Hessenberg pairs of linear transformations

Let denote a field and V denote a nonzero finite-dimensional vector space over . We consider an ordered pair of linear transformations A:V→V and A^*:V→V that satisfy (i)–(iii) below.

1. [(i)]Each of A,A^* is diagonalizable on V.

2. [(ii)]There exists an ordering of the eigenspaces of A such that

where V_-1=0, V_d+1=0.

3. [(iii)]There exists an ordering of the eigenspaces of A^* such that

where , .

We call such a pair a Hessenberg pair on V. In this paper we obtain some characterizations of Hessenberg pairs. We also explain how Hessenberg pairs are related to tridiagonal pairs.

Solutions to operator equations on Hilbert -modules

Let be a C^*-algebra, E,F and G be Hilbert -modules, , and . We generalize the Douglas theorem about the operator equation TX=T^′ from Hilbert space to Hilbert C^*-module. To the equation TX=T^′ and to the system of two equations TX=T^′ and XS=S^′, we get the forms of general solutions (in the case that there exists a solution), and give some sufficient and necessary conditions for the existence of solutions, and the existence of hermitian solutions and positive solutions (in the case G=E). In addition, the forms of general hermitian solution and general positive solution (in the case that there exists a solution and G=E) to the equation TX=T^′ are given too.     

The topological structure of fuzzy sets with endograph metric

For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rⁿ, let be the family of all fuzzy sets ofRⁿ, which are upper-semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space with the topology of endograph metric is homeomorphic to the Hilbert cube Q=[-1,1]^ω iff Y is compact; and the space is homeomorphic to {(x_n)Q:sup|x_n|<1} iff Y is non-compact and locally compact.     

Optimality and invexity in optimization problems in Banach algebras (spaces)

In this paper we introduce into nonsmooth optimization theory in Banach algebras a new class of mathematical programming problems, which generalizes the notion of smooth KT-(p,r)-invexity. In fact, this paper focuses on the optimality conditions for optimization problems in Banach algebras, regarding the generalized KT-(p,r)-invexity notion and Kuhn–Tucker points.     

Fixed point theorems for nonexpansive mappings and Suzuki-generalized nonexpansive mappings on a Banach lattice

We prove the existence of fixed points for multivalued nonexpansive nonself-mappings on a weakly orthogonal reflexive Banach lattice with uniformly monotone norm. Moreover, for single-valued mappings, we extend Betiuk-Pilarska and Prus’s result [A. Betiuk-Pilarska, S. Prus, Banach lattices which are order uniformly noncreasy, J. Math. Anal. Appl. 342 (2008) 1271–1279] on the weak fixed point property to continuous mappings satisfying condition (C) on a w-weakly orthogonal OUNC Banach lattice.     

Infinitely many non-negative solutions for a Dirichlet problem involving -Laplacian

In this paper, we consider a Dirichlet problem involving the p(x)-Laplacian of the type

We prove the existence of infinitely many non-negative solutions of the problem by applying a general variational principle due to B. Ricceri and the theory of the variable exponent Sobolev spaces.     

Molecular spectroscopic insight into the binding of batatasin V isomers to human serum albumin

Fluorescence, ultraviolet-visible absorption spectroscopy, circular dichroism spectrum, and molecular docking methods were employed to study the interaction mechanisms of batatasin V and its isomer with human serum albumin. The two isomers both bond reactively to the hydrophobic activity in subdomain IIA, with an approximate binding affinity. Thermodynamic parameters and molecular modeling results manifested that hydrogen bonds and van der Waals force were the main contributors to the interaction. The secondary structure of human serum albumin was altered with the obvious decreased amount of α-helix. The results overall suggested similar binding mechanisms of batatasin V isomers with human serum albumin. This work will promote the further study of batatasins for pharmacological function. It could also help to provide some useful information for further drug design based on batatasins.     

新型微胶囊负载环多胺锰配合物的催化氧化性能

采用乳化溶剂蒸发的方法制备了负载型催化剂环多胺锰/乙基纤维素微胶囊(MnAcL-EC), 并确认了MnAcL在微胶囊内负载后结构的完整性, 对其进行了形貌结构表征, MnAcL-EC微胶囊负载型催化剂内部呈特殊的多芯结构. 该催化剂在活性蓝(C.I. Reactive Blue 49)的氧化反应中表现出了优异的催化性能. 催化反应后微胶囊粒径增大, 球体表面孔道增多; 元素分析结果显示, 微胶囊内负载的MnAcL在催化反应后几乎没有减少, 表明负载后的MnAcL是在微胶囊内部催化了外界底物分子的氧化反应. 所制备的MnAcL-EC微胶囊具备很好的循环利用性, 可以有效减少催化活性组分的流失, 方便回收利用.     

解析簇上非孤立奇点的C0-R_V-V(f) -充分性

给出了某类解析簇上具有非孤立奇点的函数芽f在某种等价关系下的C~0-R_V-V(f)-充分性及它的某些形变平凡性的充分条件.它推广了具有非孤立奇点的函数芽的R-Z-充分性的一个判别准则.     

共沉淀法制备Y(P,V)O4:Tm3+荧光粉及其光致发光

采用氨水、双氧水和磷酸氢二铵溶液作沉淀剂,通过共沉淀法制备出Y(P,V)O4：Tm^3 荧光粉,利用XRD、SEM、紫外以及真空紫外激发下的发射光谱对其进行研究。结果表明：共沉淀法制备的Y(P,V)O4：Tm^3 荧光粉的颗粒形貌好,在147nm真空紫外光和254nm紫外光激发下,荧光粉发射主峰位于476nm,色坐标范围为：0．167≤x≤0．200;0．146≤y≤0．183。从这些结果来看,Y(P,V)O4：Tm^3 体系还不能满足实际应用的要求,仍需进一步的深入研究以改善其性能。