Sobolev-Lorentz范数约束下的次临界型Adams不等式

本文在Sobolev-Lorentz空间W²L^2,q(R⁴)的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp MoserTrudinger and Adams type inequalities:a rearrangement-free argument,J.Diff Equ.,2013,255(3):298-325]的分割水平集方法.     

A note on the convexity of ruin probabilities

Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and without diffusion. An application to an optimization problem is given.     

A regularized trace formula and oscillation of eigenfunctions of a Sturm‐Liouville operator with retarded argument at 2 points of discontinuity

In this study, first, a formula for regularized sums of eigenvalues of a Sturm‐Liouville problem with retarded argument at 2 points of discontinuity which contains a spectral parameter in the boundary conditions is obtained. After that, oscillation properties of the related problem is investigated. Finally, under the condition that a subset of nodal points is dense in definition set, the potential function is determined.     

Uniform point-wise error estimates of semi-implicit compact finite difference methods for the nonlinear Schrödinger equation perturbed by wave operator

This study is devoted to analysis of semi-implicit compact finite difference (SICFD) methods for the nonlinear Schrödinger equation (NLS) perturbed by the wave operator (NLSW) with a perturbation strength described by a dimensionless parameter ε∈(0,1]$\epsilon \in (0,1]$. Uniform l^∞$l^{\infty }$-norm error bounds of the proposed SICFD schemes are built to give immediate insight on point-wise error occurring as time increases, and the explicit dependence of the mesh size and time step on the parameter ε is also figured out. In the small ε   regime, highly oscillations arise in time with O(ε²)$O({\epsilon }^2)$-wavelength. This highly oscillatory nature in time as well as the difficulty raised by the compact FD discretization make establishing the l^∞$l^{\infty }$-norm error bounds uniformly in ε   of the SICFD methods for NLSW to be a very interesting and challenging issue. The uniform l^∞$l^{\infty }$-norm error bounds in ε   are proved to be of O(h⁴+τ)$O(h^4+\tau )$ and O(h⁴+τ^2/3)$O(h^4+{\tau }^{2/3})$ with time step τ and mesh size h for well-prepared and ill-prepared initial data. Finally, numerical results are reported to verify the error estimates and show the sharpness of the convergence rates in the respectively parameter regimes.     

Ground state solution for differential equations with left and right fractional derivatives

In this work, we study the existence of positive solutions for a class of fractional differential equation given by (1) where . Using the mountain pass theorem and comparison argument, we prove that (1) at least has one nontrivial solution. Copyright © 2015 John Wiley & Sons, Ltd.     

基于状态指标的更新决策方法研究

针对设备在实际运行和执行任务时经常涉及到维修、更新报废等管理活动缺乏定量模型支撑的问题,提出了利用典型部件的预测寿命和非典型部件的历史寿命对设备系统级的健康状态进行综合评估的方法,建立了一种以状态指标为决策序列的动态规划更新决策方法。该方法能综合考虑维修费用和更新费用,确定最优更新决策,降低保障费用,有效的提高了设备的经济效益。最后经过案例分析证明了该方法的有效性,对于提高设备的保障能力和经济效益提供了理论支撑和方法指导。     

Another characterization of homogeneous Poisson processes

For a general renewal process N (allowing delay, defect and multiple simultaneous arrivals) the independence of the first renewal epochs of the marked processes got from N by Bernoulli 0/1 thinning is characterized. This independence is well-known to hold true in the case of homogeneous Poisson processes; by way of corollary one obtains the interesting observation that, when coupled with some minimal extra conditions, it in fact already identifies them. The proof is analytic in character.     

Asymptotic estimates of Gerber-Shiu functions in the renewal risk model with exponential claims

This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field.