马尔柯夫链状预测的概率计算及拓广

提出了一种马尔柯夫链状预测中的概率计算新方法：状态划分矩阵法;具有模糊状态的马尔柯夫链的概率计算公式,并用实例计算作了说明。     

广义块Pick型矩阵和带导数的Nevanlinna-Pick矩阵插值问题

建立了广义块Pick型矩阵和块Toeplitz矩阵之间的一种等价关系,并将其用于求解一类带导数的Nevanlinna-Pick矩阵插值问题     

关于渐近中位无偏估计的渐近效率(英文)

本文在几种重要的分布族中,给出了渐近中位无偏估计的渐近效率的一种定义。给出了如下一些结果：在单参数族中,提出了构造渐近有效的渐近中位无偏估计的一种方法,在具有共同支撑集的分布族中,论证了渐近中位无偏有效估计与ＢＡＮ估计之间的等价值;而在非共同支撑集的截断族中,对一般的参数向量函数构造了它们的渐近中位无偏估计,并且计算出了它们的渐近效率。     

关于Van der Waerden猜想的一个注记

给出了（ｘｉｊ）ｎ×ｎ＝（１／ｎ）ｎ×ｎ为ＶａｎｄｅｒＷａｅｒｄｅｎ猜想对应多元函数的一个极小值点的改进证明．     

具有排除体积的两维高分子链的静态标度律

运用四位置模型对具有排除体积的两维高分子链进行ＭｏｎｔｅＣａｒｌｏ模拟和标度分析,为了提高长链的抽样效率,还提出了被称为“链段伸展法”的抽样方法。对单个自避行走链的模拟结果表明,两维ＳＡＷ链有育明显不同于夫规飞行链以及三维ＳＡＷ链的特点。     

Excess and partial excess molar volumes of mixing of N,N-dibutyl-2-ethylhexamide with dodecanol

Excess and excess partial molar volumes of mixing of the system N,N-dibutyl-2-ethylhexylamide (DBEHA) + dodecanol (DDA) were determined at 25, 35, 45, 55 and 65°C. The excess molar volumes exhibit a maxima at each temperature at approximatelyx _DBEHA = 0.3 and a minima close tox _DBEHA = 0.9. The values of the excess volumes in general increase with the temperature. The partial excess molar volumes are calculated from the smoothed data and the results are discussed in the light of postulated amide-alcohol interactions.     

Acetylenic/cyanoacetylenic complexes: simulation of the Titan’s atmosphere chemistry

The structures and energies of the 1:1 acetylene/cyanoacetylene, acetylene/dicyanoacetylene and cyanoacetylene/dicyanoacetylene complexes in solid argon matrices have been investigated using FT-IR spectroscopy and ab initio calculations, at the B3LYP/6-31G** level of theory. For the three complexes, predicted frequency shifts for the L shaped structures, characterized by a hydrogen bond between the nitrogen of the cyano group and the acetylenic proton, were found to be in good agreement with those experimental. Only in the case of acetylene/cyanoacetylene complex, we obtained a second minimum with a T shaped structure characterized by an interaction between the proton of cyanoacetylene and the Π system of acetylene. It appears clearly that HC₃N acts as an electrophile or as a nucleophile in these complexes.     

Matrix-isolation-FTIR spectroscopy with an integrating sphere

The use of an integrating sphere for the measurement of absorption spectra of thin films is described. The thin film (for example a rare gas matrix) is grown directly on the inside surface of the sphere. Multiple reflections inside the integrating sphere lead to significant enhancement of weak absorptions of the film, increasing the sensitivity of such measurements.     

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.     

Volumetric properties of the water + ethylenediamine mixture at atmospheric pressure from 288.15 to 353.15 K

Densities of the water + ethylenediamine binary system were measured at atmospheric pressure over the whole range of compositions at temperatures from 288.15 to 353.15 K using an Anton Paar digital vibrating glass tube densimeter. Density increases with water content. The experimental excess molar volume data have been correlated with the Redlich-Kister equation, and partial molar volumes calculated at infinite dilution for each component.