Well-posedness of equations with fractional derivative via the method of sum

We study the well-posedness of the equations with fractional derivative Dαu(t)=Au(t)+f(t)(0 ≤t≤2π),where A is a closed operator in a Banach space X,0α1 and Dα is the fractional derivative in the sense of Weyl.Although this problem is not always well-posed in Lp(0,2π;X) or periodic continuous function spaces Cper([0,2π];X),we show by using the method of sum that it is well-posed in some subspaces of L p(0,2π;X) or C per([0,2π];X).     

On the fluid approximation for a multiclass queue under non-preemptive SBP service discipline

A multi-class single server queue under non-preemptive static buffer priority (SBP) service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.     

利用Gauss 和与Jacobi 和构造近似MUB 和SIC-POVM

MUB (mutually unbiased bases) 和SIC-POVM (symmetric informationally complete positiveoperator-valued measure) 是量子信息中的两个重要研究对象. 目前关于非素数幂维的完全MUB 是否存在还没有确定的结果, 对于SIC-POVM 目前只有有限多种维数K 有存在性结果或数值结果. 于是很多弱化了内积条件的近似MUB 和SIC-POVM 被人们所考虑. 本文使用Klappenecker 等人给出的近似MUB 和SIC-POVM 的定义, 利用Gauss 和与Jacobi 和对于素数方幂q给出了一类q-1 维q-近似MUB (AMUB)、一类q-1 维(q+1)AMUB 以及q+1 维qAMUB, 还利用Gauss 和给出了一类q-1 维近似SIC-POVM (ASIC-POVM).     

关于“序列号”方法的讨论

对于无放回抽样和有放回抽样两种情形,研究了"序列号"方法,给出并讨论了某些相关的估计量的优良性.     

A new property of entire functions of exponential type not vanishing in a half-plane and applications

Let H be the open upper half-plane, and H its closure. If ? is a non-constant transcendental entire function of exponential type such that |?(x)| ≥ μ > 0 on the real axis, then it may happen that |?(z)| is not greater than μ anywhere in H even if ?(z) in H. We show that if ? is an entire function of exponential type not vanishing in H such that inf _x∈?|?(x)| = μ > 0, then inf _{z∈ H} |?(z)| = μ if and only if h_? (π/2) := lim sup _y →∞y ^? log|?(iy) ≥ 0, and that |?(z)| = mu for some z ∈ H only if ? is a constant. This result, which can be seen as a ‘minimum modulus principle’ for entire functions of exponential type not vanishing in a half-plane, helps us to obtain generalizations of two inequalities of Boas, and one of Turán.     

基于Copula函数TVaR和EVaR的风险评估和资金配置

In this paper,the expressions of tail value of risk(TVaR)and exponential tail value of risk(EVaR)for the total risk portfolio are given,which are splitted into two cases: the bivariate case and the multivariate case according to the number of the insurances.Then the risk contributions of the insurances portfolio and the credit portfolio are also obtained. Further more,for clarifying the above results,a numerical example is given.     

Morgenstern族次序统计量的协变量的分布

本文研究了Morgenstern族次序统计量的协变量的分布及其在筛选测验中的应用.利用排序集抽样的方法,获得了分组测验情形下每组协变量的极值的分布.最后,将上述结果应用至总体为Gumbel二维指数分布和二维均匀分布的情形,给出了不同的样本量下选择问题的筛选效率.     

Analysis of a two-phase cell division model

In this paper we mainly study an equal mitosis two-phase cell division model. By using the C₀-semigroup theory, we prove that this model is the well-posed in L¹[0, 1] × L¹[0, 1], and exhibits asynchronous exponential growth phenomenon as time goes to infinity. We also give a comparison between this two-phase model with the classical one-phase model. Finally, we briefly study the asymmetric two-phase cell division model, and show that similar results hold for it.     

Moment exponential stability and integrability of stochastic functional differential equations

The main objective of the paper is to present sufficient conditions ensuring the pth mean and almost sure exponential stability, as well as the pth mean integrability of solutions to non-linear stochastic functional differential equations and, especially, to stochastic differential equations with time-varying lags. Some examples are given to illustrate the theoretical considerations.