1,571 research outputs found
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
A quasi-optimal coarse problem and an augmented Krylov solver for the Variational Theory of Complex Rays
The Variational Theory of Complex Rays (VTCR) is an indirect Trefftz method
designed to study systems governed by Helmholtz-like equations. It uses wave
functions to represent the solution inside elements, which reduces the
dispersion error compared to classical polynomial approaches but the resulting
system is prone to be ill conditioned. This paper gives a simple and original
presentation of the VTCR using the discontinuous Galerkin framework and it
traces back the ill-conditioning to the accumulation of eigenvalues near zero
for the formulation written in terms of wave amplitude. The core of this paper
presents an efficient solving strategy that overcomes this issue. The key
element is the construction of a search subspace where the condition number is
controlled at the cost of a limited decrease of attainable precision. An
augmented LSQR solver is then proposed to solve efficiently and accurately the
complete system. The approach is successfully applied to different examples.Comment: International Journal for Numerical Methods in Engineering, Wiley,
201
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
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