Machine assignment in a nonlinear multi-product flowline

A group of machines for processing a set of jobs in a manufacturing system is often located in a serial line. An efficient strategy for locating these machines such that the total travel distance or the cost of transporting the jobs is minimized is desired. In this research, the assumption of a linear line with equally spaced machine location is relaxed. This research addressed problems of locating unique machines. It is found that the machine distances possess unique properties in this type of a problem. Utilizing these properties, heuristic strategies are proposed to obtain efficient solution where optimal methods are expected to be computationally prohibitive. A lower bound for the optimum solution is also proposed. Results are encouraging.     

2,2’—二硫代双(4,6—二叔丁基苯酚)的晶体和分子结构

一种塑解剂经高压液体色谱分离制备出主要成份2,2′—二硫代双(4,6二叔丁基苯酚)。由质谱分析得到分子量为474化学式为C_(28)H_(2)O_2S_2、晶体呈现孪生。基体单晶属三斜晶系,空间群为(?)PI(NO.2),晶体结构用直接法解出,=0.07。研究结果表明该分子是二硫代酚类化合物。在EI场中,S—S键断裂是主要断裂过程。晶体中,分子的一个环上的羟基是无序分布的。羟基与最邻近的硫原子形成氢键。     

THE INVERSE EIGENPROBLEM WITH RANK-ONE UPDATING AND ITS STABLITY

Let ∑, Г be two n-by-n diagonal matrices with σi,γi as their diagonals. For the inverse eigenvalue problem: look for y∈Rn such that Г + yyT is similar to ∑, we prove thatu also the sufficient condition for the solvability of this inverse problem. Its solution (set) is given explicitly. In some case, the problem is unstable. But we prove that the sums of the square of some contigious components keep stable, i.e., small sum keeps small, large sum has a small relative perturbation, see Theorem 3.     

The Organization of Interaction Between Oil Refineries

The paper deals with the appropriate form of interaction between two refineries with different demand patterns. This problem can be formulated as finding a decentralized solution of linear programming problems linked by buying and selling activities. The complete problem is first solved for central values of product demands and costs and revenues. The structure of the basis then determines the organization of the interaction in terms of which unit sets quantities and which prices, or whether centralized decisions should be made. If, for expected values of product demand and costs, the structure of the basis is the same then the related organization of trading can be used for day-to-day transactions. For a well-known oil refinery model it is found that, for fairly large demand variations, decentralized interaction is effective, but that the structure of the basis changes easily with crude price variations, and that simulations did not converge for these variations.     

Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Studies on self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals

The use of Cu-doped (K_0.5Na_0.5)_0.2(Sr_0.61Ba_0.39)_0.9Nb₂O₆ as self-pumped phase conjugators using internal reflection is reported. Reflectivities as high as 63% at 5145.5 nm and 60% at 632.8 nm were realized. It was found that the photorefractive response changes significantly at different doping concentration. The responses of the crystals to the laser wavelength, incident angle and dopant concentration are studied.     

Separation in distributive congruence lattices

We define separable sets in algebraic lattices. For a finitely generated congruence distributive variety V \mathcal{V} , we show a close connection between non-separable sets in congruence lattices of algebras in V \mathcal{V} and the structure of subdirectly irreducible algebras in V \mathcal{V} . We apply the general results to some lattice varieties.     

Mother-to-child transmission of HIV: a simulation-based approach for the evaluation of intervention strategies

Mother-to-child transmission (MTCT) of HIV is the most significant source of HIV infection in children below the age of 15 years. In 2000 alone, about 600 000 new infections occurred, the vast majority from mothers living in developing countries who were not aware of their HIV-positive status. To date, at least 4.3 million children have died from AIDS. In this paper, we discuss the development of an operational model that can be used to evaluate intervention options for the prevention of MTCT of HIV. The problem was approached by defining suitable pregnancy risk groups, prevention options and the required model outputs to evaluate different intervention strategies. The method chosen to approach the problem was a discrete-event, three-phase simulation, built in Visual Basic, with a stochastic semi-Markov structure. The developed model takes individual pregnant women through each stage of their pregnancy, labour and birth. Different intervention strategies may be modelled at any time, including short-course antiretroviral drugs and cessation of breastfeeding. The model is demonstrated with data from Botswana, which has one of the highest HIV-infection rates in the world.