NMR AND DFT STUDY OF Co-C BOND ACTIVATION MECHANISM IN VITAMIN B_(12) COMPOUNDS

This report focuses on a theoretical study of the cobalt-cabon bond activation mechanism in Vitamin B12, its co enzyme complexes, and model compounds such as cobalamins (Cbl), cobaloximes and cobalt porphyrins. In particular, emphasis is placed on the nucleotide loop and its role in the base on and base off mechanism.     

Learning Theory Estimates via Integral Operators and Their Approximations

The regression problem in learning theory is investigated with least square Tikhonov regularization schemes in reproducing kernel Hilbert spaces (RKHS). We follow our previous work and apply the sampling operator to the error analysis in both the RKHS norm and the L² norm. The tool for estimating the sample error is a Bennet inequality for random variables with values in Hilbert spaces. By taking the Hilbert space to be the one consisting of Hilbert-Schmidt operators in the RKHS, we improve the error bounds in the L² metric, motivated by an idea of Caponnetto and de Vito. The error bounds we derive in the RKHS norm, together with a Tsybakov function we discuss here, yield interesting applications to the error analysis of the (binary) classification problem, since the RKHS metric controls the one for the uniform convergence.     

F+H2→HF+H反应的全量子态分辨的散射动力学研究

利用高灵敏度的氢原子里德堡飞渡时间谱方法研究了 F H_2→HF H 反应碰撞能在5.02kJ/mol 下的交叉分子束反应态态散射动力学.所有在时间飞渡谱中被观测到的谱峰可以归属为 HF 产物的振转态结构.还观测到了明显的 HF(v’=3)前向散射,以及少许的 HF(v’=2)前向散射.     

Modeling Language Evolution

We describe a model for the evolution of the languages used by the agents of a society. Our main result proves convergence of these languages to a common one under certain conditions. A few special cases are elaborated in more depth.     

Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers V_λ^⊗N of an irreducible representation V_λ of a compact connected Lie group G. The weights are allowed to depend on N, and we obtain several regimes of pointwise asymptotics, ranging from a central limit region to a large deviations region. We use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope.     

Hypothesis testing for the generalized multivariate modified Bessel model

In this paper, we consider hypothesis testing problems in which the involved samples are drawn from generalized multivariate modified Bessel populations. This is a much more general distribution that includes both the multivariate normal and multivariate-t distributions as special cases. We derive the distribution of the Hotelling's T²-statistic for both the one- and two-sample problems, as well as the distribution of the Scheffe's T²-statistic for the Behrens–Fisher problem. In all cases, the non-null distribution of the corresponding F-statistic follows a new distribution which we introduce as the non-central F-Bessel distribution. Some statistical properties of this distribution are studied. Furthermore, this distribution was utilized to perform some power calculations for tests of means for different models which are special cases of the generalized multivariate modified Bessel distribution, and the results compared with those obtained under the multivariate normal case. Under the null hypothesis, however, the non-central F-Bessel distribution reduces to the central F-distribution obtained under the classical normal model.     

Reactions of Molecules with Two Equivalent Functional Groups. 5. Anomalous Reactivity of 1,10-Cyclooctadecanedione. Crystal and Molecular Structures of cis,cis-1,10-Diphenyl-1,10-cyclooctadiene and the Stereoisomers of 1,10-Diphenyl-1,10-cyclooctadecanediol(1)

The reaction of the title diketone (3) with phenyl Grignard produces (with rate constant k(1)) the conjugate base (6-M) of 10-hydroxy-10-phenylcyclooctadecanone (6), which is subsequently converted (with rate constant k(2)) to the conjugate base of the title diol, as a mixture of the cis (7, 55%) and trans (8, 45%) isomers. The ratio k(2)/k(1), 2.2 +/- 0.4, indicates that the carbonyl group in 6-M is 4.4 times as reactive as each carbonyl in 3. Competition experiments further demonstrate that the relative rates (per carbonyl) for addition of phenylmagnesium bromide to 3, 10-methylenecyclooctadecanone (11), and cyclopentadecanone (12) are 1.0:0.60:1.92. Possible reasons for this order of reactivity are discussed. Diols 7 and 8 undergo facile double dehydration to form the title diene 13, which is predicted by molecular mechanics calculations to be the most stable of the four possible symmetrical diene isomers. The structures of 7, 8, and 13 were secured by single-crystal X-ray studies.