Geometry

This book presents plane geometry following Hilbert's axiomatic system.

This book presents conventions, mathematical concepts, definitions and applications central to the geometric modeling of solids, shells and wires (engineering jargon) embedded in 3D space.

It is usual that existing material on computer aided geometric design oscillates between over-simplification for programmers and practitioners and over formalism for scientific or academic readers.

Este libro es el producto principal de un trabajo de investigación en etnomatemática.

This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling  in March 2015.

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature.

In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection.

The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.

The book is devoted to recent research in the global variational theory on smooth manifolds.

This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc.

This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics.

The Hauptvermutung is the conjecture that any two triangulations of a poly- hedron are combinatorially equivalent.

To our wives, Masha and Marian Interest in the so-called completely integrable systems with infinite num- ber of degrees of freedom was aroused immediately after publication of the famous series of papers by Gardner, Greene, Kruskal, Miura, and Zabusky [75, 77, 96, 18, 66, 19J (see also [76]) on striking properties of the Korteweg-de Vries (KdV) equation.

A major flaw in semi-Riemannian geometry is a shortage of suitable types of maps between semi-Riemannian manifolds that will compare their geometric properties.

REFLECTIONS ON SPACETIME - FOUNDATIONS, PHILOSOPHY AND HISTORY During the academic year 1992/93, an interdisciplinary research group constituted itself at the Zentrum fUr interdisziplinare Forschung (ZiF) in Bielefeld, Germany, under the title 'Semantical Aspects of Spacetime Theories', in which philosophers and physicists worked on topics in the interpretation and history of relativity theory.

Ordinary differential control thPory (the classical theory) studies input/output re- lations defined by systems of ordinary differential equations (ODE).

It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects.

In this book the authors develop and work out applications to gravity and gauge theories and their interactions with generic matter fields, including spinors in full detail.

This book is about the light like (degenerate) geometry of submanifolds needed to fill a gap in the general theory of submanifolds.

One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the three-dimensional Euclidean space as the only possible mathematical description of real physical space.

Domains are mathematical structures for information and approximation; they combine order-theoretic, logical, and topological ideas and provide a natural framework for modelling and reasoning about computation.

This book is dedicated to the theory of continuous selections of multi- valued mappings, a classical area of mathematics (as far as the formulation of its fundamental problems and methods of solutions are concerned) as well as !

This monograph covers one of the divisions of mathematical theory of control which examines moving objects functionating under conflict and uncertainty conditions.

This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature.

Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role.

Scale is a concept the antiquity of which can hardly be traced.

This is a monograph on geometrical and topological features which arise in quantum field theory.

This volume is based on the lectures given at the First Inter University Graduate School on Gravitation and Cosmology organized by IUCAA, Pune, in 1989.

It is well known that contemporary mathematics includes many disci- plines.

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines.

One service mathematics has rendered the human race.

In the last decade several international conferences on Finsler, Lagrange and Hamilton geometries were organized in Braov, Romania (1994), Seattle, USA (1995), Edmonton, Canada (1998), besides the Seminars that periodically are held in Japan and Romania.

This book grew out of our lectures given in the Oberseminar on 'Cod- ing Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001.

Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics.

The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups.

This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan- dardization of the mathematics of fuzzy sets established in the "e;Handbook"e;, namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish- ers, 1999).

Group cohomology has a rich history that goes back a century or more.

Gauss diagram invariants are isotopy invariants of oriented knots in- manifolds which are the product of a (not necessarily orientable) surface with an oriented line.

In this book we study sprays and Finsler metrics.

Historically, complex analysis and geometrical function theory have been inten- sively developed from the beginning of the twentieth century.

Projective geometry is a very classical part of mathematics and one might think that the subject is completely explored and that there is nothing new to be added.

The theory of foliations and contact forms have experienced such great de- velopment recently that it is natural they have implications in the field of mechanics.