关于循环图的曲面嵌入

该文集中探讨循环图的曲面嵌入性质.决定了所有循环图的最小亏格(其中包括可定向亏格与不可定向亏格)和最大亏格.对于固定的整数l(≥3)和充分大的 自然数n,只有一种方式将4 -正则循环图C(n,l)嵌入到环面上使得其每一个面都是4 -边形.特别地,循环图$C(2l+2,l)$在加入若干条新边后可以同时将环面与Klein瓶进行三角剖分.     

On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors

A class of structured multi-linear system defined by strong $\mathcal{M}_z$-tensors is considered. We prove that the multi-linear system with strong $\mathcal{M}_z$-tensors always has a nonnegative solution under certain condition by the fixed point theory. We also prove that the zero solution is the only solution of the homogeneous multi-linear system for some structured tensors, such as strong $\mathcal{M}$-tensors, $\mathcal{H}^+$-tensors, strictly diagonally dominant tensors with positive diagonal elements. Numerical examples are presented to illustrate our theoretical results.     

Mean‐square stability of the backward Euler–Maruyama method for neutral stochastic delay differential equations with jumps

This paper is mainly considered whether the mean‐square stability of neutral stochastic delay differential equations (NSDDEs) with jumps is shared with that of the backward Euler–Maruyama method. Under the one‐sided Lipschitz condition and the linear growth condition, the trivial solution of NSDDEs with jumps is proved to be mean‐square stable by using the functional comparison principle and the Barbalat's lemma. It is shown that the backward Euler–Maruyama method can reproduce the mean‐square stability of the trivial solution under the same conditions. The implicit backward Euler–Maruyama method shows better characteristic than the explicit Euler–Maruyama method for the reason that it works without the linear growth condition on the drift coefficient. Compared with some existing results, our results do not need to add extra condition on the neutral part. The conclusions can be applied to NSDDEs and SDDEs with jumps. The effectiveness of the theoretical results is illustrated by an example. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterization and structure of Finsler spaces with constant flag curvature

The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved that a Finsler space has constant flag curvature 1 (resp. 0) if and only if the Ricci curvature along the Hilbert form on the projective sphere bundle attains identically its maximum (resp. Ricci scalar). The horizontal distributionH of this bundle is integrable if and only ifM has zero flag curvature. When a Finsler space has CFC, Hilbert form’s orthogonal complement in the horizontal distribution is also integrable. Moreover, the minimality of its foliations is equivalent to given Finsler space being Riemannian, and its first normal space is vertical Project supported by Wang KC Fundation of Hong Kong and the National Natural Science Foundation of China (Grant No. 19571005).     

THE SINGULARLY PERTURBED NONLOCAL BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER NONLINEAR ELLIPTIC EQUATIONS

In this paper,a class of singular perturbation of noidocal boundary value problems forelliptic partial differentia[ equations of higher order is considered by using the differential in-equalities. The uniformly valid asymptotic expansion of solution is obtained.     

一类无界区域中的奇摄动非线性椭圆型系统

本文讨论了在半空间中的非线性椭圆型系统的奇摄动边值问题．在适当的条件下，利用比较定理，对相应边值问题解的存在性和渐近性态作了研究．     

界面裂纹问题中的弹性T项和应力强度因子

研究两相材料有限板含单边界面裂纹的断裂力学特性，对不同的材料组合用广义变分法分析了不同尺寸试件和裂纹长度下的应力强度因子和弹性T项，讨论了材料特性对应力强度因子和弹性T项的作用．分析了试件尺寸和裂纹长度对应力强度因子和弹性T项的影响．     

The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations

A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed. Foundation items: the National Natural Science Foundation of China (10071048); the “Hunfred Talents Project” by Chinese Academy of Sciences Biography: Mo Jia-qi (1937−)     

活性炭纤维阴极电-Fenton法降解艳红染料X3B

采用活性炭纤维作为电-Fenton反应的充氧阴极来降解水中活性艳红染料X3B,运用扫描电镜、紫外可见光谱、总有机碳分析等手段系统考察了电极形貌、底物吸附、铁离子初始价态、曝气等影响因素.实验结果表明,X3B在活性炭纤维表面的吸附符合Langmuir等温吸附模型,而X3B的电-Fenton降解反应则符合准一级反应动力学;通入空气能显著提高X3B的降解反应速率和矿化率,铁离子价态对此则无明显影响;X3B能被有效矿化,210min内矿化率为75.9%,表观电流效率达57.2%.     

一类非线性尘埃等离子体孤波解

研究了一类非线性尘埃等离子体孤波解. 首先构造一个变分迭代, 其次决定系统的初始近似, 最后通过变分迭代方法得到了对应模型的各次近似解. 关键词： 等离子体 变分迭代 近似解