On generalized geometric programming problems with non-positive variables

Generalized geometric programming (GGP) problems occur frequently in engineering design and management. Some exponential-based decomposition methods have been developed for solving global optimization of GGP problems. However, the use of logarithmic/exponential transformations restricts these methods to handle the problems with strictly positive variables. This paper proposes a technique for treating non-positive variables with integer powers in GGP problems. By means of variable transformation, the GGP problem with non-positive variables can be equivalently solved with another one having positive variables. In addition, we present some computationally efficient convexification rules for signomial terms to enhance the efficiency of the optimization approach. Numerical examples are presented to demonstrate the usefulness of the proposed method in GGP problems with non-positive variables.     

Effects of target-substrate geometry and ambient gas pressure on FePt nanoparticles synthesized by pulsed laser deposition

FePt nanoparticles, in the forms of nanoparticle agglomerates and floccules-like nanoparticle networks, can be synthesized by pulsed laser deposition (PLD) at different ambient gas pressures. Backward plume deposition (BPD), as special target-substrate geometry, can achieve higher uniformity in terms of agglomerate size and size distribution, compared to conventional PLD. Both as-deposited FePt nanoparticles exhibit low K_u fcc phase and post-annealing at 600 °C is required for the phase transition to high K_u fct phase. FePt nanoparticle agglomerates deposited by BPD were found to have better fct phase crystallinity after annealing, which may be caused by the higher kinetic energy of backward moving ablated species due to shorter travel distance.     

有限域上一次同余方程组的编码解法

对于有限域上n元一次同余方程组的求解问题,给出了一种基于编码理论的新解法,并给出了算法的Matlab程序实现.     

Algorithms for finding clique-transversals of graphs

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. It is NP-hard to determine the minimum cardinality τ _c of a clique-transversal of G. In this work, first we propose an algorithm for determining this parameter for a general graph, which runs in polynomial time, for fixed τ _c . This algorithm is employed for finding the minimum cardinality clique-transversal of [`(3K₂)]\overline{3K_{2}} -free circular-arc graphs in O(n ⁴) time. Further we describe an algorithm for determining τ _c of a Helly circular-arc graph in O(n) time. This represents an improvement over an existing algorithm by Guruswami and Pandu Rangan which requires O(n ²) time. Finally, the last proposed algorithm is modified, so as to solve the weighted version of the corresponding problem, in O(n ²) time.     

Shape-dependent local internal stress of α-Cr2O3 nanocrystal fabricated by pulsed laser ablation

The α-Cr₂O₃ single-crystal nanocondensates were fabricated by pulsed laser ablation in air and characterized by analytical electron microscopy regarding shape-dependent local internal stress of the anisotropic crystal. The nanocondensates formed predominantly as rhombohedra with well-developed surfaces and occasionally hexagonal plate with thin edges and blunt corners. Such nanocondensates showed Raman shift for the CrO₆ polyhedra, indicating a local compressive stress up to ca. 4 GPa on the average. Careful analysis of the lattice fringes revealed a local compressive stress (0.5% strain) at the thin edge of the hexagonal plates and a local tensile stress (0.3–1.0% strain) near the relaxed , , and (0 0 0 1) surfaces of truncated rhombohedra. The combined effects of nanosize, capillarity force at sharp edge, and specific surface relaxation account for the retention of a local internal compressive stress built up in an anisotropic crystal during a very rapid heating–cooling process.     

Generation of entangled coherent states through cavity-assisted interaction

We propose schemes to generate an n-coherent-pulse GHZ state and a cluster state via the interaction between n coherent pulses and a two-sided cavity.In these schemes,a strong coupling condition is not needed,which makes the protocols possibly able to be implemented based on the current experiment technology.     

Comparative analysis of the machine repair Problem with imperfect coverage and service pressure condition

In this paper we analyze the warm-standby M/M/R machine repair problem with multiple imperfect coverage which involving the service pressure condition. When an operating machine (or warm standby) fails, it may be immediately detected, located, and replaced with a coverage probability c by a standby if one is available. We use a recursive method to develop the steady-state analytic solutions which are used to calculate various system performance measures. The total expected profit function per unit time is derived to determine the joint optimal values at the maximum profit. We first utilize the direct search method to measure the various characteristics of the profit function followed by Quasi-Newton method to search the optimal solutions. Furthermore, the particle swarm optimization (PSO) algorithm is implemented to find the optimal combinations of parameters in the pursuit of maximum profit. Finally, a comparative analysis of the Quasi-Newton method with the PSO algorithm has demonstrated that the PSO algorithm provides a powerful tool to perform the optimization problem.     

Type II sensitivity analysis of cost coefficients in the degenerate transportation problem

This paper focuses on sensitivity analysis of the degenerate transportation problem (DTP) when perturbation occurs on one cost coefficient. The conventional Type I sensitivity analysis of the transportation problem (TP) determines the perturbation ranges for the invariant optimal basis. Due to different degenerate optimal basic solutions yielding different Type I ranges, the Type I range is misleading for the DTP. Type II sensitivity analysis, which determines the perturbation ranges for the invariant shipping pattern, is more practical for the DTP. However, it is too tedious to obtain Type II ranges by enumerating all optimal basic solutions and all primal optimal basic solutions while getting the union of each corresponding Type I ranges. Here, we propose two labeling algorithms to determine the Type II ranges of the cost coefficient. Besides, three lemmas are provided for obtaining the upper bound or lower bound of the Type II ranges of the cost coefficient directly under specific conditions of the DTP. A numerical example is given to demonstrate the procedure of the proposed labeling algorithms and computational results have been provided.     

Investigation of fast pitch angle scattering of runaway electrons in the EAST tokamak

This paper reports that an experimental investigation of fast pitch angle scattering(FPAS) of runaway electrons in the EAST tokamak has been performed.From the newly developed infrared detector(HgCdTe) diagnostic system,the infrared synchrotron radiation emitted by relativistic electrons can be obtained as a function of time.The FPAS is analysed by means of the infrared detector diagnostic system and the other correlative diagnostic systems(including electron-cyclotron emission,hard x-ray,neutrons).It is found that the intensity of infrared synchrotron radiation and the electron-cyclotron emission signal increase rapidly at the time of FPAS because of the fast increase of pitch angle and the perpendicular velocity of the energetic runaway electrons.The Parail and Pogutse instability is a possible mechanism for the FPAS.