基础解系的一种算法

文章用矩阵理论得出几个新结论,从而应用新结论得出基础解系的一种算法.     

Comparison of the Diffusion of Aqueous Glycine Hydrochloride and Aqueous Glycine

A Taylor dispersion tube has been used to measure mutual diffusion in aqueous solutions of glycine hydrochloride at 25°C and concentrations from 0.0005 to 0.5 M. Analysis of the dispersion profiles shows that the diffusion of glycine hydrochloride (GlyHCl) produces a subtantial additional flow of hydrochloric acid that is liberated by the dissociation: GlyH⁺ + Cl^- Gly + H⁺ + Cl^-. Diffusion in this system is, therefore, a ternary process described by the equations J ₁(GlyHCl) = – D ₁₁C ₁ – D ₁₂C ₂ and J ₂(HCl) = –D ₂₁C ₁ – D ₂₂C ₂ for the coupled fluxes of total glycine hydrochloride (1) and hydrochloric acid (2) components. The ratio D ₂₁/D ₁₁ of measured diffusion coefficients indicates that up to two moles of HCl are cotransported per mole of GlyHCl. Although protonated glycine diffuses with relatively mobile Cl^– counterions, the main diffusion coefficient of glycine hydrochloride, D ₁₁, is lower than or nearly identical to the diffusion coefficient of aqueous glycine. A model for the diffusion of protonated solutes is developed to interpret this result and the large coupled flows of HCl. Diffusion coefficients are also reported for the aqueous hydrochlorides of 3- and 4-aminobenzoic acids.     

结构相角二阶代数式的应用：Ⅱ.正交空间群二阶式及其应用

以作者在前文中提出的单相角二阶代数式的推导方法为依据,在完成三斜、单斜空间群推导结果的基础上,进而又完成了正交晶系59个空间群二阶式的推导,从而提供了低级晶系(三斜、单斜和正交)全部74个空间群的简明、完备的二阶代数式运算用表。对三个晶体结构进行了相角估算,结果较好。文中提出了代数法应用的新特点,即“一种类型相角可用多种二阶式求得,多种类型相角也可用一种二阶式求算”。     

有限co-H-复形上的同调分解(Ⅱ)

考虑与若干球的一点触空间∨ｌｋ＝１Ｓｎｋ有关的同调分解问题,得到有关结果．然后利用∨ｌｋ＝１Ｓｎｋ上的同调分解获得群［∨ｌｋ＝１Ｓｎｋ,Ｙ］的秩的表达式,即任取∨ｌｋ＝１Ｓｎｋ上的一个同伦可结合的ｃｏ－Ｈ－结构,都有ρ［∨ｌｋ＝１Ｓｎｋ,Ｙ］＝ｋ＞０βｋ（∨ｌｋ＝１Ｓｎｋ）γｋ（Ｙ）     

等导重根特征对的泰勒展开

讨论多参数非亏损特征对的可微性,推导了具有等同一阶偏导数的重根特征的计算公式,进而得到了它们的泰勒开展开式。     

Stochastic dominance with nonadditive probabilities

Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.     

Unusual features of micellar diffusion

Diffusion coefficients of tetradecyltrimethylammonium bromide in aqueous solutions have been determined at 25, 95 and 135 °C using the Taylor dispersion technique. The diffusion coefficient exhibits a minimum at a surfactant concentration above the critical micelle concentration (CMC). The results are interpreted in terms of electrostatic coupling and rapid exchange between micelle, surfactant monomer and counterions.     

Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

凝结热对低阶煤低温氧化过程的影响

选用Pulse Calorimeter仪器，研究了低阶煤在干燥氧气下低温氧化过程的反应热和相对湿度为80％的氮气下凝结热与温度的变化，以研究凝结热对低阶煤低温氧化过程的影响。结果表明,随着温度的上升体系的反应热增加，而凝结热减少。在26℃~60℃的低温下，体系的凝结热明显高于反应热。因此，低温下凝结热是影响低阶煤的低温氧化过程的重要因素。研究还得到了低阶煤在干燥氧气下低温氧化过程的动力学方程及活化能。     

Experimental study of the induced flow birefringence of a suspension of rigid particles at the transition from Couette flow to Taylor vortex flow

The flow birefringence induced in solutions of rigid particles is studied experimentally in the region of the axisymmetrical Taylor vortex flow which arises once the velocity gradient G in the annular gap of a conventional Couette cell reaches a critical value G _c .The measurements are performed for several values of G > G _c and for 10 radial observation points in the annular gap. Solutions of two types of rigid particles are investigated: the first is a suspension of flattened clay particles like bentonite, while the second contains rod-like particles of tobacco mosaic virus (TMV). The variations of the birefringence intensity n and of the extinction angle measured in the domain of the axisymmetrical flow show a different behavior according to the shape of the particle in solution. This fact is confirmed theoretically with a good agreement for the measurements performed with solutions of flat particles.