PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.     

Cavitated bifurcation for composed compressible hyper-elastic materials

The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials is examined. The bifurcation solution for the composed sphere under a uniform radial tensile boundary dead-load is obtained. The bifurcation curves and the stress contributions subsequent to the cavitation are given. The right and left bifurcation as well as the catastrophe and concentration of stresses are analyzed. The stability of solutions is discussed through an energy comparison. Project supported by the National Natural Science Foundation of China (No. 19802012).     

Natural and artificial light-harvesting systems utilizing the functions of carotenoids

Carotenoids are essential pigments in natural photosynthesis. They absorb in the blue–green region of the solar spectrum and transfer the absorbed energy to (bacterio-)chlorophylls, and so expand the wavelength range of light that is able to drive photosynthesis. This process is an example of singlet–singlet energy transfer and so carotenoids serve to enhance the overall efficiency of photosynthetic light reactions. Carotenoids also act to protect photosynthetic organisms from the harmful effects of excess exposure to light. In this case, triplet–triplet energy transfer from (bacterio-)chlorophyll to carotenoid plays a key role in this photoprotective reaction. In the light-harvesting pigment–protein complexes from purple photosynthetic bacteria and chlorophytes, carotenoids have an additional role, namely the structural stabilization of those complexes. In this article we review what is currently known about how carotenoids discharge these functions. The molecular architecture of photosynthetic systems will be outlined to provide a basis from which to describe the photochemistry of carotenoids, which underlies most of their important functions in photosynthesis. Then, the possibility to utilize the functions of carotenoids in artificial photosynthetic light-harvesting systems will be discussed. Some examples of the model systems are introduced.     

统计模型在中文文本挖掘中的应用

本文讨论了中文文本挖掘的三个问题:分词、关键词提取和文本分类。对分词问题,介绍了基于层叠隐马尔可夫模型的ICTCLAS分词法,以及将词与词之间的分隔视为缺失数据并用EM算法求解的WDM方法;对关键词提取问题,提出了贝叶斯因子法,并介绍了使用稀疏回归的CCS方法;对文本分类问题,介绍了根据关键词频率建立分类器的方法,以及先建立主题模型再根据主题概率建立分类器的方法。本文通过两组文本数据对上述方法进行比较,并给出使用建议。     

Computational analysis for the determination of deleterious nsSNPs in human MTHFD1 gene

Single nucleotide polymorphisms (SNPs) are the most common genetic polymorphisms and play a major role in many inherited diseases. Methylenetetrahydrofolate dehydrogenase 1 (MTHFD1) is one of the enzymes involved in folate metabolism. In the present study, the functional and structural consequences of nsSNPs of human MTHFD1 gene was analyzed using various computational tools like SIFT, PolyPhen2, PANTHER, PROVEAN, SNAP2, nsSNPAnalyzer, PhD-SNP, SNPs&GO, I-Mutant, MuPro, ConSurf, InterPro, NCBI Conserved Domain Search tool, ModPred, SPARKS-X, RAMPAGE, FT Site and PyMol. Out of 327 nsSNPs form human MTHFD1 gene, total 45 SNPs were predicted as functionally most significant SNPs, among which 17 were highly conserved and functional, 17 were highly conserved and structural residues. Among 45 most significant SNPs, 15 were predicted to be involved in post translational modifications. The p.Gly165Arg may interfere in homodimer interface formation. The p.Asn439Lys and p.Asp445Asn may interfere in binding interactions of MTHFD1 protein with cesium cation and potassium. The two SNPs (p.Asp562Gly and p.Gly637Cys) might interfere in interactions of MTHFD1 with ligand.     

Tuning the properties of a black TiO2-Ag visible light photocatalyst produced by a rapid one-pot chemical reduction

A highly efficient black TiO₂-Ag photocatalytic nanocomposite, active under both UV and visible light illumination, was synthesized by decorating the surface of 25 nm TiO₂ particles with Ag nanoparticles. The material was obtained via a rapid, one-pot, simple (surfactant and complexing agent free) chemical reduction method using silver nitrate and formaldehyde as a metal salt and reducing agent, respectively. The nanocomposite shows an increase of over 800% in the rate of photocatalytic methylene blue dye degradation, compared to commercial unmodified TiO_2, under UV-VIS illumination. Unlike pure TiO₂, the nanocomposite exhibits visible light activation, with a corresponding drop in optical reflectance from 100% to less than 10%. The photocatalytic properties were shown to be strongly enhanced by post-reduction annealing heat treatments in air, which were observed to decrease, rather than coarsen, silver particle size, and increase particle distribution. This, accompanied by a variation in the silver surface oxidation states, appear to dramatically affect the photocatalytic efficiency under both UV and visible light. This highly active photocatalyst could have wide ranging applications in water and air pollution remediation and solar fuel production.     

Integral geometry of translation invariant functionals,II: The case of general convex bodies

In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative formulas extend to arbitrary continuous and translation invariant valuations. Then, we discuss applications to Poisson particle processes and Boolean models which contain, as a special case, some new results for flag measures.     

Further study of alternating iterations for rectangular matrices

Theory of matrix splittings is a useful tool in the analysis of iterative methods for solving systems of linear equations. When two splittings are given, it is of interest to compare the spectral radii of the corresponding iteration matrices. This helps to arrive at the conclusion that which splitting should one choose so that one can reach the desired solution of accuracy or the exact solution in a faster way. In the case of many splittings are provided, the comparison of the spectral radii is time-consuming. Such a situation can be overcome by introducing another iteration scheme which converges to the same solution of interest in a much faster way. In this direction, the theory of alternating iterations for real rectangular matrices is recently proposed. In this note, some more results to the theory of alternating iterations are added. A comparison result of two different alternating iteration schemes is then presented which will help us to choose the iteration scheme that will guarantee the faster convergence of the alternating iteration scheme. In addition to these results, a comparison result for proper weak regular splittings is also obtained.     

Sturmian comparison theory for half‐linear and nonlinear differential equations via Picone identity

In this paper, Sturmian comparison theory is developed for the pair of second‐order differential equations; first of which is the nonlinear differential equations of the form (1) and the second is the half‐linear differential equations (2) where Φ_α (s ) = |s |^{α  ? 1}s and α ₁ > ? > α _m  > β  > α _{m  + 1} > ? > α _n  > 0. Under the assumption that the solution of  2 has two consecutive zeros, we obtain Sturm–Picone type and Leighton type comparison theorems for  1 by employing the new nonlinear version of Picone formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for  1 . Examples are given to illustrate the relevance of the results. Copyright © 2016 John Wiley & Sons, Ltd.     

GARCH(1,1)模型的稳健估计比较及应用

首先阐述了GARCH(1,1)模型稳健估计的构造方法,然后在模型有无异常值扩散效应约束和异常值比例不同的情况下,比较了传统QMLE估计和多种稳健M估计的表现,结果表明:在数据无异常值下,QMLE估计较优;随着异常值比例增加,稳健Andrew估计表现更好;模型施加异常值扩散效应约束对估计有一定改善但不显著.最后选取波动程度不同的两个阶段沪深300指数的收益率,用模型拟合进行了实例比较,在波动程度较大时,Andrew估计效果较优,在波动相对平稳时,LAD估计较优.