Complex Variables and Applications

The development and application of multivariate statistical techniques in process monitoring has gained substantial interest over the past two decades in academia and industry alike. Initially develo

This conference proceedings would be of interest to physicists working in the fields of complex (dusty) plasmas, plasma applications, space plasmas, fusion plasmas, and soft matter. Dusty (complex) pl

The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth meeting, celebrating the 60th birthdays of Terence Gaffney and Maria Aparecida Soares Ruas, was a special occasion attracting the best known names in the area. This volume contains contributions by the attendees, including three articles written or co-authored by Gaffney himself, and survey articles on the existence of Milnor fibrations, global classifications and graphs, pairs of foliations on surfaces, and Gaffney's work on equisingularity.

This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variabl

This is a self-contained 2010 account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of elliptic functions, modular functions and quadratic number fields and providing a concise summary of the results from class field theory. The main results are accompanied by numerical examples, equipping any reader with all the tools and formulas they need. Topics covered include: the construction of class fields over quadratic imaginary number fields by singular values of the modular invariant j and Weber's tau-function; explicit construction of rings of integers in ray class fields and Galois module structure; the construction of cryptographically relevant elliptic curves over finite fields; proof of Berwick's congruences using division values of the Weierstrass p-function; relations between ell

This self-contained book systematically explores the statistical dynamics on and of complex networks having relevance across a large number of scientific disciplines.The theories related to com

The concern of this book is the use of emergent computing and self-organization modelling within various applications of complex systems. The authors focus their attention both on the innovative conce

This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasize applications, though not at the expense of theory, so they have kept the prerequisites to a minimum; the reader need be familiar only with calculus and elementary algebra, and have a basic knowledge of Lebesgue integration. Where, for certain applications, more advanced topics are needed, the authors have included references and explained the results used. Moreover, the book has been designed so that the chapters can be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. At the end of each chapter are included exercises and further results, some 400 in all, which extend the material presented in the text and also test it. The history of functional equations is well documented in a final

Geared toward advanced undergraduates and graduate students, this substantially revised and updated edition of a popular text offers a concise treatment that provides careful and complete explanations

This book presents foundations and practical application of multi-objective optimization methods to Vehicle Design Problems, bolstered with an extensive collection of examples. Opening with a broad th

This book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappie transformation of

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

Drawn from lectures given by Raghavan Narasimhan at the University of Geneva and the University of Chicago, this book presents the part of the theory of several complex variables pertaining to unramif

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 solut

This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasize applications, though not at the expense of theory, so they have kept the prerequisites to a minimum; the reader need be familiar only with calculus and elementary algebra, and have a basic knowledge of Lebesgue integration. Where, for certain applications, more advanced topics are needed, the authors have included references and explained the results used. Moreover, the book has been designed so that the chapters can be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. At the end of each chapter are included exercises and further results, some 400 in all, which extend the material presented in the text and also test it. The history of functional equations is well documented in a final

Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations. In this book the authors give elementary accounts of many aspects of classical complex function theory including Möbius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics. This book is based on lectures given to advanced undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread applic

This text is part of the International Series in Pure and Applied Mathematics. It is designed for junior, senior, and first-year graduate students in mathematics and engineering. This edition preserve

Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.

This book offers a clear and interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. It integrates important results and recent developments into a coherent and physically consistent story, balanced between mathematical designs, scattering and optical theories, and engineering device applications. The book includes discussions of emerging device applications in metamaterials and nano-optics technology. Both academia and industry will find the book of interest as it develops the underlying physical and mathematical background in partnership with engineering applications, providing a perspective on both fundamental optical sciences and photonic device technology. Emphasizing the comprehension of physical concepts and their engineering implications over the more formal developments, this is an essential introduction to the stimulating and f

This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices.

The book provides insight into the complex mechanisms behind development of self-lubricating materials. It stresses the tribological nature of various composites and discusses compatibility of these c

Presents the latest research findings, developments, and applications in the areas of geotechnics, soil mechanics, foundations, geological engineering and share experiences in the design of complex ge

Fundamentals of 3D Food Printing and Applications provides an update on this emerging technology that can not only create complex edible shapes, but also enable the alteration of food texture and nutr

This book provides a comprehensive review of complex networks from three different domains, presents novel methods for analyzing them, and highlights applications with accompanying case studies. Speci

This book explores new alternative metaheuristic developments that have proved to be effective in their application to several complex problems. Though most of the new metaheuristic algorithms conside

Hydroclimatology provides a systematic structure for analysing how the climate system causes time and space variations (both global and local) in the hydrologic cycle. Changes in the relationship between the climate system and the hydrologic cycle underlie floods, drought and possible future influences of global warming on water resources. Land-based data, satellite data, and computer models contribute to our understanding of the complex time and space variations of physical processes shared by the climate system and the hydrologic cycle. Blending key information from the fields of climatology and hydrology - which are not often found in a single volume - this is an ideal textbook for students in atmospheric science, hydrology, Earth and environmental science, geography, and environmental engineering. It is also a useful reference for academic researchers in these fields.

Weighted Residual Methods: Principles, Modifications and Applications introduces a range of WRMs, providing examples that show how they can be used to solve complex engineering problems with greater a