Strongly and weakly almost periodic linear maps on semigroup algebras

Let S be a foundation locally compact topological semigroup. Two new topologies τ _c and τ _w are introduced on M _a (S)^*. We introduce τ _c and τ _w almost periodic functionals in M _a (S)^*. We study these classes and compare them with each other and with the norm almost periodic and weakly almost periodic functionals. For f∈M _a (S)^*, it is proved that T _f ∈ℬ(M _a (S),M _a (S)^*) is strong almost periodic if and only if f is τ _c -almost periodic. Indeed, we have obtained a generalization of a well known result of Crombez for locally compact group to a more general setting of foundation topological semigroups. Finally if P(S) (the set of all probability measures in M _a (S)) has the semiright invariant isometry property, it is shown that the set of τ _w -almost periodic functionals has a topological left invariant mean.     

Efficient Synthesis of Polyhydroquinolines via the Hantzsch Reaction Using Iron Loaded Mesoporous Materials

A simple and convenient protocol is described for the preparation of polyhydroquinolines via one‐pot, multi component reaction of an aromatic aldehyde, ethylacetoacetate, ammonium acetate and dimedone using iron loaded mesoporous materials as an efficient catalyst in good yields.     

Diaminobisbenzothiazole chain extended polyurethanes as a novel class of thermoplastic polyurethane elastomers with improved thermal stability and electrical insulation properties

This work was devoted to the development of a new class of modified polyurethane as an electrical insulating material. For this purpose, NCO‐terminated urethane prepolymers at different NCO contents were prepared and chain extended by 6,6′‐oxybis(2‐aminobenzothiazole) (ABT) to produce thermoplastic polyurethane elastomers. All of the polymers were characterized by FTIR and ¹HNMR spectroscopies and examined for their thermal, mechanical, and electrical properties. The dynamic mechanical measurements results showed two glass transitions indicating phase separation. A considerable improvement in the thermal and electrical properties in comparison to common polyurethanes was detected for these polymers. The level of enhancement in the measured properties was related to the polyol molecular weight, hard segment content, and consequently the amount of the introduced urea and benzothiazole moieties. These findings indicated the improved high service temperature performance of these materials as electrical insulator for metallic surfaces. Copyright © 2008 John Wiley & Sons, Ltd.     

Rheology, morphology and mechanical properties of polyethylene/ethylene vinyl acetate copolymer (PE/EVA) blends

Rheology, morphology and mechanical properties of binary PE and EVA blends together with their thermal behavior were studied. The results of rheological studies showed that, for given PE and EVA, the interfacial interaction in PE-rich blends is higher than EVA-rich blends, which in turn led to finer and well-distributed morphology in PE-rich blends. Using two different models, the phase inversion composition was predicted to be in 45 and 47 wt% of the PE phase. This was justified by morphological studies, where a clear co-continuous morphology for 50/50 blend was observed. The tensile strength for PE-rich blends showed positive deviation from mixing rule, whereas the 50/50 blend and EVA-rich blends displayed negative deviation. These results were in a good agreement with the results of viscoelastic behavior of the blends. The elongation at break was found to follow the same trend as tensile strength except for 90/10 PE/EVA blend. The latter was explained in terms of the effect of higher co-crystallization in 90/10 composition, which increased the tensile strength and decreased the elongation at break in this composition. The results of thermal behavior of the blends indicated that the melting temperatures of PE and EVA decrease and increase, respectively, due to the dilution effect of EVA on PE and nucleation effect of PE on EVA.     

Algorithms for an Integer Multicommodity Network Flow Problem with Node Reliability Considerations

In this paper, we consider the problem of sending a set of multiple commodities from their origin to destination nodes via intermediate hubs. Each hub node is associated with a reliability function, which depends on the total flow that crosses that hub. The probability that each commodity is successfully relayed from its origin to its destination is given by the product of hub reliabilities on the commodity’s path. The problem we consider seeks to find minimum-cost commodity paths such that each commodity reaches its destination with a sufficiently large probability. We first formulate the problem as a nonlinear multicommodity network-flow problem and prove that it is strongly NP-hard. We then present two linearization techniques for this formulation, and propose a pair of lower- and upper-bounding formulations, which can then be used within an exact cutting-plane algorithm to solve the problem. Finally, we analyze the computational effectiveness of our proposed strategies on a set of randomly generated instances.     

Projections on weak*-closed subspace of dual Banach algebras

Our first purpose in this paper is to provide necessary conditions for a weak*-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak*-closed left translation invariant subspace in Ma(S)* of a compact cancellative foundation semigroup S is the range of a weak*-weak* continuous projection on M _a (S)* commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A* and B(A*) which commutes with translations and convolution.     

Poly(4-vinylpyridinium)hydrogen sulfate: a novel and efficient catalyst for the synthesis of 14-aryl-14H-dibenzo[a,j]xanthenes under conventional heating and ultrasound irradiation

A simple and convenient procedure for the synthesis of 14-aryl-14H-dibenzo[a,j]xanthenes is described through a one-pot condensation of 2-naphthol with aryl aldehydes in the presence of poly(4-vinylpyridinium)hydrogen sulfate as an efficient, cheap, readily synthesized and eco-friendly catalyst in a solvent free media using conventional heating and ultrasound irradiation.     

The Socle and finite dimensionality of some Banach algebras

The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact groupG, G is compact if there exists a measure μ in Soc(L ¹(G)) such that μ(G) ≠ 0. We also prove thatG is finite if Soc(M(G)) is closed and every nonzero left ideal inM(G) contains a minimal left ideal.