Exponential Gelfond-Khovanskii formula in dimension one

Gelfond and Khovanskii found a formula for the sum of the values of a Laurent polynomial over the zeros of a system of Laurent polynomials in . We expect that a similar formula holds in the case of exponential sums with real frequencies. Here we prove such a formula in dimension one.

     

Means on chainable continua

By a mean on a space we understand a mapping such that and for . A chainable continuum is a metric compact connected space which admits an - mapping onto the interval for every number . We show that every chainable continuum that admits a mean is homeomorphic to the interval. In this way we answer a question by P. Bacon. We answer some other questions concerning means as well.

     

降雨背景下诱骗态协议最优平均光子数的变色龙自适应策略

为了应对降雨给采用诱骗态协议的量子通信系统带来的突发性干扰,根据降雨分布模型和退极化信道的特性,本文提出了基于变色龙算法的每脉冲最优平均光子数自适应策略;建立了降雨强度、链路距离与最优平均光子数之间的自适应关系;并对采用变色龙算法前后,系统的性能参数进行了比较.仿真结果表明,当降雨强度J为30 mm/24 h、链路距离L为30 km时,通过采用变色龙算法,系统的安全密钥生成率由2×10~(-4)提高到3.5×10~(-4);当J为60 mm/24 h,L为20 km时,系统的信道生存函数值由0.52提高到0.63;当要求生存函数不低于0.5时,系统能够应对的最大雨强由62 mm/24 h提高到74 mm/24 h.因此,根据降雨强度和链路距离,通过变色龙算法自适应地调整系统发送端信号脉冲所含的平均光子数,可以提高量子通信系统在降雨背景下的有效性和可靠性.     

线性模型回归系数c-(K,S)型估计的优良性

根据线性回归模型Y=Xβ+ε,E(ε)=0,COV(ε)=σ~2I,对回归系数的有偏估计c-(K,S)型估计进一步研究;讨论了c-(K,S)型估计的优良性,在一定的条件下获得β_c(K,S)估计与LS估计的相对效率的界,并由此得出在设计阵病态时,β_c(K,S)型估计的精度明显高于LS估计;最后,证明了c-(K,S)型估计的可容许性,从而有助于病态线性回归系数有偏估计的进一步改进.     

Non-preserved curvature conditions under constrained mean curvature flows

We provide explicit examples which show that mean convexity (i.e. positivity of the mean curvature) and positivity of the scalar curvature are non-preserved curvature conditions for hypersurfaces of the Euclidean space evolving under either the volume- or the area preserving mean curvature flow. The relevance of our examples is that they disprove some statements of the previous literature, overshadow a widespread folklore conjecture about the behaviour of these flows and bring out the discouraging news that a traditional singularity analysis is not possible for constrained versions of the mean curvature flow.     

Mean Convergence Time of Inhomogeneous Genetic Algorithm with Elitism

The theoretical study of a genetic algorithm (GA) has focused mainly on establishing its convergence in probability and almost always to the global optimum. In this article, we establishsufficient conditions for the finiteness of convergence mean time of the genetic algorithm with elitism. We obtain bounds for the probability of convergence to the global optimum in the first n iterations as a by-product.     

积分中值定理的几个相关应用

通过陈述积分中值定理及其推广定理的基本内容,分别归纳和对应给出了定理和推广形式的几个相关应用例题.