Axiomatic Digital Topology

The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any connected and non-trivial LF space is isomorphic to an abstract cell complex. The paper demonstrates that in an n-dimensional digital space only those of the (a, b)-adjacencies commonly used in computer imagery have analogs among the LF spaces, in which a and b are different and one of the adjacencies is the "maximal" one, corresponding to 3n\"i1 neighbors. Even these (a, b)-adjacencies have important limitations and drawbacks. The most important one is that they are applicable only to binary images. The way of easily using LF spaces in computer imagery on standard orthogonal grids containing only pixels or voxels and no cells of lower dimensions is suggested

Structural behavior of tapered inflated fabric cylinders under various loading conditions

Method analyzes inflatable structures and considers axial loads, torsional moment, and internal pressure. Behavior depends on anistropic nature and large deflection stress-strain characteristics of fabric material. Behavior equations for pressurized cylinder loaded in torsion are developed

Entropy solutions of Dirichlet problem for a class of nonlinear elliptic fourth order equations with L¹-data

We consider the question on solvability and uniqueness of entropy solutions of Dirichlet problem for a class of nonlinear elliptic fourth order equations with L¹-right-hand sides. We restrict ourselves with equations of the fourth order, but it is not so signicant

Multidimensional cell lists for investigating 3-manifolds

AbstractThe paper presents a new method of investigating topological properties of three-dimensional manifolds by means of computers. Manifolds are represented as block complexes. The paper contains definitions and a theorem necessary to transfer some basic knowledge of the classical topology to finite topological spaces. The method is based on subdividing the given set into blocks of cells in such a way that a k-dimensional block be homeomorphic to a k-dimensional ball. The block structure is described by the data structure known as “cell list” which is generalized here for the multidimensional case. Results of computer experiments are presented

A Journey to Inner Africa

In 1847, Russian military engineer and diplomat Egor Petrovich Kovalevsky embarked on a journey through what is today Egypt, Sudan, Eritrea, and Ethiopia, recording his impressions of a region in flux. Invited by Egyptian ruler Mohammed Ali to look for gold and construct mines in the area between the Blue and White Nile, Kovalevsky captured the social milieu of both elites and ordinary people as well as compiled a rich record of the Upper Nile’s climate and natural resources. A Journey to Inner Africa, masterfully translated into English for the first time by Anna Aslanyan, is both a tale of encounter between Russia and northern Africa and an important document in the history and development of the Russian imperial project

Algorithms in Digital Geometry Based on Cellular Topology

Abstract. The paper presents some algorithms in digital geometry based on the topology of cell complexes. The paper contains an axiomatic justification of the necessity of using cell complexes in digital geometry. Algorithms for solving the following problems are presented: tracing of curves and surfaces, recognition of digital straight line segments (DSS), segmentation of digital curves into longest DSS, recognition of digital plane segments, computing the curvature of digital curves, filling of interiors of n-dimensional regions (n=2,3,4), labeling of components (n=2,3), computing of skeletons (n=2, 3).

Specific approaches towards design of the thermoelectric oxides

Sustainable energy supply to the population based on environmentally friendly and efficient technologies represents one of the major societal challenges in 21st century. One of the solutions is thermoelectric conversion of waste heat or solar heat into electricity, using sustainable and scalable devices, with self-sufficiency to enable mobile or remote applications. This talk will feature some promising strategies to design performing oxidebased thermoelectrics, including redox-promoted enhancement of the thermoelectric properties and a self-forming nanocomposite concept, where a controllable interplay between exsolution of the nanophases and modification of the host matrix suppresses the thermal transport, while imparting the high electrical performance. Particular attention will be given to laser floating zone technique as a tool to process ceramic samples appropriate for fabrication of the thermoelectric generators.publishe