A. D. Alexandrov Selected Works Part I

A. D. Alexandrov Selected Works Part I
Author: Yu. G. Reshetnyak
Publisher: CRC Press
Total Pages: 333
Release: 2002-02-21
Genre: Mathematics
ISBN: 148228717X

Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the disci

A. D. Alexandrov Selected Works

A. D. Alexandrov Selected Works
Author: Yu. G. Reshetnyak
Publisher: CRC Press
Total Pages: 336
Release: 2002-02-21
Genre: Mathematics
ISBN: 9782881249846

Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the discipline's most difficult and enduring challenges. He was the first to apply many of the tools and methods of the theory of real functions and functional analysis that are now current in geometry. The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.

I.G.Petrovskii:Selected Wrks P

I.G.Petrovskii:Selected Wrks P
Author: Olga Oleinik
Publisher: Taylor & Francis
Total Pages: 568
Release: 2023-05-31
Genre: Mathematics
ISBN: 1000943984

This book contains the major works of Ivan Georgievich Petrowsky on systems of partial differential equations and algebraic geometry. The articles are of crucial importance for the topology of real algebraic manifolds and are the source of intensive development of theory of real algebraic manifolds.

Descriptive Theory of Sets and Functions. Functional Analysis in Semi-ordered Spaces

Descriptive Theory of Sets and Functions. Functional Analysis in Semi-ordered Spaces
Author: L.V. Kantorovich
Publisher: CRC Press
Total Pages: 384
Release: 1996-02-19
Genre: Mathematics
ISBN: 9782884490122

This book presents articles of L.V. Kantorovich on the descriptive theory of sets and function and on functional analysis in semi-ordered spaces, to demonstrate the unity of L.V. Kantorovich's creative research. It also includes two papers on the "extension of Hilbert space".

Differential Equations

Differential Equations
Author: O.A. Oleinik
Publisher: CRC Press
Total Pages: 522
Release: 1996-02-09
Genre: Mathematics
ISBN: 9782881249792

Part II of the Selected Works of Ivan Georgievich Petrowsky, contains his major papers on second order Partial differential equations, systems of ordinary. Differential equations, the theory, of Probability, the theory of functions, and the calculus of variations. Many of the articles contained in this book have Profoundly, influenced the development of modern mathematics. Of exceptional value is the article on the equation of diffusion with growing quantity of the substance. This work has found extensive application in biology, genetics, economics and other branches of natural science. Also of great importance is Petrowsky's work on a Problem which still remains unsolved - that of the number of limit cycles for ordinary differential equations with rational right-hand sides.

Applied Functional Analysis. Approximation Methods and Computers

Applied Functional Analysis. Approximation Methods and Computers
Author: S.S. Kutateladze
Publisher: CRC Press
Total Pages: 408
Release: 2010-12-12
Genre: Mathematics
ISBN: 9781420050127

This book contains the most remarkable papers of L.V. Kantorovich in applied and numerical mathematics. It explores the principal directions of Kantorovich's research in approximate methods. The book covers descriptive set theory and functional analysis in semi-ordered vector spaces.

A.D. Alexandrov

A.D. Alexandrov
Author: S.S. Kutateladze
Publisher: CRC Press
Total Pages: 444
Release: 2005-07-25
Genre: Mathematics
ISBN: 113442907X

A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian. Alexandrov's treatise begins with an outline of the basic concepts, definitions, and r

Geometric Folding Algorithms

Geometric Folding Algorithms
Author: Erik D. Demaine
Publisher: Cambridge University Press
Total Pages: 388
Release: 2007-07-16
Genre: Computers
ISBN: 1107394090

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

A. D. Alexandrov Selected Works

A. D. Alexandrov Selected Works
Author: Yu G Reshetnyak
Publisher: CRC Press
Total Pages: 332
Release: 2019-08-30
Genre: Geometry
ISBN: 9780367396312

Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the discipline's most difficult and enduring challenges. He was the first to apply many of the tools and methods of the theory of real functions and functional analysis that are now current in geometry. The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.

Convex Bodies: The Brunn–Minkowski Theory

Convex Bodies: The Brunn–Minkowski Theory
Author: Rolf Schneider
Publisher: Cambridge University Press
Total Pages: 752
Release: 2013-10-31
Genre: Mathematics
ISBN: 1107471613

At the heart of this monograph is the Brunn–Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp Brunn–Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references.