A Branch and Bound Method via d.c. Optimization Algorithms and Ellipsoidal Technique for Box Constrained Nonconvex Quadratic Problems

In this paper we propose a new branch and bound algorithm using a rectangular partition and ellipsoidal technique for minimizing a nonconvex quadratic function with box constraints. The bounding procedures are investigated by d.c. (difference of convex functions) optimization algorithms, called DCA. This is based upon the fact that the application of the DCA to the problems of minimizing a quadratic form over an ellipsoid and/or over a box is efficient. Some details of computational aspects of the algorithm are reported. Finally, numerical experiments on a lot of test problems showing the efficiency of our algorithm are presented.     

Using cutting planes to solve the symmetric Travelling Salesman problem

Two algorithms using cutting planes are developed for solving the Travelling Salesman Problem. In both algorithms the problem is started with a subset of the set of constraints that define the problem (apart from integrality requirements).However, the two algorithms differ in the order in which the omitted constraints and the cutting planes that are required are generated.The computational experience obtained suggests that cutting planes can provide a competitive approach to other efficient methods of solving the problem.     

Preventing redundant solutions in partial enumeration algorithms

Many algorithms for discrete problems use a variation of the tree-search enumeration technique as a basis for the algorithm. If a solution is the assignment of an attribute from a set ofm attributes to every variable in a set ofn variables, then redundant solutions can be generated if either the attributes or the variables contain some indistinguishable elements. A series of necessary and sufficient techniques are developed to eliminate the production of redundant solutions during enumeration. These techniques can be used to form the foundation of any partial enumeration algorithm where redundant solutions can be produced.     

Self-catalytic branch growth of SnO2 nanowire junctions

Multiple branched SnO₂ nanowire junctions have been synthesized by thermal evaporation of SnO powder. Their nanostructures were studied by transmission electron microscopy and field emission scanning electron microcopy. It was observed that Sn nanoparticles generated from decomposition of the SnO powder acted as self-catalysts to control the SnO₂ nanojunction growth. Orthorhombic SnO₂ was found as a dominate phase in nanojunction growth instead of rutile structure. The branches and stems of nanojunctions were found to be an epitaxial growth by electron diffraction analysis and high-resolution electron microscopy observation. The growth directions of the branched SnO₂ nanojunctions were along the orthorhombic [1 1 0] and . A self-catalytic vapor–liquid–solid growth mechanism is proposed to describe the growth process of the branched SnO₂ nanowire junctions.     

Effects of branching characteristics and copolymer composition distribution on non-isothermal crystallization kinetics of metallocene LLDPEs

The effects of branch content (BC) and copolymer composition distribution (CCD) on the non-isothermal crystallization kinetics of metallocene m-LLDPEs were studied using modified Avrami analysis, modulated differential scanning calorimetry (MDSC), and Crystaf. Several m-LLDPEs and an m-HDPE - all having comparable M_w and PDI - were experimented. In addition, a ZN-LLDPE was used for comparison purposes. The branch content, unlike the used cooling rates (2-6 °C/min), significantly affected the crystallization behavior. Crystallization peak temperature, , decreased linearly with increasing BC. All the m-LLDPEs showed primary and secondary crystallizations. The secondary crystallization showed to be more pronounced at high BC. The primary crystallization Avrami parameter n for m-HDPE ranged between 3.72 and 4.50, indicating spherulitic crystal growth whereas that for the m-LLDPEs, varied from 2.02 to 5.70. The ZN-LLDPE (having broader composition distribution) offered higher values of and than the m-LLDPEs with similar BC, M_w, and PDI. It, unlike the m-LLDPEs and m-HDPE, fairly agreed with the crystallization kinetic model proposed by Liu et al. The lamella thickness of the m-LLDPEs, L, calculated as per Gibbs-Thomson equation, showed to be in the range 2-16 nm, depending on BC and it decreased approximately following the relationship: L (nm) = 15.0 e^{(−0.0498BC)}.     

A branch and bound based heuristic for makespan minimization of washing operations in hospital sterilization services

In this paper, we address the problem of parallel batching of jobs on identical machines to minimize makespan. The problem is motivated from the washing step of hospital sterilization services where jobs have different sizes, different release dates and equal processing times. Machines can process more than one job at the same time as long as the total size of jobs in a batch does not exceed the machine capacity. We present a branch and bound based heuristic method and compare it to a linear model and two other heuristics from the literature. Computational experiments show that our method can find high quality solutions within short computation time.     

APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.     

激光大气传输相位不连续点的时空演化特征的数值计算

 利用激光大气传输4维程序对激光大气传输相位不连续点的时空演化特征进行了数值计算。仿真计算了相位不连续点随光波传输的产生和湮灭过程,以及某一固定传输位置处,畸变光场内的相位不连续点随时间的变化情况。计算结果表明,相位不连续点是随着波前运动的,并且可以成对地产生或湮灭;当传输路径中的某一位置固定时,垂直于传播方向的畸变光场内的相位不连续点所在的位置随时间的变化是不确定的,但在传输条件一定的情况下,该位置处的相位不连续点数目的统计平均值是可以确定的。