Perfect Modules

Erika Mares introduced the concepts of semi-perfectness and perfectness for projective modules, generalised the structure theorems of H. Bass and obtained results on the endomorphism rings of such modules. The present author has carried out an extensive study of endomorphism rings of various types of modules with two of his collaborators [3], [9]. In particular the concept of semi-perfectness was extended to modules not necessarily projective and results similar to those of Erika Mares obtained for quasi-projective semi-perfect modules. The object of the present paper is to extend the concept of perfectness to modules which are not necessarily projective and obtain results similar to those of Erika Mares, Roger Ware etc. concerning these modules.     

Partitioning multi-edge graphs

We introduce a new kind of graph called multi-edge graph which arises in many applications such as finite state Markov chains and broadcasting communication networks. A cluster in such a graph is a set of nodes such that for any ordered pair of nodes, there is a path of multi-edges from one to the other such that these edges remain within the same set. We give two algorithms to partition a multi-edge graph into maximal clusters. Both these algorithms are based on the depth-first search algorithm to find strongly connected components of the directed graph. We also discuss some applications of clustering in multi-edge graphs.     

Extraction behavior of uranium(VI), plutonium(IV), zirconium(IV), ruthenium(III) and europium(III) with γ-pre-irradiated solutions of N,N′-methylbutyl substituted amides in n-dodecane

The extraction of plutonium(IV), uranium(VI), zirconium(IV), europium(III) and ruthenium(III) with -pre-irradiated n-dodecane solutions of methylbutyl substituted hexanamide (MBHA), octanamide (MBOA) and decanamide (MBDA) from 3.5M HNO₃ has been studied as a function of absorbed dose up to 184×10⁴ Gray. The distribution ratios (K_d) of uranium(VI) decreased gradually up to a dose of 50×10⁴ Gray and became almost constant thereafter, while ruthenium(III) and europium(III) were not extracted in the entire dose range studied. The K_d values of Pu(IV) decreased gradually up to 10×10⁴ Gray, for MBOA, and 30×10⁴ Gray for MBHA and MBDA and then increased up to a dose of 72×10⁴ Gray, indicating the synergistic effect of radiolytic products at higher doses. The extraction of zirconium(IV) was found to increase gradually up to 72×10⁴ Gray. However, the steep fall in K_d values of plutonium(IV), zirconium(IV) beyond a dose of 72×10⁴ Gray was atrributed to third phase formation. The radiolytic degradation of amides was monitored by quantitative IR spectroscopy and was found to follow the order MBOA>MBDA>MBHA at 184×10⁴ Gray having the amines and carboxylic acids as the main radiolytic products.     

Heteropolyacid-catalyzed synthesis of chloromethyl methyl ether

An efficient (in terms of experiment and time) synthetic procedure for chloromethyl methyl ether (MOM-Cl) is described using heteropolyacids as catalysts.     

Modification of polystyrene maleic anhydride for efficient energy storage applications

Journal of Solid State Electrochemistry - The development of new energy storage devices has been gaining momentum in the wake of the energy crisis faced worldwide. New materials have been tried and...     

Facile Synthesis and Unusual Methanesulfonylation Reaction of (2R,3R)‐1,4‐Dimethoxy‐1,1,4,4‐tetrasubstituted‐2,3‐butanediols

A facile method for the synthesis of (2R,3R)‐1,4‐dimethoxy‐1,1,4,4‐tetrasubstituted‐2,3‐butanediols involving oxidative cleavage of benzylidene acetal as a key step is described. These sterically hindered diols unusually formed cyclic sulfites as the major product under methanesulfonylation reaction conditions.     

Cooperativity and cluster growth patterns in acetonitrile: A DFT study

Cooperativity in intermolecular interactions and cluster growth patterns of acetonitrile has been studied using M06L density functional theory. Cyclic, ladder‐type, stacked, cross‐stacked, and mixed patterns are studied. Total interaction energy (E_int) and interaction energy per monomer (E_m) show maximum stability and cooperativity in stacked clusters followed by cross‐stacked ones. As cluster size increased, magnitude of E_m showed significant increase. Compared to E_m of dimer (?2.97 kcal/mol), the increase is 2.6‐fold for 27mer . Higher stabilization in larger clusters is attributed to strong cooperativity in intermolecular C? H···N and dipolar interactions. Enhanced cooperativity in stacked structures is supported by atoms‐in‐molecule electron density (ρ) data. Sum of ρ at intermolecular bond critical points is the highest for stacked clusters. Further, area of negative‐valued molecular electrostatic potential is linearly related with E_int and showed the lowest value in stacked followed by cross‐stacked clusters, indicating maximum utilization of lone pair density and maximum cooperativity in such growth patterns. A red shift in the average C? N stretching frequencies with increase in the number of monomers and its direct correlation with E_int in stacked clusters also supported their stability. Further, two known crystal patterns of acetonitrile (α and β) with 16 monomers are optimized and compared with the most stable hexadecamer pattern and are found to show lower values for E_int and E_m compared to the latter. Based on this result, we predict the existence of a third crystal pattern for acetonitrile which will be more ordered and more stable than α and β forms. © 2014 Wiley Periodicals, Inc.