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Employs the analytic techniques based on the solution of the Neumann Problem as the main tool. This book emphasises on results where these methods are particularly important.

Constructs the general theory of submanifolds in a multidimensional projective space. This book deals with the topics such as osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds, and more.

Concerned with the problems of constructing covering codes and of estimating their parameters, this book provides an account of the theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems. It is useful for scientists, mathematicians, engineers, and others.

Provides coverage of function spaces of low Borel complexity. This book collects knowledge about general topology. It contains exercises which aim to test the reader's understanding of the material, supply proofs of statements that are used in the text and provide additional information.

Provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This book is useful for graduates and researchers in both algebra and logic.

Including a description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, this book gives a treatment of this geometry. It includes the theory of connections of vectors and directions on the unitary tangent fibre bundle; and more.

Containing a variety of inequalities which find numerous applications in various branches of mathematics, this book addresses many important developments in the field. It is useful for researchers working both in pure and applied mathematics, and it can also be used as the text for an advanced graduate course.

Presents part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory. This title provides an introduction to infinite-dimensional topology; it uses for the most part geometric methods. It also presents a part of geometric topology which is meant for the more advanced mathematician interested in manifolds.

Provides an introduction into the method of inverse spectra - a powerful method successfully employed in various branches of topology. This book includes surveys (including proofs of several statements) of the Hilbert cube and Hilbert space manifold theories. It also presents the developments of the Menger and Nobeling manifold theories.

The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. This work demonstrates the efficiency of the calculus with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics.

Aims to give an account of the algorithms for calculating with finite-dimensional Lie algebras; and to provide an introduction into the theory of finite-dimensional Lie algebras.

Focuses on cross-fertilisations between stream ciphers and number theory. This work covers known connections between the two areas. It contains over thirty research problems for stimulating interactions between the two areas. It is written by leading researchers in stream ciphers and number theory.

Presents the advances in the theory of convex structures. This volume presents graphs that appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. It includes a variety of results ranging for instance from the area of partition calculus to that of continuous selection.

Provides information on the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. This book presents such results as: sharp estimates for strong and weak solutions, solvability of boundary value problems, regularity assertions for solutions near singular points, and more.

General concepts and methods that occur throughout mathematics - and now also in theoretical computer science - are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further. The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi. A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.

Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. This book offers an account of the mathematical theory of codes on Euclidean spheres. It focuses on the engineering applications and illustrates the theory by using many examples.