On the first eigenvalue of Finsler manifolds with nonnegative weighted Ricci curvature

We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed(resp.Neumann)eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle(resp.a segment).Moreover,a lower bound of the first eigenvalue of Finsler-Laplacian with Dirichlet boundary condition is also estimated.These generalize the corresponding results in recent literature.     

On SS-quasinormal and S-quasinormally embedded subgroups of finite groups

A subgroup H of a group G is said to be an SS-quasinormal (Supplement-Sylow-quasinormal) subgroup if there is a subgroup B of G such that HB = G and H permutes with every Sylow subgroup of B. A subgroup H of a group G is said to be S-quasinormally embedded inGif for every Sylow subgroup P of H, there is an S-quasinormal subgroup K in G such that P is also a Sylow subgroup of K. Groups with certain SS-quasinormal or S-quasinormally embedded subgroups of prime power order are studied.     

Existence and stability of traveling waves for an integro-differential equation for slow erosion

We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order nonlinear conservation law where the flux function includes an integral term. We show that there exist unique traveling wave solutions that connect profiles with equilibrium slope at ±∞. Such traveling waves take very different forms from those in standard conservation laws. Furthermore, we prove that the traveling wave profiles are locally stable, i.e., solutions with monotone initial data approach the traveling waves asymptotically as t→+∞$t\to +\infty$.     

A semigroup approach to an integro-differential equation modeling slow erosion

The paper is concerned with a scalar conservation law with nonlocal flux, providing a model for granular flow with slow erosion and deposition. While the solution u=u(t,x)$u=u(t,x)$ can have jumps, the inverse function x=x(t,u)$x=x(t,u)$ is always Lipschitz continuous; its derivative has bounded variation and satisfies a balance law with measure-valued sources. Using a backward Euler approximation scheme combined with a nonlinear projection operator, we construct a continuous semigroup whose trajectories are the unique entropy weak solutions to this balance law. Going back to the original variables, this yields the global well-posedness of the Cauchy problem for the granular flow model.     

Semiparametric regression analysis for clustered doubly-censored data

This paper considers clustered doubly-censored data that occur when there exist several correlated survival times of interest and only doubly censored data are available for each survival time. In this situation, one approach is to model the marginal distribution of failure times using semiparametric linear transformation models while leaving the dependence structure completely arbitrary. We demonstrate that the approach of Cai et al. (Biometrika 87:867–878, 2000) can be extended to clustered doubly censored data. We propose two estimators by using two different estimated censoring weights. A simulation study is conducted to investigate the proposed estimators.     

Simple nonparametric estimators of the bivariate survival function under random left truncation and right censoring

We consider estimating the bivariate survival function when both components are subject to random left truncation and right censoring. Using the idea of Sankran and Antony (Sankhyã 69:425–447, 2007) in the competing risks set up, we propose two types of estimators as generalizations of the Dabrowska (Ann Stat 18:1475–1489, 1988) and Campbell and Földes (Nonparametric statistical inference, North-Holland, Amsterdam 1982) estimators. The proposed estimators are easy to implement and do not require iteration. The consistency of the proposed estimators is established. Simulation results indicate that the proposed estimators can outperform the estimators of Shen and Yan (J Stat Plan Inference 138:4041–4054, 2008), which require complex iteration.     

细胞神经网络的指数稳定性

该文研究了具有可变时滞的随机细胞神经网络的指数 稳定性,应用Razumikhin定理与Lyapunov函数,建立了这种细胞神经网络均方指数稳定与几乎必然指数稳定的两类判据,一类是时滞无关而另一类是时滞相关.     

STUDY OF SPATIAL HOLE BURNING IN DISTRIBUTED PHASE-SHIFTED DISTRIBUTED FEEDBACK SEMICONDUCTOR LASERS

A new algorithm based on transfer matrix method is given to analyse a new distributed feedback (DFB) structure—the distributed phase- shifted (DPS) DFB laser. In the small signal analysis, a new model is proposed with this algorithm. Considering different structures of DFB laser diode, we define a spatial-hole-burning (SHB) factor to measure the SHB effect. Compared with the λ/4 phase-shifted DFB and 3 phase-shifted DFB, the DPS-DFB structure shows a superior characteristics both in static and dynamic behavior.     

具有脉冲扰动的非线性时滞微分方程

本文研究一类脉冲非线性时滞微分方程解的性质，讨论了其解的整体存在性及非振动解的渐近性，也给出了其所有解振动的充分条件．     

纳米复合永磁Pr9Fe74Co12B5Snx(x=0, 0.5)的磁化行为与磁黏滞性

用熔体快淬法制备了纳米复合永磁样品Pr₉Fe₇₄Co₁₂B₅ 与Pr₉Fe₇₄Co₁₂B₅Sn_0.5，分析了样品的起始磁化、反磁化过程，测得样品的总磁化率、可逆磁化率以及样品的磁黏滞性.结果表明，两样品在室温下均表现为单一硬磁相磁化行为，在低温下表现为双相行为，且由于添加Sn后使晶粒均匀化从而导致样品低温下的双相行为更加明显.添加Sn后引起样品中软磁相含量和软磁相晶粒尺寸的增加，使磁化反转中可逆磁化部分增多，且使反磁化形核场降低.磁黏滞性研究表明，热激活体积与软磁相晶粒的大小有关. 关键词： 纳米复合永磁 磁化反转 磁粘滞