Asymptotic expansions of the distributions of some test statistics

Summary A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as the Wald and Rao statistics under both the null and alternative hypotheses are obtained. The powers of these statistics are compared and its is shown that for special structures of parameters some statistics have same power in the sence of order . The results obtained are applied for testing the hypothesis about the covariance matrix of the multivariate normal distribution and it is shown that none of the tests based on the above statistics is uniformly superior. Research supported by the National Science Foundation Grant MCS 830149.     

Equilibrium conformations of polymer chains Part II. Conformons in networks

With regard to the ideal network it is shown that the concept ofN non-interacting polymer chains can be transformed in a problem of non interacting excitations (called conformons) for rubber elasticity. Modelling the interaction on permanent crosslinks as a scattering problem and taking the finite chain length into account, an interpretation of the second Mooney coefficient can be given. There is some evidence that the junctions move by constrained self diffusion.Dedicated to Prof. Dr. W. Ruland on the occasion of his 60th birthday.     

胆汁酸的薄层层析——数理统计法用于层析溶剂系统的选择

本文选择氯仿、乙醇、乙酸乙酯、醋酸和水等五种溶剂作为胆汁酸薄层层析的展开剂,采用正交设计法[L_(16)(4~5)]安排实验,对胆固醇、胆酸、脱氧胆酸、甘氨胆酸、甘氨脱氧胆酸、牛磺胆酸、牛磺脱氧胆酸和卵磷脂等八种化合物的R_f值及层析谱斑点的集中情况,用直观分析和方差分析法处理,得到了单向一次薄层层析全部分离胆汁的溶剂系统,较文献报道方法为佳。     

关于统计学中一个新兴化学分支学科的建立、定义和教育

本文追溯了统计学发展、建立中的大事, 陈述了它的定义及其化学分支发展、建立的梗概; 鉴于化学界对该新兴化学分支学科的名称长期存在争议, 提出了以化学统计学而不以化学计量学为该学科名称的理由, 把化学统计学定义为一个研究有关数据的收集或产生、描述、分析、综合和解释, 以获得新化学知识或信息的学科; 阐明了许多公认属于统计学的方法, 如显著性检验、方差分析、回归和相关, 以及一些尚未认定属于统计学的方法, 如模型建立、蒙特卡罗方法、傅立叶变换和人工神经网络, 都含有统计学5 个内涵中的一个或多个; 探讨了化学统计学家成长的模式, 认为当务之急是把化学统计学纳入化学专业的教学计划, 以培养懂统计学的化学家。     

Wave chaos in quantum systems with point interaction

We study perturbations of the quantized version ₀ of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of ₀ are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf     

Metastable systems driven by colored noise: The stationary state

The influence of the Bardeen-Herring back-jump correlations on the Fermi-Dirac statistics of the one-dimensional nonhomogeneous fermionic lattice gas is studied by the Monte Carlo simulation technique and semianalytically. The resulting distribution is obtained, exhibiting increased population of the lower levels in comparison to the Fermi-Dirac statistics.     

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.     

通用模拟退火用于稳健多元分析校正

模拟退火是一种全局优化算法，具有跨越局部最优点的机制，最小一乘是一种较常用的最小二乘更为稳健的优化准则，更适用于可能偏离正态分布的实际数据集，本文探讨了用最小一乘为准则并利用模拟退火方法同时测定多组分体系的可能性。应用于2－3组分药物体系分析，获得了满意的结果，本文还探讨了改变步长提高模拟退火算法优化精度的方法。     

光催化研究与发展的文献计量分析

对ＣＡ１９６１－１９９６年期间卷双期号期刊中收录的与光催化有关的各种文献进行了详细的统计,结果表明,光催化研究正处于快速的发展期,以消除环境污染为目的应用研究是该快速发展期中的主题,日本,美国,俄罗斯和中国发表文献量居世界前４位。