Some exact expressions for the mean and higher moments of functions of sample moments

Examples of exact expressions for the moments (mainly of the mean) of functions of sample moments are given. These provide checks on alternative developments such as asymptotic series for n, and simulation processes. Exact expressions are given for the mean of the square of the sample coefficient of variation, particularly in uniform sampling; Frullani integrals studied by G. H. Hardy arise. It should be kept in mind that exact results for (joint) moment generating functions (mgfs) are of interest as they produce a means of obtaining exact results for (cross) moments—including moments with negative indices. Thus an exact expression for the joint mgf of the 1st two noncentral moments can be used to obtain the mean of the (c.v.)² (but not for the mean of the c..). A general expression is given for the moment generating function of the sample variance. The limitations of Fisher's symbolic formula for the characteristic function of sample moments (or more general statistics) are noted.This research was sponsored by the Applied Mathematical Sciences Research program, Office of Energy Research, U. S. Department of Energy under contract DE-AC0584OR21400 with the Martin Marietta Energy Systems. Inc.     

Comparative Characteristics of Some Physicochemical Properties of Azoles

We have carried out a correlation analysis of some physicochemical characteristics of pyrrole, pyrazole, imidazole, triazole, and tetrazole, calculated by the semiempirical quantum-chemical AM1 method. We have found the linear dependences of the ionization potential, the dipole moment, and the acidity on the -electron excess, and also the dependence of the ionization potential on the enthalpy of formation of the studied azoles.     

Solvatochromism of 3-[2-(aryl)benzoxazol-5-yl]alanine derivatives

The photophysical properties of N-Boc-3-[2-(9-anthryl)benzoxazol-5-yl]-l-alanine methyl ester (BoxAnt) and N-Boc-3-[2-[4-(9′-(10′-butyl)anthryl)phenyl]benzoxazol-5-yl]-l-alanine methyl ester (BoxPhAnt) were studied in a series of solvents. Their absorption spectra are less sensitive to the solvent polarity than the corresponding fluorescence spectra which show a pronounced solvatochromic effect leading to large Stokes shifts. Using an efficient solvatochromic method, based on the empirical solvent polarity parameter , a large change of the dipole moment on excitation for BoxPhAnt has been found. From an analysis of the solvatochromic behaviour of the absorption and fluorescence spectra in terms of bulk solvent polarity functions, f(_r, n) and g(n), a larger excited-state dipole moment (about 8 D, ψ = 56) was obtained for BoxPhAnt than for BoxAnt (about 3 D, ψ = 0). Both applied methods gave similar values of the excited-state dipole moments for both compounds studied.     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-II hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size, we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively, and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.     

Two-worker blocking congestion model with walk speed m in a no-passing circular passage system

This paper introduces a blocking model and closed-form expression of two workers traveling with walk speed m (m = integer) in a no-passing circular-passage system of n stations and assuming n = m + 2, 2m + 2, …. We develop a Discrete-Timed Markov Chain (DTMC) model to capture the workers’ changes of walk, pick, and blocked states, and quantify the throughput loss from blocking congestion by deriving a steady state probability in a closed-form expression. We validate the model with a simulation study. Additional simulation comparisons show that the proposed throughput model gives a good approximation of a general-sized system of n stations (i.e., n > 2), a practical walk speed system of real number m (i.e., m ? 1), and a bucket brigade order picking application.     

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

Stark Hole-Burning Spectroscopy of Cresylviolet Perchlorate in Amorphous Hosts

Stark hole-burning spectroscopy is used to investigate the effective dipole moment change of cresylviolet perchlorate (CVP) in various glass and polymer hosts such as ethanol:methanol (EM), polyvinyl alcohol (PVA), poly (2-hydroxyethyl) methacrylate (PHEMA), polyvinylbutyral (PVB), and formamide. The strong correlation between effective dipole moment change of the guest molecule and the holeburning efficiencies of the host matrices illustrates the sensitivity of the dipole moment change as a direct measure of guest-host interactions. Hole-burning is found to be more efficient as the dipole induced reaction field increases. This relationship is discussed in terms of the unusual hole-burning mechanism suggested for this molecule. The effective dipole moment change of cresylviolet perchlorate ranges from 0.14 to 0.59 Debye.