The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected...The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.展开更多
In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a ...In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.展开更多
Addresses the design problems of robust L2-L∞ filters with pole constraint in a disk for uncertain continuous-time linear systems. The uncertain parameters are assumed to belong to convex bounded domains. The aim is ...Addresses the design problems of robust L2-L∞ filters with pole constraint in a disk for uncertain continuous-time linear systems. The uncertain parameters are assumed to belong to convex bounded domains. The aim is to determine a stable linear filter such that the filtering error system possesses a prescribed L2-L∞ noise attenuation level and expected poles location. The filtering strategies are based on parameter-dependent Lyapunov stability results to derive new robust L2-L∞ performance criteria and the regional pole placement conditions. From the proposed multi-objective performance criteria, we derive sufficient conditions for the existence of robust L2-L∞ filters with pole constraint in a disk, and cast the filter design into a convex optimization problem subject to a set of linear matrix inequality constraints. This filtering method exhibits less conservativeness than previous results in the quadratic framework. The advantages of the filter design procedures are demonstrated by means of numerical examples.展开更多
Multi-target neural circuit-magnetic stimulation has been clinically shown to improve rehabilitation of lower limb motor function after spinal cord injury. However, the precise underlying mechanism remains unclear. In...Multi-target neural circuit-magnetic stimulation has been clinically shown to improve rehabilitation of lower limb motor function after spinal cord injury. However, the precise underlying mechanism remains unclear. In this study, we performed double-target neural circuit-magnetic stimulation on the left motor cortex and bilateral L5 nerve root for 3 successive weeks in a rat model of incomplete spinal cord injury caused by compression at T10. Results showed that in the injured spinal cord, the expression of the astrocyte marker glial fibrillary acidic protein and inflammatory factors interleukin 1β, interleukin-6, and tumor necrosis factor-α had decreased, whereas that of neuronal survival marker microtubule-associated protein 2 and synaptic plasticity markers postsynaptic densification protein 95 and synaptophysin protein had increased. Additionally, neural signaling of the descending corticospinal tract was markedly improved and rat locomotor function recovered significantly. These findings suggest that double-target neural circuit-magnetic stimulation improves rat motor function by attenuating astrocyte activation, thus providing a theoretical basis for application of double-target neural circuit-magnetic stimulation in the clinical treatment of spinal cord injury.展开更多
基金supported by the National Natural science Foundation of china(70271069)
文摘The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.
文摘In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.
文摘Addresses the design problems of robust L2-L∞ filters with pole constraint in a disk for uncertain continuous-time linear systems. The uncertain parameters are assumed to belong to convex bounded domains. The aim is to determine a stable linear filter such that the filtering error system possesses a prescribed L2-L∞ noise attenuation level and expected poles location. The filtering strategies are based on parameter-dependent Lyapunov stability results to derive new robust L2-L∞ performance criteria and the regional pole placement conditions. From the proposed multi-objective performance criteria, we derive sufficient conditions for the existence of robust L2-L∞ filters with pole constraint in a disk, and cast the filter design into a convex optimization problem subject to a set of linear matrix inequality constraints. This filtering method exhibits less conservativeness than previous results in the quadratic framework. The advantages of the filter design procedures are demonstrated by means of numerical examples.
基金supported by the National Natural Science Foundation of China,Nos. 81772453 and 81974358 (both to DSX)Shanghai Municipal Key Clinical Specialty Program,No. shslczdzk02701 (to QX)。
文摘Multi-target neural circuit-magnetic stimulation has been clinically shown to improve rehabilitation of lower limb motor function after spinal cord injury. However, the precise underlying mechanism remains unclear. In this study, we performed double-target neural circuit-magnetic stimulation on the left motor cortex and bilateral L5 nerve root for 3 successive weeks in a rat model of incomplete spinal cord injury caused by compression at T10. Results showed that in the injured spinal cord, the expression of the astrocyte marker glial fibrillary acidic protein and inflammatory factors interleukin 1β, interleukin-6, and tumor necrosis factor-α had decreased, whereas that of neuronal survival marker microtubule-associated protein 2 and synaptic plasticity markers postsynaptic densification protein 95 and synaptophysin protein had increased. Additionally, neural signaling of the descending corticospinal tract was markedly improved and rat locomotor function recovered significantly. These findings suggest that double-target neural circuit-magnetic stimulation improves rat motor function by attenuating astrocyte activation, thus providing a theoretical basis for application of double-target neural circuit-magnetic stimulation in the clinical treatment of spinal cord injury.
