Permanence of a delayed discrete mutualism model with feedback controls

This paper discusses a two species discrete model of mutualism with delays and feedback controls. Sufficient conditions are obtained for the permanence of the system. The results show that feedback control variables have no influence on the persistence property of the system.     

Low rank approximation in G0W0 calculations

The single particle energies obtained in a Kohn-Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green’s function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The G₀W₀ approximation is a widely used technique in which the self energy is expressed as the convolution of a noninteracting Green’s function (G₀) and a screened Coulomb interaction (W₀) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating W₀ at multiple frequencies. In this paper, we discuss how the cost of G₀W₀ calculation can be reduced by constructing a low rank approximation to the frequency dependent part of W₀. In particular, we examine the effect of such a low rank approximation on the accuracy of the G₀W₀ approximation. We also discuss how the numerical convolution of G₀ and W₀ can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.     

Kolmogorov Type Law of the Logarithm for Arrays

In this paper, we establish the analogue of Kolmogorov-type law of the logarithm for an array of independent random variables. The main methods are to develop the classic Bernstein’s and Kolmogorov’s inequality and replace the boundedness condition by conditions on the cumulant transform.     

Dimensions of spline spaces over non-rectangular T-meshes

Spline spaces over rectangular T-meshes have been discussed in many papers. In this paper, we consider spline spaces over non-rectangular T-meshes. The dimension formulae of spline spaces over special simply connected T-meshes have been obtained. For T-meshes with holes, we discover a new type of dimension instability. We construct a relationship between the dimension of the spline space over a T-mesh \(\mathcal {T}\) with holes and the dimension of the spline space over a simply connected T-mesh associated with \(\mathcal {T}\).     

退化时滞微分系统的Hopf分支

本文讨论了一般二雏退化时滞微分系统当r≠0时平衡点稳定性的范围，并以滞量r为分支参数研究系统出现Hopf分支的条件．     

Nontrivial solutions of Schrödinger equations with indefinite nonlinearities

We prove the existence of nontrivial solutions for the Schrödinger equation −Δu+V(x)u=aγ(x)f(u) in RN, where f is superlinear and subcritical at zero and infinity respectively, V is periodic and a(x) changes sign.     

两类无界域边界上的奇异积分方程

给出两类无界域边界上完全奇异积分方程的直接解法．方程的系数和核密度在该无异域上具某种解析性．     

Uniform designs for mixture-amount experiments and for mixture experiments under order restrictions

With order statistics of the uniform distribution on [0, l], exponential and beta distributions, a stochastic representation is obtained for the uniform distribution over various domains, where A-type domains are closely associated with reliability growth analysis, order restricted statistical inference and isotonic regression theory, V-type domains are connected with the mixture-amount experiments, and T-type domains are well related to mixture experiments. With these stochastic representations, the corresponding uniform distribution and number-theoretic nets can be generated. This approach seems to be new and is called order statistics method. Some examples on reliability growth analysis and experimental design are presented. This work was partially supported by a Hong Kong UGC-RGC grant, the Statistics Research and Consultancy Centre of HK-BU, and the Chinese Academy of Sciences.     

A relation between long-range correlation and dielectric anomaly

A double-well potential model is established to explain the dielectric anomaly of ferroelectrics. The dielectric constant consists of two parts. One part is independent of the long-range correlation, following 1/T law. The other part originates from the long-range correlation, and can be described by the correlation length well. The deviation from Curie-Weiss law in a small size sample originates from the decrease of the long-range correlation. Project supported by the Climbing Program of Foundamental Research of China.