Related papers: On the development of differential geometry in Est…
In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are…
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of…
We present some episodes from the history of interactions between geometry and physics over the past century.
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
These notes, based on a graduate course I gave at Hamburg University in 2003, are intended to students having basic knowledges of differential geometry. Their main purpose is to provide a quick and accessible introduction to different…
This paper establishes the basis of the quaternionic differential geometry ($\mathbbm H$DG) initiated in a previous article. The usual concepts of curves and surfaces are generalized to quaternionic constraints, as well as the curvature and…
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus,…
Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…
Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open…
This manuscript, titled Differential Geometry of Curves and Surfaces in Three-dimensional Euclidean Space, is intended for undergraduate students of mathematics and other sciences with the need of use of Euclidean differential geometry. We…
The present document is the draft of a book which presents an introduction to infinite-dimensional differential geometry beyond Banach manifolds. As is well known the usual calculus breaks down in this setting. Hence, we replace it by the…
The article is devoted to the problem of incorporation geographic information systems (GIS) in world school practice. The authors single out the stages of GIS application in school geographical education based on the retrospective analysis…
We briefly review a number of important recent experimental and theoretical developments in the field of dynamic fracture. Topics include experimental validation of the equations of motion for straight tensile cracks (in both infinite media…
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an…
In this paper we give a brief overview of the geometry of involute gears, from a mathematical more than an engineering perspective. We also list some of the many variant geared mechanisms and discuss some of our 3D printed mechanisms.
The theory of one-relator groups is now almost a century old. The authors therefore feel that a comprehensive survey of this fascinating subject is in order, and this document is an attempt at precisely such a survey. This article is…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise,…