Quasi-compactness and absolutely continuous kernels

We show how the essential spectral radius r _e (Q) of a bounded positive kernel Q, acting on bounded functions, is linked to the lower approximation of Q by certain absolutely continuous kernels. The standart Doeblin’s condition can be interpreted in this context, and, when suitably reformulated, it leads to a formula for r _e (Q). This results may be used to characterize the Markov kernels having a quasi-compact action on a space of measurable functions bounded with respect to some test function, when no irreducibilty and aperiodicity are assumed.      

Selectively reductive cleavage of the protected taxol side chain with sodium borohydride

During the course of our studies on the taxol chemistry,we have ever tried thereductive cleavage of the acotyl group at 20-C in compound 1a~(1,2) with the hydroxylgroup assistance at 4-C by sodium borohydride. However, the major product 2a~2(27%)still had the acetyl group at 20-C and the signal for the 10-C proton at 6.61 ppm(s)was shifted to 6.31 ppm(d, J=3.79 Hz). A new doublet signal at 3.62 ppm(d, J=3.80     

连续时间遗传算法模型及其强收敛性分析

本文在隐马尔可夫链的框架下利用隐马尔可夫链{Xt:t∈[0,∞)}的观测链的概率分布提出一个连续化遗传算法模型，并给出其一个强收敛结果，讨论了其离散骨架的性质。     

具有苯烷基侧链的芳香液晶聚酯的合成及性质

以熔融缩聚方法全盛了具有苯烷基侧链取代的全芳香液晶聚酯，用TG，DSC，热台偏光显微镜研究了聚酯的热性能，并讨论了取代基对聚酯热性能的影响，所有合成的聚酯均为热致型液晶，且具有较低的相转变温度。特别是当聚对苯二甲酸对苯二酚酯的两个苯环上分别取代了叔丁基和苯烷基，或取代了两个苯烷基侧链后，聚酯的熔融温度下降到225℃以下，并可在室温下溶于普通的有机溶剂中。     

Two machine open shop scheduling problem to minimize an arbitrary machine usage regular penalty function

The paper present a linear-time algorithm for solving the two machine open shop scheduling problem to minimize an arbitrary regular penalty function depending on the lengths of periods during which the machines are used. Both the preemptive and the nonpreemptive cases of the problem are considered.     

Open shop problems with unit time operations

We show that them-machine open shop problem in which all operations have unit processing times can be polynomially transformed to a special preemptive scheduling problem onm identical parallel machines. Many results published recently as well as some new results are derived by using this transformation. The new results include solutions of open problems mentioned in a recent paper by Kubiak et al. p]A similar relationship is derived between no-wait open shop problems with unit time operations andm-machine problems with jobs having unit processing times.This work was supported by Deutsche Forschungsgemeinschaft (Project JoPTAG).     

Homolytic cyclization of 1,3-propanedithiol to 1,2-dithiolane in the presence of 2,5-dimethyl-2,4-hexadiene

2,2-Diethyl-1,3-propanedithiol undergoes cyclization to 4,4-diethyl-1,2-dithiolane upon interaction with 2,5-dimethyl-2,4-hexadiene in benzene in the presence of azodiisolbutyronitrile. The reaction proceeds according to the radical chain mechanism. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2078–2080, October, 1998.     

Nonlinear elastic waves in a monatomic chain with nonlinear interaction

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A dual strategy for solving the linear programming relaxation of a driver scheduling system

A Mathematical Programming model of a driver scheduling system is described. This consists of set covering and partitioning constraints, possibly user-supplied side constraints, and two pre-emptively ordered objectives. The previous solution strategy addressed the two objectives using separate Primal Simplex optimisations; a new strategy uses a single weighted objective function and a Dual Simplex algorithm initiated by a specially developed heuristic. Computational results are reported.