A Predictor–Corrector Algorithm for QSDP Combining Dikin-Type and Newton Centering Steps

Recently, we have extended SDP by adding a quadratic term in the objective function and give a potential reduction algorithm using NT directions. This paper presents a predictor–corrector algorithm using both Dikin-type and Newton centering steps and studies properties of Dikin-type step. In this algorithm, when the condition K(XS) is less than a given number K ₀, we use Dikin-type step. Otherwise, Newton centering step is taken. In both cases, step-length is determined by line search. We show that at least a constant reduction in the potential function is guaranteed. Moreover the algorithm is proved to terminate in O log(1/)) steps. In the end of this paper, we discuss how to compute search direction (X,S) using the conjugate gradient method.     

A Study of the Equivalence of the BLUEs between a Partitioned Singular Linear Model and Its Reduced Singular Linear Models

Abstract Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ² V, where σ² is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X ₁ : X ₂) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ ₁: β′₂ )′ with β₁ and β₂ being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased estimators of M ₂ X ₁β₁under the model and its best linear unbiased estimators under the reduced linear models of are given, where M ₂ = I -X ₂ X ₂ ⁺ . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of M ₂ X ₁β₁ under the model and those under its reduced linear models are established. Lastly, we also study the connections between the model and its linear transformation model. *This work is supported by the National Natural Science Foundation of China, Tian Yuan Special Foundation (No. 10226024), Postdoctoral Foundation of China and Lab. of Math. for Nonlinear Sciences at Fudan University. This research is supported in part by The International Organizing Committee and The Local Organizing Committee at the University of Tampere for this Workshop **The work is supported in part by an NSF grant of China. Results in this paper were presented by the first author at The Eighth International Workshop on Matrices and Statistics: Tampere, Finland, August 1999     

Estimation with Sequential Order Statistics from Exponential Distributions

The lifetime of an ordinary k-out-of-n system is described by the (n–k+1)-st order statistic from an iid sample. This set-up is based on the assumption that the failure of any component does not affect the remaining ones. Since this is possibly not fulfilled in technical systems, sequential order statistics have been proposed to model a change of the residual lifetime distribution after the breakdown of some component. We investigate such sequential k-out-of-n systems where the corresponding sequential order statistics, which describe the lifetimes of these systems, are based on one- and two-parameter exponential distributions. Given differently structured systems, we focus on three estimation concepts for the distribution parameters. MLEs, UMVUEs and BLUEs of the location and scale parameters are presented. Several properties of these estimators, such as distributions and consistency, are established. Moreover, we illustrate how two sequential k-out-of-n systems based on exponential distributions can be compared by means of the probability P(X < Y). Since other models of ordered random variables, such as ordinary order statistics, record values and progressive type II censored order statistics can be viewed as sequential order statistics, all the results can be applied to these situations as well.     

Characterization of stress degradation products of amodiaquine dihydrochloride by liquid chromatography with high‐resolution mass spectrometry and prediction of their properties by using ADMET Predictor™

The degradation behavior of amodiaquine dihydrochloride, an antimalarial drug, was investigated in solution as well as solid states. The drug was subjected to hydrolytic, photolytic, oxidative, and thermal stress conditions, according to International Conference on Harmonization guideline Q1A(R2). It showed extensive hydrolysis in acidic, alkaline, and neutral solutions both with and without light, while it proved to be stable to thermal and oxidative conditions. In total, six degradation products were formed, which were separated on a C8 column, employing a gradient reversed‐phase high‐performance liquid chromatography method in which acetonitrile and 10 mM ammonium formate (pH 3.0) were used in the mobile phase. To characterize the degradation products, mass fragmentation behavior of the drug was established by direct infusion of solution to quadrupole time‐of‐flight and multiple‐stage mass spectrometry systems. Liquid chromatography with high‐resolution mass spectrometry studies were subsequently carried out on the stressed samples using the same gradient high‐performance liquid chromatography method employed for the separation of the degradation products. Hydrogen/deuterium exchange studies were additionally conducted to determine the number of labile hydrogen atoms. The degradation pathway of the drug was delineated, justified by mechanistic explanation. Lastly, ADMET Predictor™ software was employed to predict relevant physicochemical and toxicity data for the degradation products.     

A Re‐Examination of Sharpe's Ratio for Log‐Normal Prices

The purpose of this paper is to examine the exact properties of Sharpe's ratio when prices are log‐normal. Depending on the definition of returns, different expressions are formed for unbiased estimators of Sharpe's ratio.     

复合材料层合壳有限元分析的预测-修正法

对于复合材料层合壳的有限元分析，本文根据Reissner-Mindlin型的全局位移场给出了一个预测一修正法。首先按照一般的有限元分析过程(没有引入剪切修正系数)计算出全局响应(如挠度，频率和屈曲载荷等)的预测值；然后利用Lagrange插值构造横向剪应力的一般形式，使得满足层间连续和表面上为零的条件，通过最小二乘法拟合三维应力平衡方程获得横向剪应力；最后在单元上计算和引入剪切修正系数，再经过有限元分析计算出全局响应的修正值。     

两个线性模型间最优线性无偏预测的等价性

设M1和M2是两个带有预测量的线性模型,通过使用矩阵秩方法,本文给出了模型M1下预测量的最优线性无偏预测同时也是模型M2下的最优线性无偏预测的充分必要条件.作为这个结果的应用,我们给出了两个线性混合模型间最优线性无偏预测等价性的充分必要条件.     

A fractional order HIV/AIDS model based on the effect of screening of unaware infectives

In this paper, a fractional order model for the spread of human immunodeficiency virus (HIV) infection is proposed to study the effect of screening of unaware infected individuals on the spread of the HIV virus. For this purpose, local asymptotic stability analysis of the disease‐free equilibrium is investigated. In addition, the model is studied for different values of the fractional order to show the relation between the variations of the reproduction number and the order of the proposed model. Finally, numerical solutions are simulated by using a predictor‐corrector method to illustrate the dynamics between susceptible individuals and unaware infected individuals.     

On one twoepoch linear model with the nuisance parameters

The optimum linear estimators of the useful mean value parameters within a linear regression model with the stable and variable parameters and with the nuisance parameters are derived including their characteristics of accuracy. Some verification of theoretical results is presented.      

两种近似计算GM(1,1)参数的有效方法

给出了两种计算灰色模型参数的新方法,并证明通过这些方法所求的预测公式均具有白化指数律重合性,伸缩变换预测公式具有形式不变性,具有齐次性(或称具有伸缩变换一致性).并通过实例展示了方法的简易性和有效性.