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KAM tori for higher dimensional beam equation with a fixed constant potential 被引量:1
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作者 XU XinDong GENG JianSheng 《Science China Mathematics》 SCIE 2009年第9期2007-2018,共12页
In this paper, we consider the higher dimensional nonlinear beam equation:utt+△2u+σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t nea... In this paper, we consider the higher dimensional nonlinear beam equation:utt+△2u+σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t near u=0 and σ is a positive constant. It is proved that for any fixed σ>0, the above equation admits a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system. 展开更多
关键词 beam equation KAM tori Birkhoff normal form 37k60 37K55
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Ruin probability of the renewal model with risky investment and large claims 被引量:4
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作者 WEI Li School of Finance,Renmin University of China,Beijing 100872,China 《Science China Mathematics》 SCIE 2009年第7期1539-1545,共7页
The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper.For claim sizes with common distribution of extended regular variation,we study the asym... The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper.For claim sizes with common distribution of extended regular variation,we study the asymptotic behaviour of the ruin probability.As a corollary,we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims. 展开更多
关键词 ASYMPTOTICS extended regular variation renewal risk model risky investment strategy ruin probability 60G70 60K30 60K37
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Scheduling jobs on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties 被引量:2
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作者 CHENG CongDian TANG HengYong ZHAO ChuanLi 《Science China Mathematics》 SCIE 2008年第5期864-879,881-888+880,共25页
This article addresses the problem of scheduling n jobs with a common due date on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties.We investigate the problem under the conditions t... This article addresses the problem of scheduling n jobs with a common due date on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties.We investigate the problem under the conditions that the uptimes follow an exponential distribution,and the objective measure in detail is to minimize the expected sum of the absolute deviations of completion times from the common due date.We proceed to study in two versions (the downtime follows an exponential distribution or is a constant entailed for the repeat model job),one of which is the so-called preempt- resume version,the other of which is the preempt-repeat version.Three terms of work have been done.(i)Formulations and Preliminaries.A few of necessary definitions,relations and basic facts are established.In particular,the conclusion that the expectation of the absolute deviation of the completion time about a job with deterministic processing time t from a due date is a semi-V-shape function in t has been proved.(ii) Properties of Optimal Solutions.A few characteristics of optimal solutions are established.Most importantly,the conclusion that optimal solutions possess semi-V- shape property has been proved.(iii) Algorithm.Some computing problems on searching for optimal solutions are discussed. 展开更多
关键词 SCHEDULING stochastic breakdowns due date absolute early-tardy penalty V-shape 90B36 68M20 60K37
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Age-dependent branching processes in random environments 被引量:12
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作者 LI YingQiu LIU QuanSheng 《Science China Mathematics》 SCIE 2008年第10期1807-1830,共24页
We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the proce... We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξ n ) on ?+, and reproduce independently new particles according to a probability law p(ξ n ) on ?. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean E ξ Z(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments. 展开更多
关键词 age-dependent branching processes random environments probability generating function integral equation extinction probability exponential growth rates of expectation and conditional expectation random walks and renewal equation in random environments renewal theorem 60J80 60K37 60K05
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