Hilbert空间中两个K-框架的算子组合

讨论了Hilbert空间中两个K-框架{f_i}^∞_i=1与{g_i}^∞_i=1通过算子作用再求和后得到的序列{T₁ f_i+T₂g_i}^∞_i=1成为K-框架与紧K-框架的一系列等价条件,所得结果推广与修正了已有结果.     

一类随机微分方程的轨道唯一性

 在漂移项系数是非Lipschitz并且是非凹的条件下，证明了如下随机微分方程的轨道唯一性：X_t=x+∑^∞_i=1∫^t₀σ_i(X_s)dWⁱ_s+∫^t₀b(X_s)ds，其中W_i, i=1,2,…, 为一串独立的标准布朗运动。     

渐近拟非扩展型映象不动点的迭代逼近

 去掉了已有文献中的条件:"对任意子列{x_ni} {x_n},当‖Tⁿix_ni-x_ni‖^→0时就有‖Tx_ni-x_ni‖^→0"后,研究了Banach空间中渐近拟非扩展型映象不动点的迭代逼近问题;所得结果推广和发展了已有文献中的成果.     

二元小波紧框架存在的充分条件

 讨论框架多分辨分析{V_j}_j∈Z的子空间V₁中若干个二元函数生成小波紧框架的条件.运用矩阵理论、泛函分析方法与逼近论思想,给出s(s≥3)个二元函数生成小波紧框架的充分条件.     

具p-Laplacian非线性奇异边值系统正解的存在性

研究了下面带有p-Laplacian算子的非线性奇异边值系统:(ф_p(u'_i))'+a_i(t)f_i(u₁,u₂)=0, 0＜t＜1,α_iф_p(u_i(0))-β_iф_p(u'_i(0))=0, γ_iф_p(u_i(1))+δ_iф_p(u'_i(1))=0,(i=1,2)正解的存在性。其中ф_p(s)为p-Laplacian 算子,即ф_p(s)=|s|^p-2s, p>1, (ф_p)^-1=ф_q,1/p+1/q=1, α_i＞0, β_i≥0, γ_i＞0, δ_i≥0, i=1,2.这里f_{i是下半连续函数(i=1,2). 通过使用锥上的不动点定理,在相当弱的条件下, 获得了这类奇异边值系统正解的存在性.}     

濒危植物合柱金莲木开花结实物候及交配系统研究

合柱金莲木（Sauvagesia rhodoleuca）为国家二级重点保护野生植物,为了从繁殖生物学角度探讨合柱金莲木的濒危机制,为其保护和可持续利用提供科学依据,本研究对合柱金莲木的开花结实物候进行观测并利用微卫星分子标记测定其交配系统。结果表明：（1）成龄合柱金莲木植株的平均地径、平均株高和平均冠幅分别为0.70、129.67和81.98 cm,平均每株结花序15.56串。合柱金莲木于3月下旬至4月中上旬进入抽（花）序期,4月中下旬进入现蕾期,4月下旬至5月中下旬为开花期,5月下旬至8月中旬为果实发育期,8月中旬至10月上旬为果实成熟期。合柱金莲木的单花开放在1天内完成,其开花进程可分蕾松、初开、盛开和落花4个阶段,其花序的单花数约27朵/串,果序的蒴果数约18个/串,结果植株平均每株的种子数达5 881.68粒,种子量极大。（2）合柱金莲木的多位点异交率（t_m）和单位点异交率（t_s）分别为0.982和0.752,t_m>t_s,说明在物种水平上合柱金莲木存在一定比例的近交,双亲的近交比例为0.230,其存在近交衰退（δ=4.332>0）。合柱金莲木在物种水平上的多位点相关度（r_pm）和单位点相关度（r_ps）分别为0.272和0.314,说明其物种内部存在明显分化的种群遗传结构,其异交子代间亲本相关性（r_p）为0.213,表明部分子代共享了亲本。交配系统中存在一定程度的近交可能是合柱金莲木濒危的重要因素之一。     

一类强相依非平稳高斯序列最大值的几乎处处收敛

 设{X_n,n≥1}为存在样本缺失的标准化强相依非平稳高斯序列,其相关系数r_ij=EX_iX_j.在r_ijln(j-i)→r∈(0,∞)的情况下,得到了完整样本的最大值与非完整样本的最大值的联合极限分布,并证明了其几乎处处收敛.     

一类非线性薛定谔方程的孤子解

 研究了具有V(x,t)=f₁(t)x+f₂(t)x²形式的外部势的非线性薛定谔方程的单一孤立子解.结果表明:当孤立子的中心满足带有势V(x,t)的牛顿方程,孤立子的内部结构由"体固定"坐标系决定.孤立子的结构与f₁(t)无关.若f₂(t)与t无关,孤立子是固定的.原则上,若f₂(t)剧烈变化,则孤立子将扩散.但数值计算表明,在一定条件下,孤立子还是经得起f₂(t)的剧烈变化.     

信息传播的最优结构

 研究连通网络中的信息传播问题,即有信息的节点vi在每个单位时间里能同时向它的至多k_i(k_i≥1)个邻点发送信息,要求传播的最短时间,使得网络中所有顶点均有此种信息.鉴于在任意网络中该问题是NP-完备的,特研究一种特殊的网络,即m维立方体网络.通过应用递推技巧,揭示了在m维立方体网络上信息传播的诸多好的特性及有趣的现象,显示了m维立方体网络是信息传播问题的最优结构.     

线性交换子的加权估计

 多线性交换子T_b(f)(x)=∫_Rⁿ∏_i=1^m(b_i(x)-b_i(y))k(x,y)f(y)dy在L^p(Rⁿ)(1K是一个标准的Calderón-Zygmund核.主要研究交换子Mf(x)=sup_x∈Q∫_Q|f(y)|dy,其中f∈L_loc(Rⁿ),x∈Rⁿ,Q是任何包含x的方体,并用Sharp极大估计得到了该多线性交换子在Herz空间的一个加权有界性.     

网络中信息传播的最短时间算法

研究信息在网络中传播的最短时间问题,建立了ki-传播模型,即有信息的节点vi在每个时间单位里能同时向它的至多ki(ki≥1)个邻点发送信息,要求传播的最短时间,使得网络的所有顶点均有此种信息.指出了该问题在任意网络中是NP-完备的,对该问题给出了一个多项式时间算法来求解在树状网络中信息传播的最短时间,并且能够求出树状网络的传播中心.       

软件定义网络中基于优先级的在线流调度策略

为了保证服务质量(quality of service, QoS),进入网络中的数据流可被赋予不同的优先级。在未来到达流请求信息未到达的情况下,进行在线优先级流调度,以最大化网络吞吐量是一项挑战。基于网络带宽资源、请求流的优先级和带宽需求的约束研究了软件定义网络(software defined networking, SDN)中的在线流请求调度策略。首先,提出了流路由成本和利润的概念,并创新性地设计了一个考虑边际成本的模型来描述链路资源和路由路径的使用成本。然后,将优先级流请求调度问题刻画为混合整数线性规划模型(mixed integer linear programming, MILP),提出在线优先级流调度算法(online priority traffic scheduling algorithm, OPTSA)来求解,最后分析了OPTSA的竞争比。仿真结果显示,与基准算法相比,所提出的算法可以确保网络负载均衡,同时有效提高网络的累积带宽和吞吐量。     

Generalized ridge estimation of a semiparametric regression model

We considered the following semiparametric regres-sion model yi = X iT β+ s ( t i ) + ei (i =1,2,,n). First,the general-ized ridge estimators of both parameters and non-parameters are given without a restrained design matrix. Second,the generalized ridge estimator will be compared with the penalized least squares estimator under a mean squares error,and some conditions in which the former excels the latter are given. Finally,the validity and feasibility of the method is illustrated by a simulation example.     

An Optimal Content Caching Framework for Utility Maximization

For desirable quality of service, content providers aim at covering content requests by large network caches. Content caching has been considered as a fundamental module in network architecture. There exist few studies on the optimization of content caching. Most existing works focus on the design of content measurement,and the cached content is replaced by a new one based on the given metric. Therefore, the performance for service provision with multiple levels is decreased. This paper investigates the problem of finding optimal timer for each content. According to the given timer, the caching policies determine whether to cache a content and which existing content should be replaced, when a content miss occurs. Aiming to maximize the aggregate utility with capacity constraint, this problem is formalized as an integer optimization problem. A linear programming based approximation algorithm is proposed, and the approximation ratio is proved. Furthermore, the problem of content caching with relaxed constraints is given. A Lagrange multiplier based approximation algorithm with polynomial time complexity is proposed. Experimental results show that the proposed algorithms have better performance.     

An efficient certificateless ring signature scheme

To overcome the drawbacks such as high computational cost, unreasonable security model and long signature length in existing certificateless ring signature schemes, we propose an efficient certificateless ring signature scheme in this paper. Our construction is inspired by some efficient ID-based ring signature schemes, and uses bilinear pairings as a basic tool. Using a reasonable security model, the unforgeability of the proposed scheme is proven based on the intractability of the computational Diffie-Hellman （CDH） problem. The signature length of the new scheme is only ｜G2｜＋n｜G1｜ （｜Gi｜ is the bit length of an element in group Gi, i =1, 2）. Compared with other existing certificateless ring signature schemes, the newly proposed scheme has a shorter signature length and is more efficient and practical.     

交换折叠超立方体的连通度

P.K.K.Loh等人从超立方体Qn中系统地移除了一些边后获得了交换超立方体EH(s,t)。李等人在EH(s,t)的基础上增加了一些边获得了一个新的互联网络交换折叠超立方体EH(s,t)。连通度是衡量网络容错性的一个重要参数,并且连通度越大网络越可靠。本文证明了EH(s,t)的连通度等于其最小度。     

Quantitative Estimates of Outcrossing Rates in a Natural Population of Caldesia grandis （Alismataceae）

Outcrossing rate in a natural population of Caldesia grandis was estimated by the dominant random amplified polymorphism DNA (RAPD) marker using 10 open-pollinated progeny arrays of 24 individuals. The multilocus outcrossing rate estimated based on all 25 RAPD loci was 0.872 ±0.033 and the single-locus outcrossing rate was 0.795 ±0.032. Multilocus estimates did not differ significantly from the single-locus estimates. The fixation index, F, in the progeny estimated from RAPD data was -0.142 ±0.000. The estimates of multilocus outcrossing rates (t_m) and single-locus outcrossing rates (t_s) obtained from MLDT clearly indicate that outcrossing is predominant in the open-pollinated C. grandis population. An empirical analysis suggests that 15 should be the minimum number of dominant marker loci necessary to achieve robust estimates of t_m.     

Some Results about the Sample Path Properties of Markov Processes with Independent Self-Similar Components

This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.