Proves the existence of supremum and infimum in the noncompact fuzzy number space E ～, redefines E ～ valued (M) integral, and then discusses the relations between (M) integral and (G) integral of E ～ va...Proves the existence of supremum and infimum in the noncompact fuzzy number space E ～, redefines E ～ valued (M) integral, and then discusses the relations between (M) integral and (G) integral of E ～ valued functions.展开更多
In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜...In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.展开更多
Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the...Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.展开更多
Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools ar...Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools are the Lyapunov functions and Razu mikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.展开更多
In this paper,we prove that the supremum sup{∫B∫B|u(y)|^p(|y|)|u(x)|^p(|x|)/|x-y|^u dxdy:u∈H0^1,rad(B),‖▽u‖L^2(B)=1}is attained,where B denotes the unit ball in R^N(N≥3),μ∈(0,N),p(r)=2^xμ+r^t,t∈(0,min{N/2-...In this paper,we prove that the supremum sup{∫B∫B|u(y)|^p(|y|)|u(x)|^p(|x|)/|x-y|^u dxdy:u∈H0^1,rad(B),‖▽u‖L^2(B)=1}is attained,where B denotes the unit ball in R^N(N≥3),μ∈(0,N),p(r)=2^xμ+r^t,t∈(0,min{N/2-μ/4,N-2})and 2μ^*=(2N-μ)/(N-2)is the critical exponent for the Hardy-Littlewood-Sobolev inequality.展开更多
We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of t...We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.展开更多
In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with 'supremum' and...In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with 'supremum' and the existence of maximal and minimal solutions are obtained.展开更多
The authors investigate the tail probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distribut...The authors investigate the tail probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distributed random variables with Osubexponential integrated distributions.A uniform upper bound is derived for the distribution of the supremum of a random walk with independent but non-identically distributed increments,whose tail distributions are dominated by a common tail distribution with an O-subexponential integrated distribution.展开更多
传统无线传感器网络(wireless sensor network,WSN)基于IP网络,难以发挥出智能配电网中多种接入网络的性能;同时,在气象灾害或巡检无人机等动态场景下难以获取节点IP地址,无法及时有效完成数据收集任务。命名数据网络(named data networ...传统无线传感器网络(wireless sensor network,WSN)基于IP网络,难以发挥出智能配电网中多种接入网络的性能;同时,在气象灾害或巡检无人机等动态场景下难以获取节点IP地址,无法及时有效完成数据收集任务。命名数据网络(named data networking,NDN)的出现,为解决上述问题提供了可能。NDN以数据需求为驱动,符合WSN只关注数据收集任务本身的初衷。结合NDN新型网络架构对于底层网络协议透明的优势,提出了一种智能配电网中感知数据收集协议——T-ND-WSN。仿真实验表明,该协议结合网内缓存机制,在满足智能配电网数据通信时延上确界前提下,在数据传输服务质量上具有明显优势。展开更多
文摘Proves the existence of supremum and infimum in the noncompact fuzzy number space E ～, redefines E ～ valued (M) integral, and then discusses the relations between (M) integral and (G) integral of E ～ valued functions.
基金Supported by the National Natural Science Foundation of China (10671176, 10771192, 70871103)
文摘In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(12ZB082)the Scientific research cultivation project of Sichuan University of Science&Engineering(2013PY07)+1 种基金the Scientific Research Fund of Shanghai University of Finance and Economics(2017110080)the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing(2018QZJ01)
文摘Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.
文摘Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools are the Lyapunov functions and Razu mikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.
基金supported by National Natural Science Foundation of China(Grant Nos.11831009 and 11571130)
文摘In this paper,we prove that the supremum sup{∫B∫B|u(y)|^p(|y|)|u(x)|^p(|x|)/|x-y|^u dxdy:u∈H0^1,rad(B),‖▽u‖L^2(B)=1}is attained,where B denotes the unit ball in R^N(N≥3),μ∈(0,N),p(r)=2^xμ+r^t,t∈(0,min{N/2-μ/4,N-2})and 2μ^*=(2N-μ)/(N-2)is the critical exponent for the Hardy-Littlewood-Sobolev inequality.
基金Acknowledgements The authors were grateful to the two reviewers for their valuable comments and suggestions to improve the present paper. This work was supported by the National Natural Science Foundation of China （NO. 11071182） and the Doctor Introduction Foundation of Nantong University （No. 12R066）.
文摘We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.
基金Research supported by the foundation of Educational Department of Fujian Province (K200ll04)and Zhangzhou Teachers College.
文摘In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with 'supremum' and the existence of maximal and minimal solutions are obtained.
基金supported by the National Natural Science Foundation of China (No.11001052)the Postdoctoral Science Foundation of China (No.20100471365)+3 种基金the Jiangsu Provincial Natural Science Foundation of China (No.BK2010480)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No.10KJB110010)the Jiangsu Provincial Postdoctoral Research Program of China (No.0901029C)the Jiangsu Government Scholarship for Overseas Studies,Qing Lan Project
文摘The authors investigate the tail probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distributed random variables with Osubexponential integrated distributions.A uniform upper bound is derived for the distribution of the supremum of a random walk with independent but non-identically distributed increments,whose tail distributions are dominated by a common tail distribution with an O-subexponential integrated distribution.
文摘传统无线传感器网络(wireless sensor network,WSN)基于IP网络,难以发挥出智能配电网中多种接入网络的性能;同时,在气象灾害或巡检无人机等动态场景下难以获取节点IP地址,无法及时有效完成数据收集任务。命名数据网络(named data networking,NDN)的出现,为解决上述问题提供了可能。NDN以数据需求为驱动,符合WSN只关注数据收集任务本身的初衷。结合NDN新型网络架构对于底层网络协议透明的优势,提出了一种智能配电网中感知数据收集协议——T-ND-WSN。仿真实验表明,该协议结合网内缓存机制,在满足智能配电网数据通信时延上确界前提下,在数据传输服务质量上具有明显优势。
