For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smalle...For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.展开更多
In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdin...In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.展开更多
This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the li...This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.展开更多
Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying ...Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying the well-known stochastic decomposition property of the steady-state queue size,the probability generating function of the steady-state queue length distribution is obtained.Moreover,the explicit expressions of the expected queue length and the additional queue length distribution are derived by some algebraic manipulations.Finally,employing the renewal reward theorem,the explicit expression of the long-run expected cost per unit time is given.Furthermore,we analyze the optimal policy for economizing the expected cost and compare the optimal Min(N,D)-policy with the optimal N-policy and the optimal D-policy by using numerical examples.展开更多
The instability property of the standing wave uω（t, x） = eiωtφ（x） for the Klein–Gordon– Hartree equation is investigated. For the case N≥3 and w2 〈2/N＋4-γ,it is shown that the standing wave eiwtφ（x） is...The instability property of the standing wave uω（t, x） = eiωtφ（x） for the Klein–Gordon– Hartree equation is investigated. For the case N≥3 and w2 〈2/N＋4-γ,it is shown that the standing wave eiwtφ（x） is strongly unstable by blow-up in finite time.展开更多
This paper studies an k-out-of-n:G system with redundant dependency and repair equipment procurement lead time where the operating times and repair times of components follow exponential distributions and phase-type d...This paper studies an k-out-of-n:G system with redundant dependency and repair equipment procurement lead time where the operating times and repair times of components follow exponential distributions and phase-type distributions,respectively.When one component breaks down,it is repaired by a repair equipment.The repair equipment may fail during the repair period and the following repair is not‘as good as new’.After a number of repairs,it is replaced by a new one.The new spare repair equipment for replacement is only available by an order,and the procurement lead time for delivering follows a phase-type distribution.Moreover,in the multi-component system,the redundant dependency is taken into account.Applying the matrix-analytical method,the system availability,the rate of occurrence of failures of the system,the expected number of broken components,the availability and the rate of occurrence of failures of the repair equipment are derived.Finally,numerical examples are given to show these theoretical results.展开更多
In this paper,we introduce the notion of a product structure on a 3-Bihom-Lie algebra,which is a Nijenhuis operator with some conditions.We prove that a 3-Bihom-Lie algebra has a product structure if and only if it is...In this paper,we introduce the notion of a product structure on a 3-Bihom-Lie algebra,which is a Nijenhuis operator with some conditions.We prove that a 3-Bihom-Lie algebra has a product structure if and only if it is the direct sum of two vector spaces which are also Bihom-subalgebras.Then we give four special conditions under each of which a 3-Bihom-Lie algebra has a special decomposition.Similarly,we introduce a complex structure on a 3-Bihom-Lie algebra and there are also four types of special complex structures.Finally,we establish the relation between a complex structure and a product structure.展开更多
This paper investigates a multi-component repairable system with double threshold control policy.The system is composed of n identical and independent components which operate simultaneously at the beginning,and it is...This paper investigates a multi-component repairable system with double threshold control policy.The system is composed of n identical and independent components which operate simultaneously at the beginning,and it is down when the number of operating components decreases to k−1(k≤n).When the number of failed components is less than the value L,the repairman repairs them with a low repair rate.The high repair rate is activated as soon as L failed components present,and continues until the number of failed components drops to the value N−1.Applying the matrix analytical method,the Laplace transform technique and the properties of the phase type distribution,various performance measures including the availability,the rate of occurrence of failures,and the reliability are derived in transient and stationary regimes.Further,numerical examples are reported to show the behaviour of the system.展开更多
基金supported by the National Natural Science Foundation of China(11201324)the Fok Ying Tuny Education Foundation(141114)the Sichuan Technology Program(2022ZYD0011,2022NFSC1852).
文摘For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.
基金supported by National Science Foundation of China (11071177)
文摘In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.
基金Supported by National Science Foundation of China (11071177)Excellent Youth Foundation of Sichuan Province (2012JQ0011)
文摘This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.
基金supported by the National Natural Science Foundation of China(No.71571127)the National Natural Science Youth Foundation of China(No.72001181).
文摘Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying the well-known stochastic decomposition property of the steady-state queue size,the probability generating function of the steady-state queue length distribution is obtained.Moreover,the explicit expressions of the expected queue length and the additional queue length distribution are derived by some algebraic manipulations.Finally,employing the renewal reward theorem,the explicit expression of the long-run expected cost per unit time is given.Furthermore,we analyze the optimal policy for economizing the expected cost and compare the optimal Min(N,D)-policy with the optimal N-policy and the optimal D-policy by using numerical examples.
基金The first author is supported by the Key Project of Chinese Ministry of Education(Grant No.211162)Sichuan Province Science Foundation for Youths(Grant No.2012JQ0011)the second author is supported byNational Natural Science Foundation of China(Grant No.11371267)
文摘The instability property of the standing wave uω（t, x） = eiωtφ（x） for the Klein–Gordon– Hartree equation is investigated. For the case N≥3 and w2 〈2/N＋4-γ,it is shown that the standing wave eiwtφ（x） is strongly unstable by blow-up in finite time.
基金This research was supported by the National Natural Science Foundation of China[grantnumber 72001181],[grant number 71571127]the funding of V.C.&V.R.Key Lab of Sichuan Province(SCVCVR2019.05VS).
文摘This paper studies an k-out-of-n:G system with redundant dependency and repair equipment procurement lead time where the operating times and repair times of components follow exponential distributions and phase-type distributions,respectively.When one component breaks down,it is repaired by a repair equipment.The repair equipment may fail during the repair period and the following repair is not‘as good as new’.After a number of repairs,it is replaced by a new one.The new spare repair equipment for replacement is only available by an order,and the procurement lead time for delivering follows a phase-type distribution.Moreover,in the multi-component system,the redundant dependency is taken into account.Applying the matrix-analytical method,the system availability,the rate of occurrence of failures of the system,the expected number of broken components,the availability and the rate of occurrence of failures of the repair equipment are derived.Finally,numerical examples are given to show these theoretical results.
基金Supported by NNSF of China(No.12271085 and No.12071405)supported by Sichuan Science and Technology Program(No.2023NSFSC1287).
文摘In this paper,we introduce the notion of a product structure on a 3-Bihom-Lie algebra,which is a Nijenhuis operator with some conditions.We prove that a 3-Bihom-Lie algebra has a product structure if and only if it is the direct sum of two vector spaces which are also Bihom-subalgebras.Then we give four special conditions under each of which a 3-Bihom-Lie algebra has a special decomposition.Similarly,we introduce a complex structure on a 3-Bihom-Lie algebra and there are also four types of special complex structures.Finally,we establish the relation between a complex structure and a product structure.
基金This research was supported by the National Natural Science Foundation of China(No.71571127)the funding of V.C.&V.R.Key Lab of Sichuan Province(SCVCVR2019.05VS)the Sichuan Science and Technology Program(Nos.2020YFS0318,2019YFS0155,2019YFS0146,2020YFG0430,2020YFS0307).
文摘This paper investigates a multi-component repairable system with double threshold control policy.The system is composed of n identical and independent components which operate simultaneously at the beginning,and it is down when the number of operating components decreases to k−1(k≤n).When the number of failed components is less than the value L,the repairman repairs them with a low repair rate.The high repair rate is activated as soon as L failed components present,and continues until the number of failed components drops to the value N−1.Applying the matrix analytical method,the Laplace transform technique and the properties of the phase type distribution,various performance measures including the availability,the rate of occurrence of failures,and the reliability are derived in transient and stationary regimes.Further,numerical examples are reported to show the behaviour of the system.
