反平面V形切口塑性应力奇异性分析

论文提出了用插值矩阵法计算幂硬化塑性材料反平面V形切口和裂纹尖端区域的应力奇异性.首先在切口和裂纹尖端区域采用自尖端径向度量的渐近位移场假设,将其代入塑性全量理论的基本微分方程后,推导出包含应力奇异性特征指数和特征角函数的非线性常微分方程特征值问题.然后采用插值矩阵法迭代求解导出的控制方程,得到一般的塑性材料反平面V形切口和裂纹的前若干阶应力奇异阶和相应的特征角函数,该法的重要优点是以上求解的特征角函数和它们各阶导函数具有同阶精度,并且一次性地求出前若干阶特征对.同时,插值矩阵法计算量小,易于和其他方法联合使用,这些优点在后续求解尖端区域完全应力场非常优越.论文方法的计算结果与现有结果对照,发现吻合良好,表明了论文方法的有效性.     

Solutions for conformally invariant fractional Laplacian equations with multi-bumps centered in lattices

In this paper, we consider the following nonlinear elliptic equation involving the fractional Laplacian with critical exponent:

${(?\mathrm{\Delta })}^{s}u=K(x)u^{\frac{N+2s}{N?2s}},u>0\mathrm{in}{\mathbb{R}}^N,$

where $s\in (0,1)$ and $N>2+2s$, $K>0$ is periodic in $(x_1,\dots ,x_k)$ with $1\le k<\frac{N?2s}{2}$. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in ${\mathbb{R}}^k$, including infinite lattices. On the other hand, to obtain positive solution with infinite bumps such that the bumps locate in lattices in ${\mathbb{R}}^k$, the restriction on $1\le k<\frac{N?2s}{2}$ is in some sense optimal, since we can show that for $k\ge \frac{N?2s}{2}$, no such solutions exist.     

分子环境变化对振动退相时间影响的实验研究

物质分子振动退相时间测量是一种非标记无损分子检测方法, 用超连续谱时间分辨相干反斯托克斯拉曼散射方法可同时获得分子振动谱和退相时间. 实验以苯甲腈和甲醇为样品, 研究当分子环境变化时, 其主要振动谱的振动退相时间变化情况. 将苯甲腈与无水乙醇混合, 测量了苯甲腈分子1017, 2247和3085 cm^-1三个典型分子振动的退相时间随环境变化的规律, 并得到了变化后的振动退相时间. 测量了甲醇分子2851, 2960 cm^-1两个相邻分子振动的退相时间随环境的变化情况, 给出实验变化规律. 这种方法具有检测分子所处环境变化和分子相互作用的能力, 在生命科学、分子生物学和材料科学等研究领域中具有重要的应用前景.     

混合区组试验的设计与分析

本文设计了一种混合区组试验，这种试验是在试验环境的一个方向上采用随机区组设计，在另一个方向上采用平衡不完全区组设计，从而可以控制两个方向上的环境差异，适用于不能安排拉丁方设计和３义向随机区组设计的试验，其精确度相当于拉丁方试验的精确度。本文通过实例分析说明了混合区组试验设计具有较高的实用价值。     

Fiber-optic sensor for iodine based on a covalently immobilized aminobenzanthrone Schiff base.

An aminobenzanthrone Schiff base has been synthesized as a new fluorescence carrier for the preparation of an optical chemical sensor for iodine. The response of the sensor is based on fluorescence quenching of the aminobenzanthrone Schiff base by iodine. The sensor shows a linear response toward iodine in the range of 1.0 x 10(-5) to 1.0 x 10(-3) mol l(-1), with a detection limit of 6.0 x 10(-6) mol l(-1) at pH 8.0. Leaching of the fluorophore from the membrane is effectively hindered by covalent immobilization, resulting in an enhanced sensor lifetime. In addition to satisfactory reproducibility and reversibility, the prepared sensor exhibits sufficient selectivity toward iodine with respect to other coexisting ions. The sensor has been applied to the determination of iodine in common salt samples.     

Evolutions of morphology and crystalline ordering upon annealing of quenched isotactic polypropylene

Quenched mesomorphic isotactic polypropylene precursor material has been investigated as well as the material annealed at different temperatures. At room temperature, morphology and crystalline ordering of the materials have been studied by atomic force microscopy (AFM) and wide‐angle X‐ray diffraction (WAXD). The nodular morphology of the mesomorphic precursor remains constant for annealing temperatures T_a below 120 °C. Needle‐like or leaf‐like crystals form when T_a approaches the melting temperature of the precursor. WAXD data analyzed by peak‐fitting indicate that the crystalline ordering along both the chain axis and the lateral directions quickly develops during the mesomorphic‐to‐monoclinic transition, but slowly after the transition (T_a > 140 °C). Combining the AFM and WAXD results it is proposed that two decoupled structure evolution mechanisms are occurring. During the transition, only the crystalline ordering is increasing, but not the size of the nodules. After the transition, the geometry of the nodules changes considerably, whereas there is little additional increase of crystalline ordering. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1703–1712, 2009     

Some stability results of optimal investment in a simple Lévy market

We investigate some investment problems of maximizing the expected utility of the terminal wealth in a simple Lévy market, where the stock price is driven by a Brownian motion plus a Poisson process. The optimal investment portfolios are given explicitly under the hypotheses that the utility functions belong to the HARA, exponential and logarithmic classes. We show that the solutions for the HARA utility are stable in the sense of weak convergence when the parameters vary in a suitable way.     

On steady state computation of turbulent flows using k–ε models approximated by the time splitting method

The time splitting method is frequently used in numerical integration of flow equations with source terms since it allows almost independent programming for the source part. In this paper we will consider the question of convergence to steady state of the time splitting method applied to k–ε turbulence models. This analysis is derived from a properly defined scalar study and is carried out with success for the coupled k–ε equations. It is found that the time splitting method does not allow convergence to steady state for any choice of finite values of the time step. Numerical experiments for some typical turbulent compressible flow problems support the fact that the time splitting method is always nonconvergent, while its nonsplitting counterpart is convergent. Copyright © 2005 John Wiley & Sons, Ltd.