多目标半定规划的加权中心路径法

对于线性型多目标半定规划问题，引进加权中心路径的概念，并利用单目标半定规划的中心路径法，提出了求解多目标半定规划问题的加权中心路径法，先得型对一个叔向量的有效解，然后在此基础上，提出了通过一次迭代得到对应一定范围内其他任意权向量的有效解的一步修正方法．     

Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).     

HILBERTIAN INVARIANCE PRINCIPLE FOR EMPIRICAL PROCESS ASSOCIATED WITH A MARKOV PROCESS

The authors establish the Hilbertian invariance principle for the empirical process of a stationary Markov process, by extending the forward-backward martingale decomposition of Lyons-Meyer-Zheng to the Hilbert space valued additive functionals associated with general non-reversible Markov processes.     

Central quotients of biautomatic groups

The quotient of a biautomatic group by a subgroup of the center is shown to be biautomatic. The main tool used is the Neumann-Shapiro triangulation of S ^n-1, associated to a biautomatic structure on . Among other applications, a question of Gersten and Short is settled by showing that direct factors of biautomatic groups are biautomatic. Received: October 4, 1994     

Spectral distributions in nuclei: General principles and applications

The subject of spectral distribution methods where one derives and applies the locally smoothed forms of observables in nuclei is briefly reviewed. It is well understood that the local forms (with respect to energy) of the level density function, expectation values and strength densities are Gaussian, linear (or ratio of Gaussians) and a bivariate Gaussian respectively. To accomodate symmetries in the above forms, one has to deal with multivariate distributions in general; for example the angular-momentum (J) decomposition leads to a bivariate Gaussian form for the level density. These results extend to indefinitely large spaces by method of partitioning and they generate convolution forms. The origin of these remarkable spectral properties is discussed and shell model examples are given to substantiate their applicability to nuclear systems. Spectral distribution theory is a practical, usable theory because the smoothed forms are defined in terms of traces of low particle-rank operators, and the trace information propagates. Finally we discuss the application of the spectral methods for a wide range of nuclear problems; these include binding energies, orbit occupancies, electromagnetic andβ-decay sum rule quantities, analysis of operators, symmetry breaking, numerical level densities, and determination of bounds on time-reversal non-invariant part of nucleon-nucleon interaction.     

测定透镜厚度新法及其误差探讨

本文介绍利用景深短、高倍率、大口径的物镜，采用光学方法，对被测透镜上下表面调焦，从而测定其中心厚度的一种新方法，并对测量误差进行了探讨。     

交换自同构群的若干结果

借助于环论的方法研究了具有交换自同构群的有限群,提出了一种新的自同构构作技术,并用之证明了这样的非交换有限群具有非循环的中心子群,以及其每个极大子群的中心子群也都非循环.     

Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

Optimization of culture parameters for production of podophyllotoxin in suspension culture of Podophyllum hexandrum

The root explants of the germinated seedlings of Podophyllum hexandrum were grown in MS medium supplemented with indole acetic acid (IAA) (2 mg/L) and activated charcoal (0.5%), and healthy callus culture was obtained after incubation for 3 wk at 20°C. The cultivation of plant cells in shake flask was associated with problems such as clumping of cells and browning of media, which were solved by the addition of pectinase and polyvinylpyrrolidone. The effect of major media components and carbon source was studied on the growth and podophyllotoxin production in suspension culture. It was found that glucose was a better carbon source than sucrose and that NH₄ ⁺:NO₃ ⁻ ratio (total nitrogen concentration of 60 mM) and PO₄ ³⁻ did not have much effect on the growth and product formation. The relative effect of culture parameters (inoculum level, pH, IAA, glucose, NH₄ ⁺:NO₃ ⁻ ratio, and PO₄ ³⁻) on the overall growth and product response of the plant cell suspension culture was further investigated by Plackett-Burman design. This indicated that inoculum level, glucose, IAA, and pH had significant effects on growth and production of podophyllotoxin. To identify the exact optimum concentrations of these parameters on culture growth and podophyllotoxin production, central composite design experiments were formulated. The overall response equations with respect to growth and podophyllotoxin production as a function of these culture parameters were developed and used to determine the optimum concentrations of these parameters, which were pH 6.0, 1.25 mg/L of IAA, 72 g/L of glucose, and inoculum level of 8 g/L.     

Fractionation and Bioaccessibility of Manganese,Copper, Zinc,Cadmium, and Lead in Commercial Vegetable and Rice Baby Foods Using Inductively Coupled Plasma - Mass Spectrometry (ICP-MS) with Central Composite Design (CCD)

Abstract

Herein the bioaccessibility of Mn, Cu, Zn, Cd, and Pb, selected from essential and toxic elements, was determined in commercially sold vegetable purees intended for infant and toddler consumption. Chemical fractionation studies using water, acetone, diethyl ether, chloroform:methanol, and n-hexane were employed to predict the importance of the protein and lipid parts of a matrix to assess the bioaccessibility data. In addition, in-vitro gastrointestinal digestion was performed to determine the bioaccessibility of the elements using a five level, three factor central composite design (CCD) to maximize the elemental solubility. The total elemental concentrations in all of the fractions were determined by inductively coupled plasma – mass spectrometry (ICP-MS). Based on the consumption of one jar of vegetable/rice-based baby food, Zn was 1.3% of the recommended dietary allowance and Mn was 4.2% of the adequate intake level, while Cu was almost 100% of the adequate intake level. Additionally, Pb was always below the detection limit and Cd was sometimes under the detection limit for the percent bioaccessibility. However, in some samples, Cd was as high as 80% of the tolerable weekly intake level depending on the body weight.