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This volume deals with the integration of modern China into processes of global exchange and cross-border interaction. The articles explore the broader theme in different ways and in different subfields, ranging from the history of political ideas to the history of institutions, from global migration of people to the transmigration of academic discourses. Focusing on modern as well as contemporary periods, the studies demonstrate that China in the course of the twentieth century became an ever more important nodal point in a complex set of worldwide networks and engagements. The integration into global networks, together with the global consciousness that corresponded with it, made possible significant connections transcending national borders. The essays also show that the effects could be homogenizing (or globalizing), but at the same time the growing interactions also produced opposition and fragmentation.
The McKay conjecture is the origin of the counting conjectures in the representation theory of finite groups. This book gives a comprehensive introduction to these conjectures, while assuming minimal background knowledge. Character theory is explored in detail along the way, from the very basics to the state of the art. This includes not only older theorems, but some brand new ones too. New, elegant proofs bring the reader up to date on progress in the field, leading to the final proof that if all finite simple groups satisfy the inductive McKay condition, then the McKay conjecture is true. Open questions are presented throughout the book, and each chapter ends with a list of problems, with varying degrees of difficulty.
Stark's conjectures on the behavior of USDLUSD-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory. The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to themes currently under exploration in the area, such as non-abelian and USDpUSD-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and interested in number theory.
This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
The Good Life and the Greater Good in a Global Context offers a timely contribution to the debates about the good life that surround us every day in the media, politics, the humanities, and social sciences. The authors’ examine the relationship between the good life and the greater good as represented across different genres, media, cultures, and disciplines. This enables them to develop a framework of values that transcends the overly rational and individualistic model of the good life advanced by neoliberalism and the “happiness industry.” Thus, over and against normative conceptualizations of the good life that reduce meaning to money, creativity to consumption, and compassion to self-help, the contributors propose an ethically charged philosophy of living that views the care for the self, for the other, and for the planet as the catalysts of true human flourishing. In addition to recovering the original usage of “the good life” from classical thought—especially the Aristotelian understanding of eudaimonia as living well and doing well—the essays gathered here highlight its entanglement with distinctly modern ideas of happiness, wellbeing, flourishing, progress, revolution, democracy, the American Dream, utopia, and sustainability. As such, the essays capture the breadth and depth of the conversation about the good life that is of central importance to how we relate to the past, engage the present, and envision the future.
This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.
What is the relationship between politics and international law? Inspired by comparative politics and socio-legal studies, this Research Handbook develops a novel framework for comparative analysis of politics and international law at different stages of governance and in different governance systems. It applies the framework in a wide range of fields—from human rights and environmental standards, to cyber conflict and intellectual property—to show how the relationship between politics and international law varies depending on the sites where it unfolds.
Extending and generalizing the results of rational equations, Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their p
Beilinson's Conjectures on Special Values of L-Functions deals with Alexander Beilinson's conjectures on special values of L-functions. Topics covered range from Pierre Deligne's conjecture on critical values of L-functions to the Deligne-Beilinson cohomology, along with the Beilinson conjecture for algebraic number fields and Riemann-Roch theorem. Beilinson's regulators are also compared with those of Émile Borel. Comprised of 10 chapters, this volume begins with an introduction to the Beilinson conjectures and the theory of Chern classes from higher k-theory. The "simplest" example of an L-function is presented, the Riemann zeta function. The discussion then turns to Deligne's conjecture on critical values of L-functions and its connection to Beilinson's version. Subsequent chapters focus on the Deligne-Beilinson cohomology; ?-rings and Adams operations in algebraic k-theory; Beilinson conjectures for elliptic curves with complex multiplication; and Beilinson's theorem on modular curves. The book concludes by reviewing the definition and properties of Deligne homology, as well as Hodge-D-conjecture. This monograph should be of considerable interest to researchers and graduate students who want to gain a better understanding of Beilinson's conjectures on special values of L-functions.