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Complex, Contact and Symmetric Manifolds : In Honor of L. Vanhecke
This volume contains introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics and curvature, contact and symplectic geometry, complex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the key strengths of these articles is their appeal to non-specialists, as well as researchers and differential geometers.
Complex Variables with Applications
Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. It explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions. The engaging exposition is replete with discussions, remarks, questions, and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods and assumptions underlying various alternative routes that lead to the same destination.
Complex Numbers from A to … Z
It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them.The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented.The book reflects the unique experience of the authors. It distills a vast mathematical literature, most of which is unknown to the western public, and captures the essence of an abundant problem culture.
Complex Geometry : An Introduction
Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area, both for mathematicians and theoretical physicists. The book contains detailed accounts of the basic concepts and the many exercises illustrate the theory. Appendices to various chapters allow an outlook to recent research directions.
Complex dynamics : Advanced system dynamics in complex variables
Complex Dynamics: Advanced System Dynamics in Complex Variables is a graduate-level monographic textbook. It is designed as a comprehensive introduction into methods and techniques of modern complex-valued nonlinear dynamics with its various physical and non-physical applications.
Complex Artificial Environments : Simulation, Cognition and VR in the Study and Planning of Cities
This book explores the possibilities of applying the theories of complexity and self-organization developed to account for various phenomena in the natural science to artifacts traditionally the realm of humanities and social sciences. The emphasis of this volume is on the development of cities and the impact of these methods on urban simulation methods.
Complex Analysis : In the Spirit of Lipman Bers
In this book, the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory.
Completeness theory for propositional logics
Completeness is one of the most important notions in logic and the foundations of mathematics. Many variants of the notion have been de?ned in literature. We shallconcentrateonthesevariants,andaspects,of completenesswhicharede?ned in propositional logic. Completeness means the possibility of getting all correct and reliable sc- mata of inference by use of logical methods. The word ‘all’, seemingly neutral, is here a crucial point of distinction. Assuming the de?nition as given by E. Post we get, say, a global notion of completeness in which the reliability refers only to syntactic means of logic and outside the correct schemata of inference there are only inconsistent ones. It is impossible, however, to leave aside local aspects of the notion when we want to make it relative to some given or invented notion of truth. Completeness understood in this sense is the adequacy of logic in relation to some semantics, and the change of the logic is accompanied by the change of its semantics.
Compendium of Theoretical Physics
Mechanics, Electrodynamics, Quantum Mechanics, and Statistical Mechanics and Thermodynamics comprise the canonical undergraduate curriculum of theoretical physics. In Compendium of Theoretical Physics, Armin Wachter and Henning Hoeber offer a concise, rigorous and structured overview that will be invaluable for students preparing for their qualifying examinations, readers needing a supplement to standard textbooks, and research or industrial physicists seeking a bridge between extensive textbooks and formula books. The authors take an axiomatic-deductive approach to each topic, starting the discussion of each theory with its fundamental equations. By subsequently deriving the various physical relationships and laws in logical rather than chronological order, and by using a consistent presentation and notation throughout, they emphasize the connections between the individual theories. The reader’s understanding is then reinforced with exercises, solutions and topic summaries.
Compendium for Early Career Researchers in Mathematics Education
The book provides a state-of-the-art overview of important theories from mathematics education and the broad variety of empirical approaches currently widely used in mathematics education research.
Comparative Third Sector Governance in Asia : Structure, Process, and Political Economy
The book – the first of its kind – establishes new theory and knowledge in the area of third sector organizations (TSOs) in Asia. The main purpose of this book is to draw the attention of Asia's TSOs on the importance of good governance. It documents variety of approaches, and identifies socio-cultural, economic, and political dynamics and impacts of different models of TSO governance. The combined information from the contributions in this work will ensure the sustainability of TSOs throughout Asia.
Comparative risk assessment and environmental decision making
Decision making in environmental projects is typically a complex and confusing process characterized by trade-offs between socio-political, environmental, and economic impacts. Comparative Risk Assessment (CRA) is a methodology applied to facilitate decision making when various activities compete for limited resources. CRA has become an increasingly accepted research tool and has helped to characterize environmental profiles and priorities on the regional and national level. CRA may be considered as part of the more general but as yet quite academic field of multi-criteria decision analysis (MCDA). Considerable research in the area of MCDA has made available methods for applying scientific decision theoretical approaches to multi-criteria problems, but its applications, especially in environmental areas, are still limited. The papers show that the use of comparative risk assessment can provide the scientific basis for environmentally sound and cost-efficient policies, strategies, and solutions to our environmental challenges.
Comparative Environmental Politics
The book explores five major topics: state-society relations; environmental non-governmental organizations (ENGOs); Green parties and environmental movements; institutions of government and policy-making; variations in the capacities of states to protect the environment; and national responses to global problems. It compares and contrasts rich and poor nations, large and small countries, liberal democracies and authoritarian states.
Comparative and Global Pedagogies : Equity, Access and Democracy in Education
This book critically examines equality, equity and democracy in education, globally as well as from various perspectives. Globally, there are increasing arguments both for the democratization of education and for the use of education to promote a democratic society. It is argued that democratic schools would better prepare for active citizenship and for a strong civil society which are seen to be the foundation of a democratic state. The book further argues that while there are inspiring examples of schools that engage in peace education or emancipatory pedagogy that work across various ethnic or religious divides, on balance, the forms, structures, ideologies and purposes of formal education interact to make national and international conflict more likely.
Compactifying Moduli Spaces for Abelian Varieties
This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.
Compact Riemann Surfaces : An Introduction to Contemporary Mathematics
Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory.
Commutative algebras of Toeplitz Operators on the Bergman Space
This book is devoted to the spectral theory of commutative C*-algebras of Toeplitz operators on the Bergman space and its applications. For each such commutative algebra there is a unitary operator which reduces Toeplitz operators from this algebra to certain multiplication operators, thus providing their spectral type representations. This yields a powerful research tool giving direct access to the majority of the important properties of the Toeplitz operators studied herein, such as boundedness, compactness, spectral properties, invariant subspaces.
Community Quality-of-Life Indicators : Best Cases VIII
Offers critical insights into the thriving international field of community indicators, incorporating the experiences of government leaders, philanthropic professionals, community planners and a wide range of academic disciplines. It illuminates the important role of community indicators in diverse settings and the rationale for the development and implementation of these innovative projects. details many of the practical “how to” aspects of the field as well as lessons learned from implementing indicators in practice. The case studies included here also demonstrate how, using a variety of data applications, leaders of today are monitoring and measuring progress and communities are empowered to make sustainable improvements in their wellbeing.
Communicative figurations : Transforming communications in times of deep mediatization
This open access volume is about how to research the influence of our changing media environment. Today, there is not one single medium that is the driving force of change. With the spreading of various technical communication media such as mobile phone and internet platforms, we are confronted with a media manifold of deep mediatization. But how can we investigate its transformative capability? This book answers this question by taking a non-media-centric perspective, researching the various figurations of collectivities and organizations humans are involved in. The first part of the book outlines a fundamental understanding of the changing media environment of deep mediatization and its transformative capacity. The second part focuses on collectivities and movements: communities in the city, critical social movements, maker, online gaming groups and networked groups of young people. The third part moves institutions and organizations into the foreground, discussing the transformation of journalism, religion, politics, and education, whilst the fourth and final part is dedicated to methodologies and perspectives.
Communication Systems
Presents main concepts of mobile communication systems, both analog and digitalIntroduces concepts of probability, random variables and stochastic processes and their applications to the analysis of linear systemsIncludes five appendices covering Fourier series and transforms, GSM cellular systems and more
