The Coordinatewise Uniformly Kadec–Klee Property in Some Banach Spaces

We introduce a new property UKK _c for a Banach space and show for an Orlicz sequence space the following: UKK _c H _{c 2}.     

On an Embedding Criterion for Interpolation Spaces and Application to Indefinite Spectral Problems

An embedding criterion for interpolation spaces is formulated and applied to the study of the Riesz basis property in the L _2,g space of eigenfunctions of an indefinite Sturm–Liouville problem u=gu on the interval (-1,1) with the Dirichlet boundary conditions, provided that the function g(x) changes sign at the origin. In particular, the basis property criterion is established for an odd g(x). Some connections with stability in interpolation scales are discussed.     

AFPP vs FPP

The main theme of this paper is that almost fixed point properties of discrete structures and fixed point properties of (topological) spaces are interdeducible via a suitable category which contains both graphs and spaces as objects. To carry out the program, we have to consider (almost) fixed points of multifunctions, and for this we need a preliminary discussion of power structures for graphs and simplicial complexes. Specific applications developed are: a digital convexity (discrete) version of Kakutani's fixed point theorem for convex-valued multifunctions; and fixed point properties of dendrites in terms of those of finite discrete trees.     

Modules with the Direct Summand Sum Property

The present work gives some characterizations of R-modules with the direct summand sum property (in short DSSP), that is of those R-modules for which the sum of any two direct summands, so the submodule generated by their union, is a direct summand, too. General results and results concerning certain classes of R-modules (injective or projective) with this property, over several rings, are presented.     

Duality Theory in Fuzzy Linear Programming Problems with Fuzzy Coefficients

The concept of fuzzy scalar (inner) product that will be used in the fuzzy objective and inequality constraints of the fuzzy primal and dual linear programming problems with fuzzy coefficients is proposed in this paper. We also introduce a solution concept that is essentially similar to the notion of Pareto optimal solution in the multiobjective programming problems by imposing a partial ordering on the set of all fuzzy numbers. We then prove the weak and strong duality theorems for fuzzy linear programming problems with fuzzy coefficients.     

Uniqueness of norm on L(G) and C(G) when G is a compact group

Let G be a compact group. If the trivial representation of G is not weakly contained in the left regular representation of G on L₀²(G) and X is either L^p(G) for 1<p?∞ or C(G), then we show that every complete norm |·| on X that makes translations from (X,|·|) into itself continuous is equivalent to ||·||_p or ||·||_∞ respectively. If 1<p?∞ and every left invariant linear functional on L^p(G) is a constant multiple of the Haar integral, then we show that every complete norm |·| on L^p(G) that makes translations from (L^p(G),|·|) into itself continuous and that makes the map t?L_t from G into bounded is equivalent to ||·||_p.     

Stopping times for quantum Markov chains

In the paper we introduce stopping times for quantum Markov states. We study algebras and maps corresponding to stopping times, give a condition of strong Markov property and give classification of projections for the property of accessibility. Our main result is a new recurrence criterium in terms of stopping times (Theorem 1 and Corollary 2). As an application of the criterium we study how, in Section 6, the quantum Markov chain associated with the one-dimensional Heisenberg (usually non-Markovian) process, obtained from this quantum Markov chain by restriction to a diagonal subalgebra, is such that all its states are recurrent. We were not able to obtain this result from the known recurrence criteria of classical probability.Supported by GNAFA-CNR, Bando n. 211.01.25.     

非线性介质F－P干涉仪光束输出特性的理论研究

本文对准直光束射入含有非线性介质的Ｆ－Ｐ干涉仪内的光场分布进行了研究．由于非线性介质与光的作用，从Ｆ－Ｐ干涉仪出射的光束截面上的相移随位置的改变呈一定的分布，进而引起了干涉仪的透射率和输出光束重新分布。当干涉仪两个面的反射系数较大时，输出光束截面出现光强和相移的跃变．这种现象与以前在平面波假设下所得的光强分布所得结论有较大的不同．     

一些高Tc超导体的弹性性质

 本文用超声相比较方法测定了高T_c超导体La_1.85Sr_0.15CuO₄，La₂CuO₄和YBa₂Cu₃O₇的纵波和横波声速，进而导出了它们的纵向模量、切变模量、杨氏模量、泊松比、德拜温度及定体比热。在La_1.85Sr_0.15CuO₄样品上，还进行了压力实验，发现所有弹性模量都是随压强增加而增加。定体比热c_V和泊松比σ在高压下则略有下降。德拜温度是随压强增加而增加的。     

Invariant Mean—Value Property and M—Harmonicity in the Unit Ball of R^n

In 1993,Ahern,Flores and Rudin showed that,if f is integrable over the unit ball BC^n of C^n and satisfies∫BC^nfoφdv=f（φ（0)) for every φ∈Aut(BC^n),then f is M-harmonic if and only if n≤11.The present paper is about an analogous question in the context of the unit ball Bn of R^n as well as in the weighted setting.