This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang...
This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researc...
During the last two decades the theory of abstract Volterra equations has under- gone rapid development. To a large extent this was due to the applications of this theory to problems in mathematical physics, such as viscoelasticity, heat conduc- tion in materials with memory, electrodynamics with memory, and to the need of tools to tackle the problems arising in these fields. Many interesting phenomena not found with differential equations but observed in specific examples of Volterra type stimulated research and improved our understanding and knowledge. Al- though this process is still going...
During the last two decades the theory of abstract Volterra equations has under- gone rapid development. To a large extent this was due to the applica...
Schrodinger Equations and Diffusion Theory addresses the question "What is the Schrodinger equation?" in terms of diffusion processes, and shows that the Schrodinger equation and diffusion equations in duality are equivalent. In turn, Schrodinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schrodinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular...
Schrodinger Equations and Diffusion Theory addresses the question "What is the Schrodinger equation?" in terms of diffusion proces...
1. Historical Remarks Convex Integration theory, first introduced by M. Gromov 17], is one of three general methods in immersion-theoretic topology for solving a broad range of problems in geometry and topology. The other methods are: (i) Removal of Singularities, introduced by M. Gromov and Y. Eliashberg 8]; (ii) the covering homotopy method which, following M. Gromov's thesis 16], is also referred to as the method of sheaves. The covering homotopy method is due originally to S. Smale 36] who proved a crucial covering homotopy result in order to solve the classification problem for...
1. Historical Remarks Convex Integration theory, first introduced by M. Gromov 17], is one of three general methods in immersion-theoretic topology f...
This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Fischer and the author. It was extended to arbitrary groups in the 1990s by the author. The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups.
This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pai...
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional...
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfac...
