An experimental study is carried out on fatigue defect of layer steel fiber reinforced concrete (LSFRC). Based on experimental data,the various relation curves are given corresponding to different stress levels 0.9, 0...An experimental study is carried out on fatigue defect of layer steel fiber reinforced concrete (LSFRC). Based on experimental data,the various relation curves are given corresponding to different stress levels 0.9, 0.85, and 0.8. Furthermore, the fatigue defect degree is defined, and the strain cycle ratio equations and defect cycle ratio equations with the correlation coefficients very close to 1, are regressed in terms of the cubic polynomial,of which the fittings are preferable.In addition,the results show that the fatigue defect of LSFRC presents three phase development regularity too.And in comparison with the plain concrete,the third phase of the fatigue defect of LSFRC is longer, therefore the fatigue failure of LSFRC is more ductile.The mechanism of the fatigue defect is discussed too.展开更多
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
The paper obtains some equivalent conditions of local asymptotics for the solutions of defective renewal equations in the heavy-tailed case. As applications, the paper gives a different proof of a classical result abo...The paper obtains some equivalent conditions of local asymptotics for the solutions of defective renewal equations in the heavy-tailed case. As applications, the paper gives a different proof of a classical result about the local distribution of the supremum of a random walk. These results are also applied in examples involving the renewal function for terminating renewal processes and the age-dependent branching processes.展开更多
We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimat...We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.展开更多
文摘An experimental study is carried out on fatigue defect of layer steel fiber reinforced concrete (LSFRC). Based on experimental data,the various relation curves are given corresponding to different stress levels 0.9, 0.85, and 0.8. Furthermore, the fatigue defect degree is defined, and the strain cycle ratio equations and defect cycle ratio equations with the correlation coefficients very close to 1, are regressed in terms of the cubic polynomial,of which the fittings are preferable.In addition,the results show that the fatigue defect of LSFRC presents three phase development regularity too.And in comparison with the plain concrete,the third phase of the fatigue defect of LSFRC is longer, therefore the fatigue failure of LSFRC is more ductile.The mechanism of the fatigue defect is discussed too.
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.
基金Supported by the National Natural Science Foundation of China (No. 10671139)the research foundation of Suzhou University of Science and Technology
文摘The paper obtains some equivalent conditions of local asymptotics for the solutions of defective renewal equations in the heavy-tailed case. As applications, the paper gives a different proof of a classical result about the local distribution of the supremum of a random walk. These results are also applied in examples involving the renewal function for terminating renewal processes and the age-dependent branching processes.
基金National Basic Research Program of China(973 Program No.2007CB814903)the National Natural Science Foundation of China(No.70671069)
文摘We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.
