Pure homology of algebraic varieties

We show that for a complete complex algebraic variety the pure term of the weight filtration in homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce image homology for noncomplete varieties.     

Matrix Valued Orthogonal Polynomials Arising from the Complex Projective Space

The main purpose of this paper is to display new families of matrix valued orthogonal polynomials satisfying second-order differential equations, obtained from the representation theory of U(n). Given an arbitrary positive definite weight matrix W(t) one can consider the corresponding matrix valued orthogonal polynomials. These polynomials will be eigenfunctions of some symmetric second-order differential operator D only for very special choices of W(t). Starting from the theory of spherical functions associated to the pair (SU(n+1), U(n)) we obtain new families of such pairs {W,D}. These depend on enough integer parameters to obtain an immediate extension beyond these cases.     

RHEOLOGICAL STUDY ON HYALURONIC ACID AND ITS DERIVATIVE SOLUTIONS

ABSTRACT

Rheological measurements were performed on Hyaluronic acid (HA) and its derivative solutions to evaluate steady flow viscosity and dynamics response with the aim to correlate the materials properties to the concentration, molecular weight and chemical structure. At low molecular weight and concentration, the HA solutions behaved as viscous liquid, whereas a soft-gel response was evident at higher molecular weight and concentration due to chains entanglement. Increasing the molecular weight was more effective than increasing concentration in promoting entanglement of molecular chains of HA. Comparing the behavior of HA solutions with that of Hyaluronic acid derivatives, it is showed that it is possible to modulate the rheological properties of HA based solutions by chemical modification preserving the bio-compatibility of the materials. The results of the rheological analysis provide a valuable tool to properly design optimal substitutes for specific biomedical application.     

On non-effective weights in Orlicz spaces

Given a weight w in Ω ⊂ ∝^N, |Ω| < ∞ and a Young function φ, we consider the weighted modular ∫_Ω ω(f(x))w(x)dx and the resulting weighted Orlicz space L_ω(w). For a Young function Ω ∉ Δ₂(∞) we present a necessary and sufficient conditions in order that L_ω(w) = L_ω(X_Ω) up to the equivalence of norms. We find a necessary and sufficient condition for ω in order that there exists an unbounded weight w such that the above equality of spaces holds. By way of applications we simplify criteria from [5] for continuity of the composition operator from L_ω into itself when ω Δ₂(∞) and obtain necessary and sufficient condition in order that the composition operator maps L_ω. continuously onto L_ω.     

The weight of a countably compact group whose cardinality has countable cofinality

We show the existence of a p-compact group whose size has countable cofinality in a forcing model. As a corollary, we show that consistently there exists a countably compact group whose size has countable cofinality and its weight is larger than the size.     

A result on the weight distributions of binary quadratic residue codes

Truong et al. [7]proved that the weight distribution of a binary quadratic residue code C with length congruent to −1 modulo 8 can be determined by the weight distribution of a certain subcode of C containing only one-eighth of the codewords of C. In this paper, we prove that the same conclusion holds for any binary quadratic residue codes.     

模糊判断矩阵排序向量的确定方法研究

首先给出模糊判断矩阵的两种一致性的定义。然后分析现有确定模糊判断矩阵排序向量的方法的特点及存在的问题，在此基础上，系统研究确定模糊判断矩阵排序向量的两类方法，第一类方法是先将模糊判断矩阵转化为AHP判断矩阵，然后将后者的排序向量作为前者的排序向量；另一类方法是直接由一致性或具有满意一致性的模糊判断矩阵计算排序向量。最后用算例说明所提出方法的应用。     

Comments on ‘‘Design of aluminium boom and arm for an excavator”

This paper comments on the recently published work dealing with the problem in the design of the backhoe excavator working device. It also includes remarks on the inadequacy in the problem approach to the device weight optimization and synthesis, and highlights mistakes in the mathematical model. This work points out the demand for a much wider approach to the optimization problem of the backhoe excavator working device.     

SDBS与HA缓蚀剂复配的实验与理论研究

通过静态失重法研究了十二烷基苯磺酸钠(SDBS)与六亚甲基四胺(HA)在盐酸溶液中对Q235钢的协同缓蚀效应, 并采用分子动力学模拟从缓蚀剂膜抑制腐蚀粒子扩散的角度对其缓蚀机理进行分析. 结果显示: SDBS和HA单独使用时, 最高缓蚀效率分别为82.82%和79.46%, 复配后最高缓蚀效率可达到92.78%; 与两种缓蚀剂单独使用时相比, SDBS与HA复配后缓蚀剂膜体系中的自由空间明显下降, 削弱了膜内缓蚀剂分子的自扩散能力, 腐蚀粒子在缓蚀剂膜携带下的被动迁移也随之减弱; SDBS与HA复配能更有效抑制腐蚀粒子在缓蚀剂膜中的扩散, 也就是说复配后的缓蚀剂具有更好的缓蚀性能.