Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming

This paper aims at showing that the class of augmented Lagrangian functions for nonlinear semidefinite programming problems can be derived, as a particular case, from a nonlinear separation scheme in the image space associated with the given problem. By means of the image space analysis, a global saddle point condition for the augmented Lagrangian function is investigated. It is shown that the existence of a saddle point is equivalent to a regular nonlinear separation of two suitable subsets of the image space. Without requiring the strict complementarity, it is proved that, under second order sufficiency conditions, the augmented Lagrangian function admits a local saddle point. The existence of global saddle points is then obtained under additional assumptions that do not require the compactness of the feasible set. Motivated by the result on global saddle points, we propose two modified primal-dual methods based on the augmented Lagrangian using different strategies and prove their convergence to a global solution and the optimal value of the original problem without requiring the boundedness condition of the multiplier sequence.     

Dimension-Independent Estimates on the Densities of Wiener Functionals via the Log-Sobolev Inequality

Using the log-Sobolev inequality, we shall present in this note some estimates on the density of finite dimensional non-degenerate Wiener functionals which are independent on the dimension. We shall take the Gaussian measure as the reference measure, contrary to the customary choice of Lebesgue measure in the literature. As an application, we show that the limit in probability of a uniformly bounded sequence of non-degenerate Wiener functionals has a density with respect to the Gaussian measure.     

Estimation of relative risk using a log-binomial model with constraints

The relative risk/prevalence ratio and odds ratio are very popular in medical research and epidemiological studies. The odds ratio is overused in practice due to its direct relation with the logistic regression. Interpreting the odds ratio in terms of “relative risk” may lead to incorrect inference on the prevalence of certain event. In this paper, we propose to estimate the relative risk using the log-binomial model by maximizing the likelihood with a linear constraint, which can be easily implemented by an existing function, such as “constrOptim” in R. Furthermore, we review other existing methods and compare their performance under a variety of settings using simulated data. We suggest the proposed and COPY methods in practice, based on its performance in the simulations. For illustration, we investigate the vigorous physical activity effects on obesity using data from the National Health and Nutrition Examination Survey, and the treatment effects on lung cancer mortality using data in R.     

矩阵多分裂迭代法的收敛条件

本文给出了求解非奇异线性方程组的矩阵多分裂并行迭代法的一些新的收敛结果.当系数矩阵单调和多分裂序列为弱正则分裂时,得到了几个与已有的收敛准则等价的条件,并且证明了异步迭代法在较弱条件下的收敛性.对于同步迭代,给出了与异步迭代不同且较为宽松的收敛条件.     

Metabonomic study on women of reproductive age treated with nutritional intervention: screening potential biomarkers related to neural tube defects occurrence

Nutritional intervention is effective in reducing the risk of neural tube defects (NTDs). To determine the effects of nutritional supplementation on human metabolism, a metabonomic study was carried out on 96 women of reproductive age. Subjects with nutritional intervention were given fortified wheat flour (containing folic acid, vitamin B₁, vitamin B₂, ferric sodium edetate and zinc oxide) for 8 months. Serum metabolic fingerprinting was detected via ultraperformance liquid chromatography in tandem with time‐of‐flight mass spectrometry (UPLC‐TOF MS), and data acquired was processed by multivariate statistical analysis. The result revealed a significant difference between the control and intervention group. Twenty potential biomarkers, including fructose 6‐phosphate, sphingosine 1‐phosphate, docosahexaenoic acid and hexadecanoic acid, were located and identified by the accurate mass measurement of TOF MS. These compounds are believed to be functionally related to anti‐oxidative competence in vivo. In conclusion, metabonomics study is a valuable approach in exploring the effect mechanism of nutritional intervention on NTD prevention. Copyright © 2010 John Wiley & Sons, Ltd.     

Nanoparticles consisting of optically active helical polymers: Preparation via aqueous catalytic miniemulsion polymerization and the effects of particles size on their optical activity

This article reports a class of nanoscale materials, that is, optically active nanoparticles consisting of helical‐substituted polyacetylenes. Such nanoparticles were prepared via aqueous catalytic miniemulsion polymerization, by which nanoparticles with a wide range of size (diameter: 60–400 nm) can be easily prepared. The nanoparticles could be obtained in quantitative monomer conversions. Large specific rotations and intense circular dichroism effects demonstrated that the nanoparticles possessed large optical activities; moreover, the optical activities were found to increase with a decrease in particle size. From the obtained polymer nanoparticles and with poly(vinyl alcohol) (PVA) as supporting material, composite films were further prepared and also exhibited considerable optical activities. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1661–1668, 2010     

On local regularization for an inverse problem of option pricing

We explore the theoretical and numerical application of local regularization methods to an ill-posed inverse problem arising from financial option pricing. In addition, we provide an algorithm and show results through numerical examples.     

Amorphous hydrogenated carbon synthesized by pulsed laser deposition from cyclohexane

It is demonstrated that a liquid hydrocarbon precursor, cyclohexane, is appropriate for laser-induced carbon deposition. Amorphous hydrogenated carbon films (a-C:H) were deposited by KrF excimer laser irradiation of single-crystal silicon surface immersed under cyclohexane. The technique is simple and easy to operate. IR absorption spectra of the deposited films confirmed the presence of carbon in the diamond phase. Raman and XPS studies showed diamond-like character of the deposited films. Moreover, these two studies provided strong evidence that laser fluence played an important role in the formation of DLC bondings and the quality of the deposited films. Received: 15 September 1998 / Accepted: 5 January 1999 / Published online: 5 May 1999