旋转带电体磁矩计算的若干法则与算例

本文在文献 [1]、[2 ]等的基础上给出关于旋转带电体的磁矩计算的若干法则 ,均以定理形式表达 ,并列表枚举其相关算例     

Analysis of blockwise shrinkage wavelet estimates via lower bounds for no-signal setting

A blockwise shrinkage is a popular procedure of adaptation that has allowed the statisticians to establish an impressive bouquet of asymptotic mathematical results and develop softwares for solving practical problems. Traditionally risks of the estimates are studied via upper bounds that imply sufficient conditions for a blockwise shrinkage procedure to be minimax. This article suggests to analyze the estimates via exact (non-asymptotic) lower bounds established for a no-signal setting. The approach complements the familiar minimax, Bayesian and numerical analysis, it allows to find necessary conditions for a procedure to attain desired rates, and it sheds a new light on popular choices of blocks and thresholds recommended in the literature. Mathematical results are complemented by a numerical study. Supported in part by NSF Grants DMS-9971051 and DMS-0243606.     

Microwave structural studies of organoselenium compounds 1. Microwave spectra, molecular structure, and methyl barrier to internal rotation of dimethyl diselenide

The rotational spectra of nine isotopomers of dimethyl diselenide, CH₃SeSeCH₃, have been measured with a molecular-beam Fourier transform microwave spectrometer. The spectra were complex due to the presence of many isotopomers in natural abundance and the splitting caused by the interactions with two methyl internal rotors. The spectra were assigned and fit to experimental precision to an effective rotational Hamiltonian for molecules with two periodic internal motions. The spectra of the symmetric isotopomers are consistent with a C₂ equilibrium structure. The rotational constants were used to determine the r_s structure of the C-Se-Se-C frame with the results r(SeSe)=2.306(3) Å, r(SeC)=1.954(6) Å, ?(CSeSe)=99.8(2)°, ?(CSeSeC)=85.2(1)°. A barrier to internal rotation of the methyl groups of 395 ± 2 cm⁻¹ was derived from the internal rotation splittings.     

A saxpy formulation for plane rotations

An algorithm for pre- or post-multiplication of a matrix by a plane rotation, using only three vector saxpy operations instead of the four vector operations usually considered necessary, is described. No auxiliary storage for overwriting is required. The method is shown to be numerically stable.     

Sample path analysis of level crossings for the workload process

We examine level crossings of sample paths of queueing processes and investigate the conditions under which the limiting empirical distribution for the workload process exists and is absolutely continuous. The connection between the density of the workload distribution and the rate of downcrossings is established as a sample path result that does not depend on any stochastic assumptions. As a corollary, we obtain the sample path version of the Takács formula connecting the time and customer stationary distributions in a queue. Defective limiting empirical distributions are considered and an expression for the mass at infinity is derived.This research has been supported in part by NSF Grants ECS-8811003 and DDM-8905638.     

嵌套病例对照研究中的两步估计方法（英）

本文讨论嵌套病例对照研究中相对危险率的估计问题，引入了相对危险率的两步估计，并在一般嵌套病例对照抽样的假设下讨论了相对危险率的两步估计的相合性问题，最后给出了几个例子。     

Rotational Motion of a Solute Molecule in a Highly Viscous Liquid Studied byC NMR: 1,3-Dibromoadamantane in Polymeric Chlorotrifluoroethene

The viscosity-dependent retarding effect of a polymeric solvent on the rotation of small solute molecules is investigated by¹³C NMR relaxation measurements. It is found that the relaxation data of 1,3-dibromoadamantane in highly viscous polymeric chlorotrifluoroethene can be explained neither by isotropic nor by realistic anisotropic tumbling in a single environment. The experimental data are rationalized in terms of fast exchange between at least two environments with correlation times differing by up to two orders of magnitude. The study shows that a uniform retardation of molecular tumbling by a polymeric solvent, desirable for shifting the NMR observation window in studies of intramolecular mobility, is not always feasible.     

Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

液相色谱法测定地质样品中的芳香化合物

发展了用液相色谱法检测地质样品中芳香化合物的方法。对观察到的色谱峰进行了定性分析，了该法对油气地球化学勘探的意义。