Facial reduction in partially finite convex programming

We consider the problem of minimizing an extended-valued convex function on a locally convex space subject to a finite number of linear (in)equalities. When the standard constraint qualification fails a reduction technique is needed to derive necessary optimality conditions. Facial reduction is usually applied in the range of the constraints. In this paper it is applied in the domain space, thus maintaining any structure (and in particular lattice properties) of the underlying domain. Applications include constrained approximation and best entropy estimation.Research partially supported by the Natural Sciences and Engineering Research Council of Canada.     

<Emphasis Type="Italic">A</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> theory,L.S. category,and strong category

Relations between category and strong category are studied. The notion of a homotopy coalgebra of order r over the Ganea comonad is introduced. It is shown that cat(X) =Cat(X) holds if a finite 1-connected complex X carries such a structure with r sufficiently large.     

On operations in which graphs are appended to trees

We consider the effects on the algebraic connectivity of various graphs when vertices and graphs are appended to the original graph. We begin by considering weighted trees and appending a single isolated vertex to it by adding an edge from the isolated vertex to some vertex in the tree. We then determine the possible set vertices in the tree that can yield the maximum change in algebraic connectivity under such an operation. We then discuss the changes in algebraic connectivity of a star when various graphs such as trees and complete graphs are appended to its pendant vertices.     

Optimal time-variant systems and factorization of operators, I: Minimal and optimal systems

For a contractive block lower triangular operatorT optimal and star-optimal time-variant dissipative scattering realizations are introduced and their main properties are derived by state space considerations only. Two constructions of minimal and optimal realizations are given.     

Synthesis of substituted acetylenes, aryl-alkyl ethers, 2-alkene-4-ynoates and nitriles using heterogeneous mesoporous Pd-MCM-48 as reusable catalyst

Pd-MCM-48 has been employed as a heterogeneous catalyst for the synthesis of substituted acetylenes via Sonogashira reactions under copper and amine-free reaction conditions. In addition, the catalyst exhibited excellent regioselectivity for primary alcohols towards C-O coupling leading to formation of alkyl-aryl ethers in high yields. A green procedure for the stereoselective synthesis of 2-alkene-4-ynoates and nitriles from the reactions of vic-(E)-diiodoalkenes with activated alkenes has also been demonstrated using Pd-MCM-48 catalyst. The catalyst was easily recovered from the reaction mixture by filtration and reused for at least six times with minimal loss of activity.     

Positivity and matrix semigroups

We study various aspects of how certain positivity assumptions on complex matrix semigroups affect their structure. Our main result is that every irreducible group of complex matrices with nonnegative diagonal entries is simultaneously similar to a group of weighted permutations. We also consider the corresponding question for semigroups and discuss the effect of the assumption that a fixed linear functional has nonnegative values when restricted to a given semigroup.     

On the continuity of the generalized spectral radius in max algebra

Given a bounded set Ψ of n×n non-negative matrices, let ρ(Ψ) and μ(Ψ) denote the generalized spectral radius of Ψ and its max version, respectively. We show that

     

Line graph eigenvalues and line energy of caterpillars

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. A caterpillar is a tree in which the removal of all pendant vertices makes it a path. Let d?3 and n?2(d-1). Let p=[p₁,p₂,…,p_d-1] with p₁?1,p₂?1,…,p_d-1?1 such that

p₁+p₂+?+p_d-1=n-d+1.     

A bound on the generalized competition index of a primitive matrix using Boolean rank

For a positive integer m where 1?m?n, the m-competition index (generalized competition index) of a primitive digraph is the smallest positive integer k such that for every pair of vertices x and y, there exist m distinct vertices v₁,v₂,…,v_m such that there are directed walks of length k from x to v_i and from y to v_i for 1?i?m. The m-competition index is a generalization of the scrambling index and the exponent of a primitive digraph. In this study, we determine an upper bound on the m-competition index of a primitive digraph using Boolean rank and give examples of primitive Boolean matrices that attain the bound.     

Ce-MCM-48介孔分子筛的合成、表征和催化性能

尝试以混合模板剂pH调节水热合成掺入铈的介孔分子筛CeMCM48,并采用X射线衍射、高分辨透射电镜、紫外可见漫反射、X射线荧光光谱、氮气吸附脱附测试手段对样品进行表征.结果表明,新合成的掺铈介孔材料仍保持立方介孔的有序结构,有序性及吸附性能得到改善.所合成的掺铈的立方介孔分子筛对环己烷的液相氧化反应的催化活性和选择性较高.CeMCM48催化环己烷氧化反应的转化率较MCM48催化的转化率提高了8.3%～14.2%,对主要产物的选择性提高了63.4%～68.8%.