带干扰的Erlang(2)风险模型的不破产概率

本文讨论了带干扰的Erlang(2)风险模型,通过构造一个延迟更新过程,我们得到了不破产概率满足的积分-微分方程,进而得到了不破产概率的明确表达式．     

STABILITY AND BOUNDEDNESS OF SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

This paper studies the stability and boundedness of the solutions of Volterra integral differential equations with infinite delay in the phase space (Ch, |·|h), the h-uniform stability, h-uniformly asymptotic stability and h-boundedness of solutions are obtained.     

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.     

On existence of solutions for some hyperbolic-parabolic-type chemotaxis systems

In this paper, we discuss the local and global existence ofweak solutions for some hyperbolic–parabolic systems modellingchemotaxis.     

Computing strategies for achieving acceptability: A Monte Carlo approach

We consider a trader who wants to direct his or her portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a Monte Carlo algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and whose outputs are the numerical values of initial capital requirement and the functional form of a trading strategy for achieving acceptability. We also prove optimality of the capital obtained. Explicit theoretical evaluations of hedging strategies are extremely difficult, and we avoid the problem by resorting to such computational methods. The main idea is to utilize the finite Vapnik–C?ervonenkis dimension of a class of possible strategies.     

The categoricity of the group of all computable automorphisms of the rational numbers

We prove that there is a first-order sentence ϕ such that the group of all computable automorphisms of the ordering of the rational numbers is its only model among the groups that are embeddable in the group of all computable permutations. Supported by a Scheme 2 grant from the London Mathematical Society. __________ Translated from Algebra i Logika, Vol. 46, No. 5, pp. 649–662, September–October, 2007.     

Deformations of functionals and bifurcations of extremals

We study homology characteristics of critical values and extremals of Lipschitz functionals defined on bounded closed convex subsets of a reflexive space that are invariant under deformations. Sufficient conditions for the existence of a bifurcation point of a multivalued potential operator (the switch principle for the typical number of an extremal) are established.     

The Cauchy Problem of the Nonlinear Schr■dinger Equations in R~(1 1)

In this paper,we consider the local and global solution for the nonlinear Schrdinger equationwith data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data.Thetechniques to be used are adapted from the Strichartz type estimate,Kato's smoothing effect and the maximalfunction(in time)estimate for the free Schrdinger operator.     

Binding energy of impurity states in an inverse parabolic quantum well under magnetic field

 We have investigated the effects of the magnetic field which is directed perpendicular to the well on the binding energy of the hydrogenic impurities in an inverse parabolic quantum well (IPQW) with different widths as well as different Al concentrations at the well center. The Al concentration at the barriers was always x_max=0.3. The calculations were performed within the effective mass approximation, using a variational method. We observe that IPQW structure turns into parabolic quantum well with the inversion effect of the magnetic field and donor impurity binding energy in IPQW strongly depends on the magnetic field, Al concentration at the well center and well dimensions.     

具非线性中立项的二阶时滞微分方程的振动性质

By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.