On the Maximal and Minimal Left Ideals of Certain Banach Algebras on Locally Compact Groups

Let ${L_0^\infty(G)}$ be the Banach space of all essentially bounded measurable functions on a locally compact group G vanishing at infinity. In this paper, we describe maximal and minimal left ideals in the Banach algebra ${L_0^\infty(G)^*}$ equipped with an Arens type product. We also investigate some spectral properties of ${L_0^\infty(G)^*}$ .     

Scheduling linear deteriorating jobs to minimize the number of tardy jobs

In this paper a problem of scheduling a single machine under linear deterioration which aims at minimizing the number of tardy jobs is considered. According to our assumption, processing time of each job is dependent on its starting time based on a linear function where all the jobs have the same deterioration rate. It is proved that the problem is NP-hard; hence a branch and bound procedure and a heuristic algorithm with O(n ²) is proposed where the heuristic one is utilized for obtaining the upper bound of the B&B procedure. Computational results for 1,800 sample problems demonstrate that the B&B method can solve problems with 28 jobs quickly and in some other groups larger problems are also solved. Generally, B&B method can optimally solve 85% of the samples which shows high performance of the proposed method. Also it is shown that the average value of the ratio of optimal solution to the heuristic algorithm result with the objective ??(1 ? Ui) is at most 1.11 which is more efficient in comparison to other proposed algorithms in related studies in the literature.     

A comprehensive study of sound pressure in a finite-length fluid-filled multi-walled carbon nanotube

The aim of this paper is to analyze vibrational behavior and the sound wave propagation in the finite-length fluid-filled multi-walled carbon nanotubes (MWCNTs) and to determine the exact sound pressure load effect on it, and compare it to what has been used by the other researchers. For this purpose, the solution of the modified complex Helmholtz equation is derived by considering the non-rigidity of the CNT and the wave reflections at the open ends of the MWCNT. These investigations are very important for potential application of CNT-filled polymeric foam that is used as sound absorber. In this paper, in formulating the sound pressure load exerted on the innermost tube of the finite-length fluid-filled MWCNT, the following points have been studied for the first time: (i) the energy loss in the fluid, which cannot be ignored in the high frequency analysis; (ii) the non-rigidity of the MWCNT through considering finite acoustical impedance for its walls; (iii) the wave reflections at the open ends of the finite-length MWCNT to calculate the sound pressure load term which is coupled with the dynamic equations of motion for the finite-length fluid-filled MWCNT. The results show that ignoring the mentioned points would cause errors in the prediction of the sound pressure load exerted on the finite-length fluid-filled MWCNT.     

Investigation and Modeling of Temperature Dependence Recovery Behavior of Shape‐Memory Crosslinked Polyethylene

Shape memory was induced in crosslinked low‐density polyethylene by a heating‐stretching‐cooling cycle. The effect of crosslink content on thermal properties and temperature dependence recovery behavior was studied experimentally. The importance of stretching temperature and crosslink content on recovery behavior could be reasonably explained by the observed changes in the thermal properties which were attributed to the differences in crystalline structures and mechanism of crystal formation during the heating‐stretching‐cooling process. A mechanical model was developed to describe qualitatively and quantitatively the temperature dependence recovery behavior of the prepared shape memory crosslinked polyethylene at nonisothermal state under various conditions by driving constitutive equations using a set of model constants. These model constants were determined with the help of a set of optimization codes using a genetic algorithm method. By choosing a suitable set of model constants one can describe with high accuracy the temperature dependence recovery behavior of any shape memory polymer.