单形内任一点的一个含参不等式

本文证明了与ｎ维单形内部任意一点有关的一个含参数不等式,并应用它得到了几个与ｎ维单形体积有关的不等式。     

改进的单纯形优化法用于混合稀土的同时测定

本文应用改进的单纯形优化法较好地弥补了目前在分析化学计量学中得到广泛应用的卡尔曼滤波法所存在的不足，交法应用于混合稀土的同时测定中，获得了满意的结果，结果准确度较卡尔滤波法的有显著的提高。     

Synthesis and reactions of 2-deoxy-β-D-ribofuranosyl derivatives of 3-aryl-4H-pyrrolo[2,3-d]pyrimidin-4-imines

Summary 3-Aryl-7-(2-deoxy--D-erythro-pentofuranosyl)-3,7-dihydro-4H-pyrrolo[2,3-d]-pyrimidin-4-imines (4) as well as 4-arylamino-7-(2-deoxy--D-erythro-pentofuranosyl)-2-methyl-5-phenyl-7H-pyrrolo[2,3-d]pyrimidines (7) have been synthesized by glycosylation of the sodium salt of the corresponding nucleobases with 2-deoxy-3,5-di-O-p-toluyl--D-erythro-pentofuranosyl chloride (2) followed by subsequent deprotection with sodium methoxide in methanol. The deprotected nucleoside4 undergoes aDimroth rearrangement on reflux for 24 h in water to furnish the 4-arylamino nucleoside7.

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Synthese und Reaktionen von 2-Deoxy--D-ribofuranosylderivaten von 3-Aryl-4H-pyrrolo[2,3-d]pyrimidin-4-iminen

Zusammenfassung 3-Aryl-7-(2-deoxy--D-erythro-pentafuranosyl)-3,7-dihydro-4H-pyrrolo[2,3-d]-pyrimidin-4-imine (4) und 4-Arylamino-7-(2-deoxy--D-erythro-pentofuranosyl)-2-methyl-5-phenyl-7H-pyrrolo[2,3,-d]pyrimidine (7) wurden durch Glycosylierung der Natriumsalze der entsprechenden Nucleosidbasen mit 2-Deoxy-3,5-di-O-p-toluyl--D-erythro-pentofuranosylchlorid (2) und anschließende Entfernung der Schutzgruppe mit Natriummethoxid in Methanol hergestellt. Das entschützte Nucleosid4 ergibt bei 24-stündigem Erhitzen in Wasser unter Rückfluß über eineDimroth-Umlagerung das 4-Aminonucleosid7.

     

单纯形算法动态优化毛细管胶束电动色谱分离体系

采用控制加权可变步长单纯形算法对ＰＴＣ氨基酸的毛细管胶束电动色谱分离体系进行动态优化。寻优过程中同时考虑背景电解质的ｐＨ值、十二烷基硫酸钠浓度和有机添加剂浓度对体系分离效果的影响。分别使用Ｌｏｎｇ系数法和均匀设计表法确定初始单纯形顶点对分离体系进行动态优化。优化结果使１７种ＰＴＣ氨基酸获得了比较满意的分离。     

Fitting complex potential energy surfaces to simple model potentials: application of the simplex-annealing method

A stochastic method of optimization, which combines simulated annealing with simplex, is implemented to fit the parameters of a simple model potential. The main characteristic of the method is that it explores the whole space of the parameters of the model potential, and therefore it is very efficient in locating the global minimum of the cost function, in addition to being independent of the initial guess of the parameters. The method is employed to fit the complex intermolecular potential energy surface of the dimer of water, using as a reference the spectroscopic quality anisotropic site-site potential of Feller et al. The simple model potential chosen for its reparameterization is the MCY model potential of Clementi et al. The quality of the fit is assessed by comparing the geometry of the minimum, the harmonic frequencies, and the second virial coefficients of the parameterized potential with the reference one. Finally, to prove more rigorously the robustness of this method, it is compared with standard nonstochastic methods of optimization.     

Simplex-optimization with a new criterion. Applications to dual-column ion chromatography

A new optimization criterion for chromatography is presented. It was designed to evaluate the quality of chromatograms in a way similar to human estimation. Selectivity, efficiency, and time of analysis as well as the number of peaks were taken into account. The criterion has been tested in comparison with expert estimations and some modern criteria. A better agreement of the new criterion with human estimation of chromatographic quality compared to some literature criteria is shown. A number of successful optimization runs has been performed using the criterion together with simplex optimization.     

线性规划中大M法的参数M估值问题

在线性规划的单纯形法中,为求初始的可行基有著名的大M法,即惩罚因子法.在通常的运筹学教材中,只说明当M充分大时,大M法是有效的,并没有给出参数M的确切估计值.现给出一个确定的常数M0,并证明当M>M0时,大M法收敛于原问题的最优解.     

第一阶段原有单纯形和对偶单纯形算法的计算比较

线性最优化广泛应用于经济与管理的各个领域.在线性规划问题的求解中,如果一个初始基本可行解没有直接给出,则常采用经典的两阶段法求解.对含有"≥"不等式约束的线性规划问题,讨论了第一阶段原有单纯形法和对偶单纯形法两种算法形式,并根据第一阶段问题的特点提出了改进的对偶单纯形枢轴准则.最后,通过大规模数值试验对两种算法进行计算比较,结果表明,改进后的对偶单纯形算法在计算效率上明显优于原有单纯形算法.     

一类条件不等式的控制证明与应用

通过判断相关函数的Schur凸性、Schur几何凸性和Schur调和凸性,证明并推广了一类条件不等式,并据此建立了某些单形不等式.