Stability of Multiplier Ideal Sheaves

Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.     

Strong edge-coloring for planar graphs with large girth

A strong edge-coloring of a graph $G=(V,E)$ is a partition of its edge set $E$ into induced matchings. Let $G$ be a connected planar graph with girth $k\ge 26$ and maximum degree $\Delta$. We show that either $G$ is isomorphic to a subgraph of a very special $\Delta$-regular graph with girth $k$, or $G$ has a strong edge-coloring using at most $2\Delta +\lceil \frac{12(\Delta -2)}{k}\rceil$ colors.     

Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity

This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity $u_{tt}-\Delta u-\Delta u_t={\phi }_p\left(u\right)log\left|u\right|$ in a bounded domain $\Omega \subset {\mathbb{R}}^n$. We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique.     

野外砾石统计方法的应用与对比

砾石对于研究构造活动和气候变化具有重要意义，而砾石粒径是其中的重要参数，如何准确地获取粒径数据则是砾石统计分析中的基础性工作。为了能更全面地了解和使用砾石统计方法，对地表砾石统计和地层砾石统计这2种方法从操作流程、抽样过程、样本容量、误差分析和适用条件等方面进行了分析和总结。地表砾石统计，主要有沃尔曼法和面积样本法，前者强调抽样的随机性，多适用于对粒径>2 mm砾石的统计，常用于研究砾质河床的砾石粒径顺流变化趋势；后者适用的粒径范围更广，可达细砂级沉积物，多用于探索河床砾-砂转换带和生物栖息环境划分等领域。地层砾石统计，大多使用体积样本法，强调砾石的成层性，可根据研究目的确定相应的网格筛，粒径范围也可达细砂级别，多用于沉积地层粒度对气候与构造的响应、河床监测和泥沙运移等方面。砾石统计方法的选择很大程度上取决于研究目的及野外工作条件，可根据实际情况灵活选择。     

Modeling and testing of snow penetration

Penetration by a cone into snow is commonly used to characterize snow properties. However, the effects of the diameter and half-angle of the cone on the mechanical properties of snow have not been systematically studied. In addition, no estimation of material parameters in a physically-based model has been made such that the results from penetration provide only an index of snow properties. In this paper, modeling and experimental methods are used to examine the effects of cone geometry on the maximum penetration force and associated hardness, with penetrometers ranging from 2.5 to 4 mm in diameter, 15° to 45° in cone half-angle, and testing both fine-grained and coarse-grained snows. The material point method, in conjunction with the Drucker–Prager cap plasticity model, was used to obtain the theoretical penetration force-distance relationship. Global sensitivity studies were conducted that indicate that the cohesion accounts for 86% of the penetration force, followed distantly by friction angle which accounts for 27%. A general trend, for the simulation results was established: for a given half-angle, the penetration force increases with the increase of diameter which holds for most of the test data as well; for a given diameter, the penetration force decreases with the increase of half-angle, which holds for some of the test data. In addition, for a given half-angle, the hardness decreases with the increase of diameter; for a given diameter, the hardness decreases with the increase of half-angle. To take into consideration the uncertainty of test data, a simple interval-based metric was used to compare test data with simulation results; the comparison was satisfactory. The material parameters from the simulations can thus be considered as calibrated ones for the snow studied.