Modelling and analysis of a software system with improvements in the testing phase

In this paper, we consider the error detection phenomena in the testing phase when modifications or improvements can be made to the software in the testing phase. The occurrence of improvements is described by a homogeneous Poisson process with intensity rate denoted by λ. The error detection phenomena is assumed to follow a nonhomogeneous Poisson process (NHPP) with the mean value function being denoted by m(t). Two models are presented and in one of the models, we have discussed an optimal release policy for the software taking into account the occurrences of errors and improvements. Finally, we discuss the possibility of an improvement removing k errors with probability p_k, k ≥ 0 in the software and develop a NHPP model for the error detection phenomena in this situation.     

Regularized solution for nonlinear elliptic equations with random discrete data

The aim of this paper is to study the Cauchy problem of determining a solution of nonlinear elliptic equations with random discrete data. A study showing that this problem is severely ill posed in the sense of Hadamard, ie, the solution does not depend continuously on the initial data. It is therefore necessary to regularize the in‐stable solution of the problem. First, we use the trigonometric of nonparametric regression associated with the truncation method in order to offer the regularized solution. Then, under some presumption on the true solution, we give errors estimates and convergence rate in L²‐norm. A numerical example is also constructed to illustrate the main results.     

Existence results of second order impulsive functional differential equations with infinite delay and fractional damping

In this paper we prove the existence, uniqueness, regularity and continuous dependence of mild solutions for second order impulsive functional differential equations with infinite delay and fractional damping in Banach spaces. We generalize the existence theorem of integer order differential equations to the fractional order case. The results obtained here improve and generalize some known results.     

Existence for neutral impulsive functional differential equations with nonlocal conditions

In this paper, we study a class of neutral impulsive functional differential equations with nonlocal conditions. We suppose that the linear part satisfies the Hille-Yosida condition on a Banach space and it is not necessarily densely defined. We give some sufficient conditions ensuring the existence of integral solutions and strict solutions. To illustrate our abstract results, we conclude this work by an example.     

具有不同初值的Dynamo抛物方程对初始时刻几何的连续依赖性

In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An explicit continuous dependence inequality is obtained even with different prescribed data.     

Optimal control and properties of nonlinear multistage dynamical system for planning horizontal well paths

The goal of planning a horizontal well path is to obtain a trajectory that arrives at a given target subject to various constraints. In this paper, the optimal control problem subject to a nonlinear multistage dynamical system (NMDS) for horizontal well paths is investigated. Some properties of the multistage system are proved. In order to derive the optimality conditions, we transform the optimal control problem into one with control constraints and inequality-constrained trajectories by defining some functions. The properties of these functions are then discussed and optimality conditions for optimal control problem are also given. Finally, an improved simplex method is developed and applied to the optimal design for well Ci-16-Cp146 in Oil Field of Liaohe, and the numerical results illustrate the validity of both the model and the algorithm.     

一类具有奇异性与真空的非牛顿流局部强解的爆破准则

探讨了如下一类非牛顿流pt+(pu)χ=0,(pu)χ+(pu2)χ-(︱uχ︱p-2uχ)χ+πχ=pf,π=π(p)=Apr,(χ,t)∈Ωr1,A>0,r>1,其初边值条件为(p,u)|t=0=(p0,u0),χ∈(-1,I),u|χ=1=u|χ=-1=0,t∈(0,T1).利用迭代方法,讨论了该模型的局部强解的爆破准则,证明了:如果T_*是强解(ρ,u)存在的最大时间且T*相似文献   

Continuity and generators of dynamical semigroups for infinite Bose systems

For a class of quasifree quantum dynamical semigroups on the algebra of the canonical commutation relations (CCR) we give sufficient conditions for these semigroups to extend to ultraweakly continuous semigroups of normal operators on the von Neumann algebra associated with a representation of the CCR. Then the explicit form of the generators of the extended semigroups is calculated.     

一类具有可修故障和不可修故障的两部件并联可修系统的适定性问题

主要用强连续半群理论,研究了一类具有可修故障和不可修故障的两部件并联系统非负时间依赖解的存在惟一性问题.     

两相同部件并联部分可修复系统的可靠性分析

用C_0半群理论,研究了一类两相同部件并联部分可修复系统解的存在惟一性及指数稳定性,并从本征向量的角度讨论了此系统的一些主要可靠性指标,给出了瞬态可用度的数值模拟.     

The existence of strong solution for a class of fully nonlinear equation

This article mainly investigates the existence of global strong solution of a class of fully nonlinear evolution equation and the strong solution of its steady-state equation. By using the T-compulsorily weakly continuous operator theory, the existence of the global strong solution of the fully nonlinear evolution equation is obtained. In addition, based on the acute angle principle, the W^2,p-strong solution for the corresponding stationary equation is also derived.     

Dynamical analysis of chemotherapy models with time-dependent infusion

Classical mathematical models for chemotherapy assume a constant infusion rate of the chemotherapy agent. However in reality the infusion rate usually varies with respect to time, due to the natural (temporal or random) fluctuation of environments or clinical needs. In this work we study a non-autonomous chemotherapy model where the injection rate and injection concentration of the chemotherapy agent are time-dependent. In particular, we prove that the non-autonomous dynamical system generated by solutions to the non-autonomous chemotherapy system possesses a pullback attractor. In addition, we investigate the detailed interior structures of the pullback attractor to provide crucial information on the effectiveness of the treatment. The main analytical tool used is the theory of non-autonomous dynamical systems. Numerical experiments are carried out to supplement the analysis and illustrate the effectiveness of different types of infusions.     

Bifurcation analysis for a three-species predator-prey system with two delays

In this paper, a three-species predator-prey system with two delays is investigated. By choosing the sum τ of two delays as a bifurcation parameter, we first show that Hopf bifurcation at the positive equilibrium of the system can occur as τ crosses some critical values. Second, we obtain the formulae determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included.     

与渐近非扩张半群不动点问题相关的分裂等式混合均衡问题及其应用

研究了与渐近非扩张半群不动点问题相关的分裂等式混合均衡问题.在等式约束下,为同时逼近两个空间中混合均衡问题和渐近非扩张半群不动点问题的公共解,借助收缩投影方法引出了一种迭代程序.在适当条件下,该迭代算法的强收敛性被证明.文末还把所得结果应用于分裂等式混合变分不等式问题和分裂等式凸极小化问题.     

弹性振动点观测反馈控制古典解的存在性

本文运用有界线性算子的积分半群理论证明弹性振动点观测反馈控制方程古典解的存在性     

Global analysis of continuous analogues of the Levenberg-Marquardt and Newton-Raphson methods for solving nonlinear equations

Summary Global analyses are given to continuous analogues of the Levenberg-Marquardt methoddx/dt=−(J ^t(x)J(x)+δI)⁻¹J^t(x)g(x), and the Newton-Raphson-Ben-Israel methoddx/dt=−J ⁺(x)g(x), for solving an over- and under-determined systemg(x)=0 of nonlinear equations. The characteristics of both methods are compared. Erros in some literature which dealt with related continous analogue methods are pointed out. The Institute of Statistical Mathematics     

一类随机种群方程解的存在性和指数稳定性

首先对一类半线性随机发展方程建立其解的存在性和渐近行为的结果,这类方程的线性部分生成一强连续半群.然后将抽象结果应用于依赖年龄的随机种群方程,获得它的存在性和渐近性质.