First Alexandroff Decomposition Theorem for Topological Lattice Group Valued Measures

Let (X, F) be an Alexandroff space, let A(F) be the Boolean subalgebra of 2 ^X generated by F, let G be a Hausdorff commutative topological lattice group and let rba_F(A(F), G) denote the set of all order bounded F-inner regular finitely additive set functions from A(F) into G. Using some special properties of the elements of rba_F(A(F), G), we extend to this setting the first decomposition theorem of Alexandroff.     

On the étale Descent Problem for Topological Cyclic Homology and Algebraic K-Theory

We investigate étale descent properties of topological Hochschild and cyclic homology. Using these properties we deduce a general injectivity result for the descent map in algebraic K-theory, and show that algebraic K-theory has étale descent for rings of integers in unramified and tamely ramified p-adic fields.     

Large volume growth and finite topological type

It is shown in this paper that a complete noncompact -dimensional Riemannian manifold with nonnegative Ricci curvature, sectional curvature bounded from below, and large volume growth is of finite topological type provided that the volume growth rate of the complement of the cone of rays from a fixed base point is less than .

     

Shell Analysis and Effective Disorder in a 2D Froth

The static and evolutionary properties of two-dimensional cellular structures, or froths, are discussed in the light of recent work on structuring of the froth into concentric shells. Of interest is the dual role of a topological dislocation (defect) in an otherwise uniform froth, considered both as a source of disorder and also as a source generating a shell-structured froth. We present simulations on an initially uniform hexagonal froth. A defect is introduced by forcing either a T1 or T2 process in the stable structure, after which the froth is allowed to evolve according to von Neumann's law. In the first case, topological inclusions are found in the first few layers early in the evolution. In the second case, no inclusions appear over the entire evolutionary period. The growing disorder (as measured by the second moment of the side distribution, ₂) is isotropic. For the special case of a T2-formed froth in a uniform network, the SSI structure is retained with ₂0 only for the zeroth, first, and second layers. The ratio between topological perimeter and radius of the shells is close to 6, the value for a hexagonal froth.     

关于拓扑对策中的I~2(K)I(K)问题

证明了如果空间类κ为D-空间类或闭遗传不可约空间类,则I(κ)(∈)κ.这一结果对于κ为D空间类和闭遗传不可约空间类,肯定地回答了I(κ)是否包含I2(κ)问题.     

Static reanalysis for topological modifications of structures

A procedure for reanalysis of various structures subjected to various topological modifications is presented. The procedure is based on the results of a single exact analysis and the factorization of the stiffness matrix of initial structures. It is suitable for the case of addition of joints, where the number of the degrees of freedom is increased. The method deals with the stiffness matrix of structures directly, so it can be used with a general finite element system. It is shown that the proposed approximation method is most effective in terms of accuracy, efficiency, and ease of implementation.     

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using φ-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a δ function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of φ-mapping. In our solution, the flux of this soliton is naturally quantized.     

Topological estimation of proton-ligand formation constants of potential antitumour agents: Salicylhydroxamic acids

Proton-ligand formation constants of salicylhydroxamic acids (SHA) and their nuclear substituted derivatives have been estimated topologically using the normalized Wiener index, referred to as mean square Wiener index (Wms). Regression analysis of the data indicates that Wms can be used successfully for estimating and monitoring proton-ligand formation constants.     

THREE-POINT BOUNDARY VALUE PROBLEM FOR p-LAPLACIAN DIFFERENTIAL EQUATION AT RESONANCE

By topological degree theory,the three-point boundary value problem for p-Laplacian differential equation at resonance is studied. Some new results on the existence of solutions are obtained,which improve and extend some known ones in the previous literatures.     

Influence of pressure on electron spectra of metals and semiconductors

Abstract

We have already reported the results of direct observations of electron-topological phase transition (ETT) in cadmium'. The appearance of new dHvA-frequencies corresponding to the Fermi surface (FS) change, i.e. restoring of folding of hole “monster” and electron “needle” appearance is observed under pressure. In t h i s report we are going to enlarge on the ETT consequences study in cadmium-on the advent of anomalous electronic features in transverse magnetoresistance and thermoelectric power.