0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A partially ordered by inclusion forms a lattice. This is the subsystem lattice of A. (In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years. This trend was formed first in group theory; basic relevant information up to the early seventies is contained in...

The last few years have witnessed an enormous interest in application of GIS in hydrology and water resources. This is partly evidenced by organization of sev eral national and international symposia or conferences under the sponsorship of various professional organizations. This increased interest is, in a large measure, in response to growing public sensitivity to environmental quality and management. The GIS technology has the ability to capture, store, manipulate, analyze, and visualize the diverse sets of geo-referenced data. On the other hand, hydrology is inherently spatial and...

This book is concerned with important problems of robust (stable) statistical pat tern recognition when hypothetical model assumptions about experimental data are violated (disturbed). Pattern recognition theory is the field of applied mathematics in which prin ciples and methods are constructed for classification and identification of objects, phenomena, processes, situations, and signals, i. e., of objects that can be specified by a finite set of features, or properties characterizing the objects (Mathematical Encyclopedia (1984)). Two stages in development of the mathematical theory of...

This book aims to provide a comprehensive study of the mathematical theory of the vortex method, from its origins in the 1930s, through the developments of the '70s when the use of computers made advanced research possible, to current work on this subject in China and elsewhere.
The five chapters treat vortex methods for the Euler and Navier-Stokes equations; mathematical theory for incompressible flows; convergence of vortex methods for the Euler equations; convergence of viscosity splitting; and convergence of the random vortex method.
Audience: This volume will be of...

We have tried to design this book for both instructional and reference use, during and after a first course in algebraic topology aimed at users rather than developers; indeed, the book arose from such courses taught by the authors. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. A certain amount of redundancy is built in for the reader's convenience: we hope to minimize: fiipping back and forth, and we have provided some appendices for reference. The first three are concerned with background...

(2) Green's functions were constructed and studied for general elliptic boundary-va lue problems ( BeRI]- Ber3], Kovl], and Kov2]). (3) Generalized eigenfunctions, spectral function, etc., were investigated in spectral theory Ber]. (4) Elliptic boundary-value problems with arbitrary power singularities on the right hand sides were investigated ( Roi6], Kos2, ] and Ser)). (5) A family of elliptic problems was studied in a family of expanding domains; the obtained results were applied to the investigation of elliptic problems with time deriva tives in the boundary conditions and parabolic...

This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil tonian. Klauder quantization also takes into account the role of the connection one-form along with...

This book has grown out of graduate courses given by the author at Southern Illinois University, Carbondale, as well as a series of seminars delivered at Curtin University of Technology, Western Australia. The book is intended to be used both as a textbook at the graduate level and also as a professional reference. The topic of one-factorizations fits into the theory of combinatorial designs just as much as it does into graph theory. Factors and factorizations occur as building blocks in the theory of designs in a number of places. Our approach owes as much to design theory as it does to...

THE PRESENT STATUS OF THE QUANTUM THEORY OF LIGHT In August of 1995, a group of over 70 physicists met at York University for a three-day symposium in honour of Professor Jean-Pierre Vigier. The attendance included theoretical and experimental physicists, mathematicians, astronomers and colleagues concerned with issues in the philosophy of science. The symposium was entitled "The Present Status of the Quantum Theory of Light" in accordance with Professor Vigier's wishes but in fact encompassed many of the areas to which Professor Vigier has contributed over his long and distinguished career....

In the 100 years since the legume-Rhizobium symbiotic nitrogen fixation interaction was first described, interest in this field has grown rapidly. The types of studies have been cyclical in nature, involving a cross-section of disciplines. The availability of cheap nitrogenous fertilizers caused much of the biological nitrogen fixation research to become more theoretical in the developed world. The high cost of energy, coupled with environmental concerns and the interest in sustainable agriculture, has stimulated research in symbiotic nitrogen fixation. The development of modern genetic...