic polities. Heilbrunn thus calls for a long-overdue reassessment of the impact of hydrocarbons on developing economies.

Every year, there are over 1.6 million violent deaths worldwide, making violence one of the leading public health issues of our time. And with the 20th century just behind us, it's hard to forget that 191 million people lost their lives directly or indirectly through conflict. This collection of engaging case studies on violence and violent deaths reveals how violence is reconstructed from skeletal and contextual information. By sharing the complex methodologies for gleaning scientific data from human remains and the context they are found in, and complementary perspectives for examining violence from both past and contemporary societies, bioarchaeology and forensic anthropology prove to be fundamentally inseparable. This book provides a model for training forensic anthropologists and bioarchaeologists, not just in the fundamentals of excavation and skeletal analysis, but in all subfields of anthropology, to broaden their theoretical and practical approach to dealing with everyday viol

In South America indigenous languages are extremely diverse. There are over one hundred language families in this region alone. Contributors from around the world explore the history and structure of these languages, combining insights from archaeology and genetics with innovative linguistic analysis. The book aims to uncover regional patterns and potential deeper genealogical relations between the languages. Based on a large-scale database of features from sixty languages, the book analyses major language families such as Tupian and Arawakan, as well as the Quechua/Aymara complex in the Andes, the Isthmo-Colombian region and the Andean foothills. It explores the effects of historical change in different grammatical systems and fills gaps in the World Atlas of Language Structures (WALS) database, where South American languages are underrepresented. An important resource for students and researchers interested in linguistics, anthropology and language evolution.

Combining an analysis of literature and art, this book contends that the 'domesticated landscape' is key to understanding women's complex negotiation of private and public life in a period of revolution and transition. As more women became engaged in horticultural and botanical pursuits, the meaning of gardens - recognized here both as sites of pleasure and labor, and as conceptual and symbolic spaces - became more complex. Women writers and artists often used gardens to educate their readers, to enter into political and cultural debates, and to signal moments of intellectual and spiritual insight. Gardens functioned as a protected vantage point for women, providing them with a new language and authority to negotiate between domestic space and the larger world. Although this more expansive form of domesticity still highlighted the virtues associated with the feminized home, it also promised a wider field of action, re-centering domesticity outward.

Plato's dialogues frequently criticize traditional Greek myth, yet Plato also integrates myth with his writing. Daniel S. Werner confronts this paradox through an in-depth analysis of the Phaedrus, Plato's most mythical dialogue. Werner argues that the myths of the Phaedrus serve several complex functions: they bring nonphilosophers into the philosophical life; they offer a starting point for philosophical inquiry; they unify the dialogue as a literary and dramatic whole; they draw attention to the limits of language and the limits of knowledge; and they allow Plato to co-opt cultural authority as a way of defining and legitimating the practice of philosophy. Platonic myth, as a species of traditional tale, is thus both distinct from philosophical dialectic and similar to it. Ultimately, the most powerful effect of Platonic myth is the way in which it leads readers to participate in Plato's dialogues and to engage in a process of self-examination.

Provides a modern mathematical approach to the design of communication networks for graduate students, blending control, optimization, and stochastic network theories. A broad range of performance analysis tools are discussed, including important advanced topics that have been made accessible to students for the first time. Taking a top-down approach to network protocol design, the authors begin with the deterministic model and progress to more sophisticated models. Network algorithms and protocols are tied closely to the theory, illustrating the practical engineering applications of each topic. The background behind the mathematical analyses is given before the formal proofs and is supported by worked examples, enabling students to understand the big picture before going into the detailed theory. End-of-chapter problems cover a range of difficulties, with complex problems broken into several parts, and hints to many problems are provided to guide students. Full solutions are available

"Energy modeling calculations for urban, complex buildings are most effective during the early design phase. And most analysis takes only four to sixteen hours to get results you can use. This softwar

"Energy modeling calculations for urban, complex buildings are most effective during the early design phase. And most analysis takes only four to sixteen hours to get results you can use. This softwar

This book presents the first full-length study of a vast and complex visual tradition produced, revered, preserved, banned and destroyed by the Hasidic movement of Chabad. This rich repository of visual artifacts provides the archaeological data for an analysis of how the movement consolidated its influence during a period of political and economic transformation and survived its immigration to America in the wake of the Holocaust. As one of the most self-documented and media-preserved modern Jewish movements, Chabad's rich material culture, including the hand-held portrait, the 'rebbishe' space, the printer's mark and the public menorah, afford scholars a wider range of interpretive strategies for understanding the movement and the role of the visual experience in religion.

Current theories of leadership, spirituality and ethics are inadequate for the global, rapidly changing and complex environment in which leaders work today. Emerging from this book’s critical analysis

This book describes the detailed processes and techniques essential for the scientific investigation of atrocity crimes. It includes methods for the location, evaluation, excavation, recovery, and recording of mass graves and the analysis of human remains and other evidence in order to establish the identity of victims and the cause and manner of their deaths. This volume establishes protocols and standard operating procedures to guide standards and approaches that can be used for both judicial and humanitarian contexts. The procedures for field and mortuary application are flexible and can meet specific project aims, constraints, and contexts. The phases of activity and detailed methodological approaches set out in this book describe components of a complex scientific process. Chapters examine the evaluation of possible sites, scene of crime management, health and safety, key roles, excavation of graves, forensic sciences, mortuary management, analysis of human remains, and ante-morte

William T. Sha first proposed the novel porous media formulation in an article in Nuclear Engineering and Design in 1980. The novel porous media formulation represented a new, flexible and unified approach to solve real-world engineering problems. It uses the concept of volume porosity, directional surface porosities, distributed resistance and distributed heat source and sink. Most practical engineering problems involve many complex shapes and sizes of solid internal structures whose distributed resistance is impossible to quantify accurately. The concept of directional surface porosities eliminates the sole reliance on empirical estimation of the distributed resistance of complex-shaped structures often involved in the analysis. The directional surface porosities thus greatly improve the resolution and modeling accuracy and facilitate mock-ups of numerical simulation models of real engineering systems. Both the continuum and conventional porous media formulations are subsets of the n

Europe and the Maritime World: A Twentieth-Century History offers a framework for understanding globalization over the past century. Through a detailed analysis of ports, shipping and trading companies whose networks spanned the world, Michael B. Miller shows how a European maritime infrastructure made modern production and consumer societies possible. He argues that the combination of overseas connections and close ties to home ports contributed to globalization. Miller also explains how the ability to manage merchant shipping's complex logistics was central to the outcome of both world wars. He chronicles transformations in hierarchies, culture, identities and port city space, all of which produced a new and different maritime world by the end of the century.

Complexity science is the study of systems with many interdependent components. Such systems - and the self-organization and emergent phenomena they manifest - lie at the heart of many challenges of global importance. This book is a coherent introduction to the mathematical methods used to understand complexity, with plenty of examples and real-world applications. It starts with the crucial concepts of self-organization and emergence, then tackles complexity in dynamical systems using differential equations and chaos theory. Several classes of models of interacting particle systems are studied with techniques from stochastic analysis, followed by a treatment of the statistical mechanics of complex systems. Further topics include numerical analysis of PDEs, and applications of stochastic methods in economics and finance. The book concludes with introductions to space-time phases and selfish routing. The exposition is suitable for researchers, practitioners and students in complexity sci

At the beginning of the twentieth century, Burma was among the most prosperous territories in the East. Yet since gaining independence in 1948, its economy has struggled. Burma's developmental failure has often been attributed to gross mismanagement of the economy by the military who took power in 1962 but in this illuminating book, Ian Brown, one of the leading economic historians of Southeast Asia, provides a fresh examination of the country's economic past, thereby setting that failure in the context of the colonial period. For the first time, a review of Burma's economic experience in the final decades of British rule is integrated with an analysis of its economy since independence, providing a detailed understanding of the complex origins of Burma's economic failure in the second half of the twentieth century. This is a compelling introduction to Burma's political and economic history for students in Southeast Asian history, development studies and political science.

At the beginning of the twentieth century, Burma was among the most prosperous territories in the East. Yet since gaining independence in 1948, its economy has struggled. Burma's developmental failure has often been attributed to gross mismanagement of the economy by the military who took power in 1962 but in this illuminating book, Ian Brown, one of the leading economic historians of Southeast Asia, provides a fresh examination of the country's economic past, thereby setting that failure in the context of the colonial period. For the first time, a review of Burma's economic experience in the final decades of British rule is integrated with an analysis of its economy since independence, providing a detailed understanding of the complex origins of Burma's economic failure in the second half of the twentieth century. This is a compelling introduction to Burma's political and economic history for students in Southeast Asian history, development studies and political science.

David B. Goldstein argues for a new understanding of Renaissance England from the perspective of communal eating. Rather than focus on traditional models of interiority, choice and consumption, Goldstein demonstrates that eating offered a central paradigm for the ethics of community formation. The book examines how sharing food helps build, demarcate and destroy relationships – between eater and eaten, between self and other, and among different groups. Tracing these eating relations from 1547 to 1680 - through Shakespeare, Milton, religious writers and recipe book authors - Goldstein shows that to think about eating was to engage in complex reflections about the body's role in society. In the process, he radically rethinks the communal importance of the Protestant Eucharist. Combining historicist literary analysis with insights from social science and philosophy, the book's arguments reverberate well beyond the Renaissance. Ultimately, Eating and Ethics in Shakespeare's England forces

Christopher Loveluck's study explores the transformation of Northwest Europe (primarily Britain, France and Belgium) from the era of the first post-Roman 'European Union' under the Carolingian Frankish kings to the so-called 'feudal' age, between c.AD 600 and 1150. During these centuries radical changes occurred in the organisation of the rural world. Towns and complex communities of artisans and merchant-traders emerged and networks of contact between northern Europe, the Mediterranean, and the Middle and Far East were redefined, with long-lasting consequences into the present day. Loveluck provides the most comprehensive comparative analysis of the rural and urban archaeological remains in this area for twenty-five years. Supported by evidence from architecture, relics, manuscript illuminations and texts, this book explains how the power and intentions of elites were confronted by the aspirations and actions of the diverse rural peasantry, artisans and merchants, producing both inten

American foreign policy often looks like a trail of man-made debris and disaster. Of course, the explanations for many poorly-made decisions are rather complex. In this brief and cogent analysis, Houg

American foreign policy often looks like a trail of man-made debris and disaster. Of course, the explanations for many poorly-made decisions are rather complex. In this brief and cogent analysis, Houg

Why do we speak the way we do? What are the social factors that influence our choices of expression? This best-selling introduction to the study of language and society encourages students to think about these fundamental questions, asking how and why we select from the vast range of different words, accents, varieties and languages available to us. In this new and updated edition, students are taken step-by-step through the analysis of linguistic expressions, speech varieties and languages in complex settings. Enriched with recent findings from different languages and speech communities around the world, this comprehensive textbook equips students with knowledge of the main concepts and gives them a coherent view of the complex interaction of language and society. • 'Questions for Discussion' help students understand how speakers' choices are conditioned by the society in which they live • New to this edition is a rich repertoire of online resources and further reading, enabling stude

Why do we speak the way we do? What are the social factors that influence our choices of expression? This best-selling introduction to the study of language and society encourages students to think about these fundamental questions, asking how and why we select from the vast range of different words, accents, varieties and languages available to us. In this new and updated edition, students are taken step-by-step through the analysis of linguistic expressions, speech varieties and languages in complex settings. Enriched with recent findings from different languages and speech communities around the world, this comprehensive textbook equips students with knowledge of the main concepts and gives them a coherent view of the complex interaction of language and society. • 'Questions for Discussion' help students understand how speakers' choices are conditioned by the society in which they live • New to this edition is a rich repertoire of online resources and further reading, enabling stude

This book, the first of its kind, examines how the phonology and grammar of the ancient Egyptian language changed over more than three thousand years of its history, from the first appearance of written documents, c.3250 BC, to the Coptic dialects of the second century AD and later. Part One discusses phonology, working backward from the vowels and consonants of Coptic to those that can be deduced for earlier stages of the language. Part Two is devoted to grammar, including both basic components such as nouns and the complex history of the verbal system. The book thus provides both a synchronic description of the five major historical stages of ancient Egyptian and a diachronic analysis of their development and relationship.

This book, the first of its kind, examines how the phonology and grammar of the ancient Egyptian language changed over more than three thousand years of its history, from the first appearance of written documents, c.3250 BC, to the Coptic dialects of the second century AD and later. Part One discusses phonology, working backward from the vowels and consonants of Coptic to those that can be deduced for earlier stages of the language. Part Two is devoted to grammar, including both basic components such as nouns and the complex history of the verbal system. The book thus provides both a synchronic description of the five major historical stages of ancient Egyptian and a diachronic analysis of their development and relationship.

Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a s

Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a s

A concise introduction to Feynman diagram techniques, this book shows how they can be applied to the analysis of complex many-particle systems, and offers a review of the essential elements of quantum mechanics, solid state physics and statistical mechanics. Alongside a detailed account of the method of second quantization, the book covers topics such as Green's and correlation functions, diagrammatic techniques and superconductivity, and contains several case studies. Some background knowledge in quantum mechanics, solid state physics and mathematical methods of physics is assumed. Detailed derivations of formulas and in-depth examples and chapter exercises from various areas of condensed matter physics make this a valuable resource for both researchers and advanced undergraduate students in condensed matter theory, many-body physics and electrical engineering. Solutions to exercises are available online.

Based on course notes from over twenty years of teaching engineering and physical sciences at Michigan Technological University, Tomas Co's engineering mathematics textbook is rich with examples, applications and exercises. Professor Co uses analytical approaches to solve smaller problems to provide mathematical insight and understanding, and numerical methods for large and complex problems. The book emphasises applying matrices with strong attention to matrix structure and computational issues such as sparsity and efficiency. Chapters on vector calculus and integral theorems are used to build coordinate-free physical models with special emphasis on orthogonal co-ordinates. Chapters on ODEs and PDEs cover both analytical and numerical approaches. Topics on analytical solutions include similarity transform methods, direct formulas for series solutions, bifurcation analysis, Lagrange–Charpit formulas, shocks/rarefaction and others. Topics on numerical methods include stability analysis,

Demonstrating not only how to write for orchestra but also how to understand and enjoy a score, The Cambridge Guide to Orchestration is a theoretical and practical guide to instrumentation and orchestration for scholars, professionals and enthusiasts. With detailed information on all the instruments of the orchestra, both past and present, it combines discussion of both traditional and modern playing techniques to give the most complete overview of the subject. It contains fifty reduced scores to be re-orchestrated and a wide range of exercises, which clarify complex subjects such as multiple stops on stringed instruments, harmonics and trombone glissandi. Systematic analysis reveals the orchestration techniques used in original scores, including seven twentieth-century compositions. This Guide also includes tables and lists for quick reference, providing the ranges of commonly used instruments and the musical names and terminology used in English, German, Italian and French.

Excel is the world’s most popular spreadsheet program and the de facto standard for numerical analysis. But this complex program can take a lifetime to learn without the right guide. That’s where Exce

This book examines and evaluates various private initiatives to enforce fair labor standards within global supply chains. Using unique data (internal audit reports and access to more than 120 supply chain factories and 700 interviews in 14 countries) from several major global brands, including NIKE, HP and the International Labor Organization's Factory Improvement Programme in Vietnam, this book examines both the promise and the limitations of different approaches to actually improve working conditions, wages and working hours for the millions of workers employed in today's global supply chains. Through a careful, empirically grounded analysis of these programs, this book illustrates the mix of private and public regulation needed to address these complex issues in a global economy.