两类记录值之和的中心极限定理

该文给出了Ｌｏｇｉｓｔｉｃ分布纪录值序列部分和的中心极限定理；对于Ｐａｒｅｔｏ分布纪录值序列的部分和T_n，获得了ｌｎT_n的中心极限定理．这一工作不仅具有概率论的极限理论方面的研究价值，而且在金融、保险等领域也具有相当重要的应用前景．     

n元等比级数

定义了n元等比数列、n元等比级数,给出了它们的通项公式及前n项和.并解决了多元等比级数的敛散性问题,求出了多元等比级数的和.指出了多元等比数列及多元等比级数在特殊情况下与一元等比数列及一元等比级数的一致性.     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

Polynomial expansion of basis sets: Alternatives to fully optimized exponents

Alternatives based on polynomial expansions of gaussian basis set exponents are introduced and evaluated. The formulas presented here outperform methods based upon the even-tempered formula or combinations of it. They closely match the performance of other methods based upon larger polynomial expansions of the logarithm of the exponents using the same or one less parameter per orbital angular symmetry.     

球面稳定同伦中的复合元素α1β1γs的非平凡性

本文证明:当p≥7任意奇素数,3≤s相似文献   

Intrinsic field theory of chemical reactions

An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

A hydrogen rearrangement of formamidine and the solvent effects thereupon

The nature of the 1,3 hydrogen rearrangement of formamidine (H₂N-CH=NH) and the solvent effects on that reaction are studied with ab initio molecular orbital calculations on the basis of the supermolecule model. The reaction path and the motion of the migrating hydrogen atom are traced by using the concept of the intrinsic reaction coordinate (IRC). Four types of orientation of one water molecule to formamidine at the transition state of reaction are examined and the results are discussed from the standpoint of the orbital interactions.     

Vibrational assignment, <Emphasis Type="Italic">ab initio</Emphasis> calculation and normal coordinate analysis of 2,2′-biquinoline

The vibrational wavenumbers and the fundamental modes of 2,2′-biquinoline were obtained by density functional theory (DFT) with the B3LYP functional using the 6-31G(d,p) basis set. The calculated wavenumbers were scaled by a single factor of 0.965 to correct them for vibrational anharmonicity, but the force constants were overestimated. Normal coordinate analysis of the molecule was also carried out by using the force field of the quinoline molecule and the force field parameters of quinoline are shown to be transferable to 2,2′-biquinoline. The potential energy distribution associated with the normal modes is also given. The theoretical wavenumbers are found to be in good agreement with the experimental data.