Cost operator algorithms for the transportation problem

A primal transportation algorithm is devised via post-optimization on the costs of a modified problem. The procedure involves altering the costs corresponding to the basic cells of the initial (primal feasible) solution so that it is dual feasible as well. The altered costs are then successively restored to their true values with appropriate changes in the optimal solution by the application of cell or area cost operators discussed elsewhere. The cell cost operator algorithm converges to optimum within (2T – 1) steps for primal nondegenerate transportation problems and [(2T + 1) min (m, n)] – 1 steps for primal degenerate transportation problems, whereT is the sum of the (integer) warehouse availabilities (also the sum of the (integer) market requirements) andm andn denote the number of warehouses and markets respectively. For the area cost operator algorithm the corresponding bounds on the number of steps areT and (T + 1) min (m, n) respectively.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie—Mellon University, under Contract N00014-67-A-0314-0007 NR 047-048 with the U.S. Office of Naval Research.     

STATISTICS OF A NOVEL CLASS OF LIQUID CRYSTAL POLYMERS

A novel class of the liquid crystal polymers with mesogens laterally attached to flexible main chain backbones has been synthesized recently by us. While the flexible backbones tend to take configuration of maximum entropy the mesogenic side groups tend to orientate because of the anisotropie soft dispersion forces. A mean field theory is presented to describe the competition between these two trends which makes it possible for this class of polymers to show anisotropic (liquid crystal) phase within certain temperature range where the polymer main chains and the side chain mesogens will take approximately parallel arrangement, which is different from the normal side chain liquid crystal polymers. The temperature range of the liquid crystal phase, its ordering and phase transition all depend on the flexibility of the backbone, the strengthof the anisotropic forces of the side groups and the hinge elasticity. The results show that the liquid crystalisotropic phase transition is of the first order. The phase diagram, i. e. the dependence of the transition temperature on the structure of the polymers is also given.     

Comparative study of the instrumental couplings of high performance liquid chromatography with microwave-assisted digestion hydride generation atomic fluorescence spectrometry and inductively coupled plasma mass spectrometry for chiral speciation of selenomethionine in breast and formula milk

A comparison of chiral separation and analysis of selenomethionine in breast and formula milk, using high performance liquid chromatography (HPLC) on a glycopeptide teicoplanin-based chiral stationary phase (Chirobiotic T), coupled to atomic fluorescence spectrometry (AFS) and inductively coupled plasma (ICP) MS detectors has been performed. The coupling HPLC-microwave-assisted digestion hydride generation requires on-line post-column analytes treatment, and a severe sample clean-up for fat and proteins elimination using centrifugation and ultrafiltration. Underivatized -selenomethionine enantiomers were completely resolved in 10 min using unbuffered water mobile phase at 1 ml min⁻¹ flow. Good selectivity and sensitivities (detection limits 3.1 and 3.5 ng ml⁻¹ as Se for - and -selenomethionine, respectively) were obtained, and method robustness and simplicity, together to the low cost of AFS detector, makes it suitable for infant milk routine analysis. HPLC–ICP-MS coupling exhibits very low detection limits (0.9 ng ml⁻¹, as Se) for each -selenomethionine enantiomers, but the method suffers from matrix influence, that produces a poor S/N ratio and low reliability.

The methods were applied to breast and formula milk samples with recoveries of 80% of the total selenium presence, which is attributable to the existence of other unknown species. -Selenomethionine was the only isomer present in breast milk, but a 30% of -selenomethionine was also detected in formula milk.     

d9配合物MOSE曲面和几何构型的研究

d~9电子构型的金属离子所形成的配合物几何构型一般为拉长八面体或平面正方形,晶体场理论和角重叠模型都对此作出了较满意的描述,但就该电子构型的中心离子与指定配体配位时易形成配合物的配位数、配体所处的位置等问题,至今尚无满意解释.本文通过分子轨道稳定化能(MOSE)的计算及其曲面的绘制,形象地解释了上述问题.     

The Mathematical Theory of Ito Diffusions on Hypersurfaces, with Applications to NMR Relaxation Problems

A mathematical framework for translational Brownian motion on hypersurfaces is presented, using an imbedding of the surface and Ito diffusions in the ambient space. This includes a survey of Ito calculus and differential geometry. Computational methods for time correlation functions relevant to spin relaxation studies on curved interfaces are given, and explicit calculations of time correlation functions and order parameters for a Rippled surface are presented.     

Structural Isomers of Bis(diphenylarsino)methane‐dichloroplatinum(II)

From a range of preparative methods, three geometric isomers of bis(diphenylarsino)methane‐dichloroplatinum(II) have been isolated, viz. cis‐PtCl₂(dpam), trans, trans‐Pt₂Cl₄(dpam)₂ and cis, trans‐Pt₂Cl₄(dpam)₂. Their structures were determined by single‐crystal X‐ray diffraction.     

High pressure studies on new chiral compounds exhibiting TGBA phase

Effects of high pressures on phase sequences of the two homologousn=16 andn=18 of the (3-fluoro-4 ((R) or (S)-methylheptyloxy) 4, (4-fluoro benzoyloxy) tolans) series have been studied. Both compounds exhibit the new twisted Smectic A phase called Twist Grain Boundary TGB_A phase. The high pressure experiments were performed by thermobarometric analysis. The order of the transitions (first or second) have been determined in respect to pressure and temperature. The pressure-temperature phase diagrams show that the TGB_A phase is stabilized by increasing pressure; an inducedN ^* phase appears under high pressure for n=18 leading to the observation of TGB_A-N ^*-I triple point.     

静止化学反应界面：理论和验证

在静止中和反应界面的基础上，提出了静止化学反应界面的概念，导出了一些静止化学反应界面方程。这些方程显示：为了建立稳定的静止化学反应界面，正、负反应离子（比如氢离子和氢氧根离子）的迁移数必须相等。分析表明，方程的理论预测与下列事实定量吻合：（１）已建立的静止中和反应界面的实验，（２）基于Ｋｏｈｌｒａｕｓｃｈ′ｓ调整函数的计算机模拟。     

A characterization of brownian motion in a lipschitz domain by its killing distributions

Let (Y _t, Q^x) be a strong Markov process in a bounded Lipschitz domainD with continuous paths up to its lifetime , and let (X _t, P^x) be a Brownian motion inD. IfY _– exists in D andQ ^x(Y_– C)=P^x(X_– C) for all Borel subsetsC of D and allx, thenY is a time change ofX.     

Probability theory and polymer physics

This study applies the theory of stochastic processes to the equilibrium statistical physics of polymers in solution. The topics treated include random copolymers and randomly branching polymers, with self-consistent mean field effects. A new and more natural way of dealing with Boltzmann weighting is discussed, which makes it possible from the beginning of a calculation to consider only the physical polymer conformations. We also show that in general the random copolymer problem can be reduced to the ordinary polymer problem, and treat the self-consistent field problem for a general branching polymer.