Simulation Optimization Using Multi-Time-Scale Adaptive Random Search

We propose a random search algorithm for seeking the global optimum of an objective function in a simulation setting. The algorithm can be viewed as an extension of the MARS algorithm proposed in Hu and Hu (2011) for deterministic optimization, which iteratively finds improved solutions by modifying and sampling from a parameterized probability distribution over the solution space. However, unlike MARS and many other algorithms in this class, which are often population-based, our method only requires a single candidate solution to be generated at each iteration. This is primarily achieved through an effective use of past sampling information by means of embedding multiple nested stochastic approximation type of recursions into the algorithm. We prove the global convergence of the algorithm under general conditions and discuss two special simulation noise cases of interest, in which we show that only one simulation replication run is needed for each sampled solution. A preliminary numerical study is also carried out to illustrate the algorithm.

Equivalent Circuit and AC conductivity of Sr1.75Co0.25P2O7 compound

Sr1.75Co0.25P2O7 compound was prepared by the solid-state reaction method. The impedance spectroscopy measurements were performed in the frequency and the temperature range of (209 Hz–1 MHz) and (622–704 K), respectively. Besides, the impedance spectra were fitted to an equivalent circuit consisting of series combination of grains and grain boundary. The AC conductivity for grain contribution is interpreted using the universal Jonscher’s power law. The approximation type OLPT model explains the universal behavior of the s exponent. The mechanism of conduction is probably due from the displacements of the Sr2+ ion in the tunnel-type cavities.

Relativistic and nonrelativistic solutions of the generalized Pöschl–Teller and hyperbolical potentials with some thermodynamic properties

By using the new approximation type, the Dirac equation is solved with the combination of Generalized Pöschl–Teller and Hyperbolical potentials within the framework of supersymmetric approach. The energy levels are obtained for both pseudospin and spin symmetries and the nonrelativistic limit is obtained with the corresponding wave functions in terms of hypergeometric functions. Some thermodynamic properties are equally obtained with the energy equation of the nonrelativistic limit.