L^2-策略休假下可修的M_1+M_2/G^x(M/G)/1匹配排队系统分析

双输人匹配排队系统是通常排队系统的一种推广．本文对该系统考察了Ｌ２－策略休假和服务台可修的两个重要因素．其中假定系统有两个不同的Ｐｏｉｓｓｏｎ输入，两类顾客按１：１作成一批进行服务，服务台的寿命服从指数分布，服务时间，修理时间和休假时间都服从一般连续型分布，利用向量马氏过程方法，得到了该排队系统的一些重要的稳态排队论指标和可靠性指标．     

The reducibility of the equations of free motion of a complex mechanical system

A mechanical system consists of an unchangeable rigid body (a carrier) and a subsystem whose configuration and composition may vary with time (the motion of its elements relative to the carrier is given). The free motion of the system in a uniform gravitational field is investigated, on the assumption that there is no dynamic symmetry. Necessary and sufficient conditions are derived for the existence of two integrals, each quadratic in the components of the absolute angular velocity of the carrier. Lt is shown that the initial dynamical system can be reduced to an autonomous gyrostat system if and only if the motion has these two quadratic integrals; the explicit form of a linear transformation to the autonomous system is indicated. The explicit form of the integrals and conditions for their existence are obtained. Examples of motion with two quadratic integrals are considered.     

Aggregation and emergence in systems of ordinary differential equations

The aim of this article is to present aggregation methods for a system of ordinary differential equations (ODE's) involving two time scales. The system of ODE's is composed of the sum of fast parts and a perturbation. The fast dynamics are assumed to be conservative. The corresponding first integrals define a few global variables. Aggregation corresponds to the reduction of the dimension of the dynamical system which is replaced by an aggregated system governing the global variables at the slow time scale. The centre manifold theorem is used in order to get the slow reduced model as a Taylor expansion of a small parameter. We particularly look for the conditions necessary to get emerging properties in the aggregated model with respect to the nonaggregated one. We define two different types of emergences, functional and dynamical. Functional emergence corresponds to different functions for the two dynamics, aggregated and nonaggregated. Dynamical emergence means that both dynamics are qualitatively different. We also present averaging methods for aggregation when the fast system converges towards a stable limit cycle.     

Nonlinear asymptotic analysis of a system of two free coupled oscillators with cubic nonlinearities

In this paper a two degrees of freedom undamped nonlinear system of two unforced coupled oscillators with cubic nonlinearities is analyzed. Through a decoupling procedure and using admissible functional transformations it is proved that this system can be reduced to an intermediate second order nonlinear ordinary differential equation (ODE) connecting both displacements to each other. By nonlinear asymptotic approximations the above equation can be further reduced to new nonlinear ODE that can be analytically solved. The solutions in the physical plane are extracted in parametric form. As generalization, the model of a damped system of two masses connected with stiffness with linear and nonlinear coefficient of rigidities respectively is analyzed and exact analytical solutions are extracted. Finally an application has been given in the case of a two mass system with cubic strong non-linearity.     

Reliability evaluation based on a dependent two-stage failure process with competing failures

This paper evaluates system reliability performance based on a dependent two-stage failure process with competing failures. The failure process of the system can be divided into two stages, i.e., the defect initialization stage, and the defect development stage. Dependence between these two stages is reflected in the fact that they share the same shock process modeled by a nonhomogeneous Poisson process. The impact of shock damage on system failure behavior is characterized by random hazard rate increments of the two stages. Based on practical failure behavior of industrial systems, we consider two typical and competing failure modes, defect-based failure and duration-based failure. Defect-based failure occurs when a defect reaches the damage threshold and duration-based failure is triggered when the duration in defective state is larger than a time threshold. We derive some results on system reliability and show that, with different parameter settings, our model reduces to several classic competing risk models. Finally, a detailed illustrative example of an oil pipeline system is given to demonstrate the applicability of the proposed model.     

Generating a new chaotic attractor by feedback controlling method

A new chaotic system is found by feedback controlling method in this paper. According to the definition of the generalized Lorenz system, the new chaotic system does not belong to generalized Lorenz systems. We analyze the new system by means of phase portraits, Lyapunov exponents, fractional dimension, bifurcation diagram, and Poincaré map. The particular interest is that this novel system can generate two one‐scroll and one two‐scroll chaotic attractors with the variation of a single parameter. The obtained results show clearly that the system is a new chaotic system and deserves a further detailed investigation. Copyright © 2011 John Wiley & Sons, Ltd.     

Extra two-fold Steiner pentagon systems

A two-fold pentagon system is a decomposition of the complete 2-multigraph (every two distinct vertices joined by two edges) into pentagons. A two-fold Steiner pentagon system is a two-fold pentagon system such that every pair of distinct vertices is joined by a path of length two in exactly two pentagons of the system. We consider two-fold Steiner pentagon systems with an additional property : for any two vertices, the two paths of length two joining them are distinct. We determine completely the spectrum for such systems, and point out an application of such systems to certain 4-cycle systems.     

Dynamics and bifurcation study on an extended Lorenz system

In this paper, we study dynamics and bifurcation of limit cycles in a recently developed new chaotic system, called extended Lorenz system. A complete analysis is provided for the existence of limit cycles bifurcating from Hopf critical points. The system has three equilibrium solutions: a zero one at the origin and two non-zero ones at two symmetric points. It is shown that the system can either have one limit cycle around the origin, or three limit cycles enclosing each of the two symmetric equilibria, giving a total six limit cycles. It is not possible for the system to have limit cycles simultaneously bifurcating from all the three equilibria. Simulations are given to verify the analytical predictions.     

具有常规原因和人为错误的两个不同部件平行系统解的性质

讨论了一个由于常规原因和人为错误引起故障的两不同部件并行系统的模型,修复后的故障系统恢复正常.在假设修复率非常数的前提下,运用纯分析的方法给出了两不同部件并行系统解的性质,绕过了该系统解是否存在的问题.     

On the accuracy of conservation of adiabatic invariants in slow-fast Hamiltonian systems

Let the adiabatic invariant of action variable in a slow-fast Hamiltonian system with two degrees of freedom have limits along the trajectories as time tends to plus and minus infinity. The difference of these two limits is exponentially small in analytic systems. An isoenergetic reduction and canonical transformations are applied to transform the slow-fast system to form of a system depending on a slowly varying parameter in a complexified phase space. On the basis of this method an estimate for the accuracy of conservation of adiabatic invariant is given.     

Optimal burn-in for maximizing reliability of repairable non-series systems

Burn-in is a manufacturing process applied to products to eliminate early failures in the factory before the products reach the customers. Various methods have been proposed for determining an optimal burn-in time of a non-repairable system or a repairable series system, assuming that system burn-in improves all components in the system. In this paper, we establish the trade-off between the component reliabilities during system burn-in and develop an optimal burn-in time for repairable non-series systems to maximize reliability. One impediment to expressing the reliability of a non-series system is in that successive failures during system burn-in cannot be described precisely because a failed component is not detected until the whole system fails. For approximating the successive failures of a non-series system during system burn-in, we considered two types of repair: minimal repair at the time of system failure, and repair at the time of component or connection failure. The two types of repair provide bounds on the optimal system burn-in time of non-series systems.     

A single-server discrete-time queue with correlated positive and negative customer arrivals

An MMBP/Geo/1 queue with correlated positive and negative customer arrivals is studied. In the infinite-capacity queueing system, positive customers and negative customers are generated by a Bernoulli bursty source with two correlated geometrically distributed periods. I.e., positive and negative customers arrive to the system according to two different geometrical arrival processes. Under the late arrival scheme (LAS), two removal disciplines caused by negative customers are investigated in the paper. In individual removal scheme, a negative customer removes a positive customer in service if any, while in disaster model, a negative customer removes all positive customers in the system if any. The negative customer arrival has no effect on the system if it finds the system empty. We analyze the Markov chains underlying the queueing systems and evaluate the performance of two systems based on generating functions technique. Some explicit solutions of the system, such as the average buffer content and the stationary probabilities are obtained. Finally, the effect of several parameters on the system performance is shown numerically.     

一类异宿环分支极限环的唯一性

本文研究平面上一类两点或三点异宿环附近极限环的分支,在一简洁条件下证明了异宿环分支极限环的唯一性,并给出了极限环唯一存在的充要条件.作为对三维余维2分支的应用,解决了所出现的两点异宿环产生唯一极限环的问题.     

On computing signatures of coherent systems

It is difficult to compute the signature of a coherent system with a large number of components. This paper derives two basic formulas for computing the signature of a system which can be decomposed into two subsystems (modules). As an immediate application, we obtain the formula for computing the signature of systemwise redundancy in terms of the signatures of the original system and the backup one. The formula for computing the signature of a componentwise redundancy system is also derived. Some examples are given to illustrate the power of the main results.     

Existence of solutions to the Kobayashi–Warren–Carter system

In this paper, a coupled system of two parabolic type initial-boundary value problems is considered. The system is known as the Kobayashi–Warren–Carter model of grain boundary motion in a polycrystal. Kobayashi–Warren–Carter model is derived as a gradient descent flow of an energy functional, which is called “free-energy”, with respect to two unknown variables and it involves a weighted-unknown dependent total variation term. The main goal of this paper is to obtain existence of solutions to this system. We solve the problem by means of a time-discretization of a relaxed system and a highly non-trivial passage to the limit. We point out that our time-discretization method is effective not only for the original Kobayashi–Warren–Carter system but also for its relaxed versions. Therefore, we provide a uniform approach for obtaining solutions to systems associated with this model.     

System dynamics in defence analysis: some case studies

System dynamics has proved to be an effective and efficient methodology for the analysis of defence problems. The paper first reviews some academic background to the defence applications of system dynamics, that is followed by a brief account of two case studies which illustrate the very wide variety of problems in this domain. Not only are the problems different but their analysis illustrates two aspects of system dynamics. Firstly its role is traditional quantitative modelling but it is shown that this is enhanced when system dynamics is combined with other methodologies, and secondly it shows system dynamics' scope for shedding light by purely qualitative, diagrammatic, analysis. However, defence is not solely a matter of the conduct of military operations of different types but also includes the special problems of finance and procurement. Work in that area is dealt with by a brief account of two applications. Finally, the reasons for the success of system dynamics in this domain are considered.     

Confined steady states of a Vlasov‐Poisson plasma in an infinitely long cylinder

We consider the two‐dimensional Vlasov‐Poisson system to model a two‐component plasma whose distribution function is constant with respect to the third space dimension. First, we show how this two‐dimensional Vlasov‐Poisson system can be derived from the full three‐dimensional model. The existence of compactly supported steady states with vanishing electric potential in a three‐dimensional setting has already been investigated in the literature. We show that these results can easily be adapted to the two‐dimensional system. However, our main result is to prove the existence of compactly supported steady states even with a nontrivial self‐consistent electric potential.     

Chaos synchronization between two different chaotic dynamical systems

This work presents chaos synchronization between two different chaotic systems by nonlinear control laws. First, synchronization problem between Genesio system and Rossler system has been investigated, and then the similar approach is applied to the synchronization problem between Genesio system and a new chaotic system developed recently in the literature. The control performances are verified by two numerical examples.     

Double Degeneracy in Multiphase Modulation and the Emergence of the Boussinesq Equation

In recent years, a connection between conservation law singularity, or more generally zero characteristics arising within the linear Whitham equations, and the emergence of reduced nonlinear partial differential equations (PDEs) from systems generated by a Lagrangian density has been made in conservative systems. Remarkably, the conservation laws form part of the reduced nonlinear system. Within this paper, the case of double degeneracy is investigated in multiphase wavetrains, characterized by a double zero characteristic of the linearized Whitham system, with the resulting modulation of relative equilibrium (which are a generalization of the modulation of wavetrains) leading to a vector two‐way Boussinesq equation. The derived PDE adheres to the previous results (such as [1]) in the sense that all but one of its coefficients is related to the conservation laws along the relative equilibrium solution, which are then projected to form a corresponding scalar system. The theory is applied to two examples to highlight how both the criticality can be assessed and the two‐way Boussinesq equation's coefficients are obtained. The first is the coupled Nonlinear Schrodinger (NLS) system and is the first time the two‐way Boussinesq equation has been shown to arise in such a context, and the second is a stratified shallow water model which validates the theory against existing results.     

具有连续时滞和比率型功能反应的竞争系统的正周期解的存在性

本文利用重合度理论中的延拓定理讨论了具有连续时滞和比率型功能反应的非自治扩散竞争系统的正周期解的存在性,得到了正周期解存在的充分条件。