Quasi Co-Hopfian Modules and Applications

We carry out an extensive study of modules M _R with the property that M/f(M) is singular for all injective endomorphisms f of M. Such modules called “quasi co-Hopfian”, generalize co-Hopfian modules. It is shown that a ring R is semisimple if and only if every quasi co-Hopfian R-module is co-Hopfian. Every module contains a unique largest fully invariant quasi co-Hopfian submodule. This submodule is determined for some modules including the semisimple ones. Over right nonsingular rings several equivalent conditions to being quasi co-Hopfian are given. Modules with all submodules quasi co-Hopfian are called “completely quasi co-Hopfian” (cqcH). Over right nonsingular rings and over certain right Noetherian rings, it is proved that every finite reduced rank module is cqcH. For a right nonsingular ring which is right semi-Artinian (resp. right FBN) the class of cqcH modules is the same as the class of finite reduced rank modules if and only if there are only finitely many isomorphism classes of nonsingular R-modules which are simple (resp. indecomposable injective).     

Combination of MCDM and covering techniques in a hierarchical model for facility location: A case study

In this paper, locating some warehouses as distribution centers (DCs) in a real-world military logistics system will be investigated. There are two objectives: finding the least number of DCs and locating them in the best possible locations. The first objective implies the minimum cost of locating the facilities and the latter expresses the quality of the DCs locations, which is evaluated by studying the value of appropriate attributes affecting the quality of a location. Quality of a location depends on a number of attributes; so the value of each location is determined by using Multi Attribute Decision Making models, by considering the feasible alternatives, the related attributes and their weights according to decision maker’s (DM) point of view. Then, regarding the obtained values and the minimum number of DCs, the two objective functions are formed. Constraints imposed on these two objectives cover all centers, which must be supported by the DCs. Using Multiple Objective Decision Making techniques, the locations of DCs are determined. In the final phase, we use a simple set partitioning model to assign each supported center to only one of the located DCs.     

Circular chromatic index of graphs of maximum degree 3

This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χ′_c(G) ≤ 11/3 provided that G does not contain H₁ or H₂ as a subgraph, where H₁ and H₂ are obtained by subdividing one edge of K (the graph with three parallel edges between two vertices) and K₄, respectively. As χ′_c(H₁) = χ′_c(H₂) = 4, our result implies that there is no graph G with 11/3 < χ′_c(G) < 4. It also implies that if G is a 2‐edge connected cubic graph, then χ′_c(G) ≤ 11/3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 325–335, 2005     

Single facility location and relocation problem with time dependent weights and discrete planning horizon

In this paper a single facility location problem with multiple relocation opportunities is investigated. The weight associated with each demand point is a known function of time. We consider either rectilinear, or squared Euclidean, or Euclidean distances. Relocations can take place at pre-determined times. The objective function is to minimize the total location and relocation costs. An algorithm which finds the optimal locations, relocation times and the total cost, for all three types of distance measurements and various weight functions, is developed. Locations are found using constant weights, and relocations times are the solution to a Dynamic Programming or Binary Integer Programming (BIP) model. The time horizon can be finite or infinite.     

Chirality and correlations in graphene

Graphene is described at low energy by a massless Dirac equation whose eigenstates have definite chirality. We show that the tendency of Coulomb interactions in lightly doped graphene to favor states with larger net chirality leads to suppressed spin and charge susceptibilities. Our conclusions are based on an evaluation of graphene's exchange and random-phase-approximation correlation energies. The suppression is a consequence of the quasiparticle chirality switch which enhances quasiparticle velocities near the Dirac point.     

An efficient one-pot method for the synthesis of novel ferrocene-triamide conjugates via pseudo five-component reaction

A simple and efficient one-pot synthesis of novel ferrocene-triamide conjugates from the reaction of ferrocenecarboxaldehyde with Meldrum’s acid and isocyanides in the presence of NH-containing compounds is described. This transformation proceeds through the creation of two CC bonds, two CN bonds, and one CO bond, leading to three peptide bonds, and presumably occurs via a domino sequence involving Knoevenagel condensation, [1+4] cycloaddition, deacetonation, and aminolysis reactions.