Generalizations of Slater's constraint qualification for infinite convex programs

In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g ₁,g ₂) andS = S ₁ ×S ₂,S _i are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg _i are, respectively, convex andS _i -convex,i = 1, 2. In particular, we consider the special case whenS ₂ is in afinite dimensional space,g ₂ is affine andS ₂ is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g ₂ is affine andS = S ₂ is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong ₂ and the finite dimensionality assumption onS ₂, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones.     

随机模糊集与随机集

本文研究了三个方面的工作：一是定义了一种模糊集上的可测结构，从而定义了随机模糊集，这些定义都与论域Ｘ上的拓扑结构无关。将通常意义下的集合看成特殊模糊集得到的通常集合上的超可测结构与文（３）中的定义一致；二是给出了随机模糊集、随机集的一些等价条件；三是研究了随机模糊集、随机集的分布与其有限维落影族的关系。     

Synthesis and Characterization of Titanium-doped Ordered Mesoporous Alumina

Titanium-doped ordered mesoporous alumina with specific structural properties has been prepared by the evaporation induced self-assembly sol-gel method. The results show that the doped titanium helps to stabilize the ordered mesoporous alumina material without influencing the ordered mesoporosity. The textural properties of the obtained sample are related to the amount of doped titanium. When the molar ratio of aluminum to titanium(n(Al)/n(Ti)) is controlled as 10.2, the titanium-doped ordered mesoporous alumina exhibits high surface area(up to 218 m2 g-1), large pore volume(0.42 cm3 g-1) and narrow pore diameter(6.1 nm) after treating at 900 ℃, showing high thermal stability. Moreover, the obtained sample calcined at 900 ℃ still maintains ordered mesoporous structure and exhibits high thermal stability.     

Lanthanide Identity Governs Guest-Induced Dimerization in LnIII[15-MC N(L-pheHA)-5])3+ Metallacrowns

Series of lanthanide-containing metallic coordination complexes are frequently presented as structurally analogous, due to the similar chemical and coordinative properties of the lanthanides. In the case of chiral (Ln^III[15-MC _N(L-pheHA)-5])³⁺ metallacrowns (MCs), which are well established supramolecular hosts, the formation of dimers templated by a dicarboxylate guest (muconate) in solution of neutral pH is herein shown to have a unique dependence on the identity of the MC's central lanthanide. Calorimetric data and nuclear magnetic resonance diffusion studies demonstrate that MCs containing larger or smaller lanthanides as the central metal only form monomeric host-guest complexes whereas analogues with intermediate lanthanides (for example, Eu, Gd, Dy) participate in formation of dimeric host-guest-host compartments. The driving force for the dimerization event across the series is thought to be a competition between formation of highly stable MCs (larger lanthanides) and optimally linked bridging guests (smaller lanthanides).     

Difference systems of sets based on cosets partitions

Difference systems of sets （DSS） are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.     

A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment

The purpose of this paper is to design a new extension of the ELECTRE, known as the elimination and choice translating reality method, for multi-criteria group decision-making problems based on intuitionistic fuzzy sets. This method is widely utilized when a set of alternatives should be identified and evaluated with respect to a set of conflicting criteria by reflecting decision makers’ (DMs’) preferences. However, handling the exact data and numerical measure is difficult to be precisely focused because the DMs’ judgments are often vague in real-life decision problems and applications. A more realistic and practical approach can be to use linguistic variables expressed in intuitionistic fuzzy numbers instead of numerical data to model DMs’ judgments and to describe the inputs in the ELECTRE method. The proposed intuitionsitic fuzzy ELECTRE utilizes the truth-membership function and non-truth-membership function to indicate the degrees of satisfiability and non-satisfiability of each alternative with respect to each criterion and the relative importance of each criterion, respectively. Then, a new discordance intuitionistic index is introduced, which is extended from the concept of the fuzzy distance measure. Outranking relations are defined by pairwise comparisons and a decision graph is depicted to determine which alternative is preferable, incomparable or indifferent in the intuitionistic fuzzy environment. Finally, a comprehensive sensitivity analysis is employed to further study regarding the impact of threshold values on the final evaluation, and a comparative analysis is demonstrated with an application example in flexible manufacturing systems between the proposed ELECTRE method and the existing intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method.     

改进Vague集评价方法在IT项目经理评价中的应用

针对Vague集评价过程中信息容易遗失的问题,提出采用Vague综合评价的思想进行计算.通过定义Vague基本运算法则,以及建立加权综合评价函数构建了新的评价方法.方法体现了Vague集理论描述不确定性问题的优点,反映了项目经理评价的一般特点.最后,通过案例计算,得到了公平公正的评价结果,并验证了计算结果的可靠性.     

Rejoinder on “Statistical reasoning with set-valued information: Ontic vs. epistemic views”

This note replies to comments made on our contribution to the Low Quality Data debate.