Loewy Modules with Finite Loewy Invariants and Max Modules with Finite Radical Invariants

Over a commutative ring R, a module is artinian if and only if it is a Loewy module with finite Loewy invariants [5 Facchini , A. ( 1981 ). Loewy and artinian modules over commutative rings . Ann. Mat. Pura Appl. 128 : 359 – 374 .[Crossref], [Web of Science ®] , [Google Scholar]]. In this paper, we show that this is not necesarily true for modules over noncommutative rings R, though every artinian module is always a Loewy module with finite Loewy invariants. We prove that every Loewy module with finite Loewy invariants has a semilocal endomorphism ring, thus generalizing a result proved by Camps and Dicks for artinian modules [3 Camps , R. , Dicks , W. ( 1993 ). On semilocal rings . Israel J. Math. 81 : 203 – 211 .[Crossref], [Web of Science ®] , [Google Scholar]]. Finally, we obtain similar results for the dual class of max modules.     

Mod-Retractable Rings

A right module M over a ring R is said to be retractable if Hom _R (M, N) ≠ 0 for each nonzero submodule N of M. We show that M ? _R RG is a retractable RG-module if and only if M _R is retractable for every finite group G. The ring R is (finitely) mod-retractable if every (finitely generated) right R-module is retractable. Some comparisons between max rings, semiartinian rings, perfect rings, noetherian rings, nonsingular rings, and mod-retractable rings are investigated. In particular, we prove ring-theoretical criteria of right mod-retractability for classes of all commutative, left perfect, and right noetherian rings.     

John Bell and the Identical Twins

I present a biographical profile of John S. Bell based upon extensive interviews I had with him. I present Bell‘s views on the quantum theory along with a simple explanation of his identity. Jeremy Bernstein is Professor Emeritus of Physics at the Stevens Institute of Technology and a former staff writer for The New Yorker.     

基于加速度响应控制时MTMD的地震特性

研究了由多个刚度和阻尼保持为常量且频率呈线性分布的TMD形成的MTMD的地震特性。基于虚拟激励法和Kanai Tajimi及Clough Penzien地震谱 ,建立了结构 MTMD系统的加速度传递函数 ,进而导出了设置MTMD时结构的加速度动力放大系数 (ADMF)明确表达式。于是MTMD的优化准则选择为 :结构最大加速度动力放大系数的最小值的最小化 [Min .Min .Max .ADMF]。通过最优搜寻得MTMD的最优频率间隔、平均阻尼比、调谐频率比和相应的控制有效性指标。选择结构受控频率与地震卓越频率比的不同取值 ,研究地震卓越频率对MTMD最优参数及有效性的影响     

Partition into cliques for cubic graphs: Planar case, complexity and approximation

Given a graph G=(V,E) and a positive integer k, the partition into cliques (pic) decision problem consists of deciding whether there exists a partition of V into k disjoint subsets V₁,V₂,…,V_k such that the subgraph induced by each part V_i is a complete subgraph (clique) of G. In this paper, we establish both the NP-completeness of pic for planar cubic graphs and the Max SNP-hardness of pic for cubic graphs. We present a deterministic polynomial time -approximation algorithm for finding clique partitions in maximum degree three graphs.     

Min–Max vs. Min–Sum Vehicle Routing: A worst-case analysis

The classical objective function of the Vehicle Routing Problem (VRP) is to minimize the total distance traveled by all vehicles (Min–Sum). In several situations, such as disaster relief efforts, computer networks, and workload balance, the minimization of the longest route (Min–Max) is a better objective function. In this paper, we compare the optimal solution of several variants of the Min–Sum and the Min–Max VRP, from the worst-case point of view. Our aim is two-fold. First, we seek to motivate the design of heuristic, metaheuristic, and matheuristic algorithms for the Min–Max VRP, as even the optimal solution of the classical Min–Sum VRP can be very poor if used to solve the Min–Max VRP. Second, we aim to show that the Min–Max approach should be adopted only when it is well-justified, because the corresponding total distance can be very large with respect to the one obtained by optimally solving the classical Min–Sum VRP.     

Rh(DMF)TPPS.5H2O的合成及光助还原水放氢的研究

为筛选光解水产氢的光敏剂, 用改进的方法, 分别合成了Rh4(CO)12和meso-四(对苯磺酸钠)卟啉(TPPS), 并在N,N-二甲基甲酰胺(DMF)中反应, 得到组成为Rh(DMF)TPPS.5H2O的新配合物, 用元素分析, 红外, 拉曼光谱, 质子核磁共振, 电子顺磁共振及热重分析, 确定了配合物的结构和Rh的价态, 并进行了Rh(DMF)TPPS-TiCl3-K2PtCl6三组份复合体系的放氢实验, 结果表明铑体系较诸钌体系有更高的放氢效率.     

应用离子选择性电极进行溶液热力学研究IV: 氯化钠5-45℃间九个温度下由水至二甲基甲酰胺-水混合溶剂的标准转移Gibbs自由能及转移熵的测定

本文应用钠离子玻璃电极及氯离子选择性电极组成无液界可逆电池, 即Cl^-选择电极|NaCl(m), w或s|Na^+玻璃电极测定电池的标准电动势, 计算NaCl从纯水到DMF-H2O混合溶剂的标准转移Gibbs自由能ΔGt°, 测定相应的电池在5℃至45℃九个温度下的电动势温度系数, 求得标准转移熵ΔSt°. 得出ΔGt°及ΔSt°随有机组份含量及温度变化的规律. 对NaCl由纯水至混合溶剂的溶剂化作用的变化, 及DMF和水的液体结构作了讨论.