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Differential Geometry and Global Analysis
This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930–2017), held January 16, 2020, in Denver, Colorado. Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today. This volume is inspired by his work and his legacy and, while recalling historical results, presents recent developments in the geometry of symmetric spaces as well as generalizations of symmetric spaces; minimal surfaces and minimal submanifolds; totally geodesic submanifolds and their classification; Riemannian, affine, projective, and conformal connections; the $(M_{+}, M_{-})$ method and its applications; and maximal antipodal subsets. Additionally, the volume features recent achievements related to biharmonic and biconservative hypersurfaces in space forms, the geometry of Laplace operator on Riemannian manifolds, and Chen-Ricci inequalities for Riemannian maps, among other topics that could attract the interest of any scholar working in differential geometry and global analysis on manifolds.
Tight and Taut Submanifolds
First published in 1997, this book contains six in-depth articles on various aspects of the field of tight and taut submanifolds and concludes with an extensive bibliography of the entire field. The book is dedicated to the memory of Nicolaas H. Kuiper; the first paper is an unfinished but insightful survey of the field of tight immersions and maps written by Kuiper himself. Other papers by leading researchers in the field treat topics such as the smooth and polyhedral portions of the theory of tight immersions, taut, Dupin and isoparametric submanifolds of Euclidean space, taut submanifolds of arbitrary complete Riemannian manifolds, and real hypersurfaces in complex space forms with special curvature properties. Taken together these articles provide a comprehensive survey of the field and point toward several directions for future research.
Pan-Asianism and the Legacy of the Chinese Revolution
"With Xi Jinping's project to revive the ancient Silk Road for the contemporary era, new analyses of pan-Asianism have proliferated. Most of these narratives focus especially on the "rise of China" as the natural leader of new capitalist bloc, foretelling a shift of power from the West to the East. What these approaches lack, however, is any historical grounding in the thought of influential twentieth-century pan-Asianists. Viren Murthy explores the writings and specific historical contexts of key pan-Asianist intellectuals in Japan, China, and India from the early 1900s to the present to clarify how current discourses distort the very foundations of pan-Asianism. At the heart of this thinking was the notion of a unity of Asian nations, of weak nations becoming powerful, and of the Third World confronting the "advanced world" on equal terms. But there was more: pan-Asianists envisioned a future beyond both imperialism and capitalism. That the resurgence of pan-Asianist discourse has emerged alongside the dominance of capitalism, Murthy argues, signals a profound misunderstanding"--
Micro-Nano Mechatronics
Micro/Nano mechatronics is currently used in broader spectra, ranging from basic applications in robotics, actuators, sensors, semiconductors, automobiles, and machine tools. As a strategic technology highlighting the 21st century, this technology is extended to new applications in bio-medical systems and life science, construction machines, and aerospace equipment, welfare/human life engineering, and other brand new scopes. Basically, the miniaturizing technology is important to realize high performance, low energy consumption, low cost performance, small space instrumentation, light-weight, and so on. This book presents the summary of our project Center of Excellence for Education and Rese...
Asymptotic Methods in the Theory of Gaussian Processes and Fields
This book is devoted to a systematic analysis of asymptotic behavior of distributions of various typical functionals of Gaussian random variables and fields. The text begins with an extended introduction, which explains fundamental ideas and sketches the basic methods fully presented later in the book. Good approximate formulas and sharp estimates of the remainders are obtained for a large class of Gaussian and similar processes. The author devotes special attention to the development of asymptotic analysis methods, emphasizing the method of comparison, the double-sum method and the method of moments. The author has added an extended introduction and has significantly revised the text for this translation, particularly the material on the double-sum method.
Nontraditional methods in mathematical hydrodynamics
This book discusses a number of qualitative features of mathematical models of incompressible fluids. Three basic systems of hydrodynamical equations are considered: the system of stationary Euler equations for flows of an ideal (nonviscous) fluid, stationary Navier-Stokes equations for flows of a viscous fluid, and Reynolds equations for the mean velocity field, pressure, and pair one-point velocity correlations of turbulent flows. The analysis concerns algebraic or geometric properties of vector fields generated by these equations, such as the general arrangement of streamlines, the character and distribution of singular points, conditions for their absence or appearance, and so on. Troshkin carries out a systematic application of the analysis to investigate conditions for unique solvability of a number of problems for these quasilinear systems. Containing many examples of particular phenomena illustrating the general ideas covered, this book will be of interest to researchers and graduate students working in mathematical physics and hydrodynamics.
Ordinary Differential Equations with Constant Coefficient
This book presents the theory of ordinary differential equations with constant coefficients. The exposition is based on ideas developing the Gelfand-Shilov theorem on the polynomial representation of a matrix exponential. Boundary value problems for ordinary equations, Green matrices, Green functions, the Lopatinskii condition, and Lyapunov stability are considered. This volume can be used for practical study of ordinary differential equations using computers. In particular, algorithms and computational procedures, including the orthogonal sweep method, are described. The book also deals with stationary optimal control systems described by systems of ordinary differential equations with constant coefficients. The notions of controllability, observability, and stabilizability are analyzed, and some questions on the matrix Lure-Riccati equations are studied.
Subgroups of Teichmuller Modular Groups
Teichmuller modular groups, also known as mapping class groups of surfaces, serve as a meeting ground for several branches of mathematics, including low-dimensional topology, the theory of Teichmuller spaces, group theory, and, mathematical physics. This title focuses on the group-theoretic properties of these groups and their subgroups.
Algebraic Geometry
Students often find, in setting out to study algebraic geometry, that most of the serious textbooks on the subject require knowledge of ring theory, field theory, local rings, and transcendental field extensions, and even sheaf theory. Often the expected background goes well beyond college mathematics. This book, aimed at senior undergraduates and graduate students, grew out of Miyanishi's attempt to lead students to an understanding of algebraic surfaces while presenting thenecessary background along the way. Originally published in Japanese in 1990, it presents a self-contained introduction to the fundamentals of algebraic geometry. This book begins with background on commutative algebras, sheaf theory, and related cohomology theory. The next part introduces schemes andalgebraic varieties, the basic language of algebraic geometry. The last section brings readers to a point at which they can start to learn about the classification of algebraic surfaces.
