Existence results for second order boundary value problem of impulsive dynamic equations on time scales

In this paper, Schaefer's fixed point theorem and nonlinear alternative of Leray-Schauder type are used to investigate the existence of solutions for second order boundary value problem for impulsive dynamic equations on time scales.     

Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian

This paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93-104].     

Predicting vibration signals of automobile engine using chaos theory

Condition monitoring and life prediction of the vehicle engine is an important and urgent problem during the vehicle development process. The vibration signals that are closely associated with the engine running condition and its development trend are complex and nonlinear. The chaos theory is used to treat the nonlinear dynamical system recently. A novel chaos method in conjunction with SVD (singular value decomposition)denoising skill are used to predict the vibration time series. Two types of time series and their prediction errors are provided to illustrate the practical utility of the method.     

On the optimization of the initial boundary value problem for a conservation law

In the present note, the theory of shift differentiability for the Cauchy problem is extended to the case of an initial boundary value problem for a conservation law. This result allows to exhibit an Euler-Lagrange equation to be satisfied by the extrema of integral functionals defined on the solutions of initial boundary value problems of this kind.     

关于曲线积分中值定理“中间点”的一个一般性结果

讨论了第一类曲线积分中值定理“中间点”的渐近性质,得到了更具一般性的新结果.     

On the Solution of Discontinuous IVPs by Adaptive Runge–Kutta Codes

In this paper an automatic technique for handling discontinuous IVPs when they are solved by means of adaptive Runge–Kutta codes is proposed. This technique detects, accurately locates and passes the discontinuities in the solution of IVPs by using the information generated by the code along the numerical integration together with a continuous interpolant of the discrete solution. A remarkable feature is that it does not require additional information on the location of the discontinuities. Some numerical experiments are presented to illustrate the reliability and efficiency of the proposed algorithms.     

Pensions modelling

Valuable insights into the problem of how to fund defined benefitpension schemes can be obtained by analysis using the standardBlack–Scholes/Merton option pricing model, consideringthe pension fund finances jointly with those of the sponsoringcompany. The nature of the fund assets and liabilities is completelydifferent, and this lies behind current controversies aboutthe appropriate discount rate, valuation, financial accountingand preferential status for pension fund claimants in insolvency.     

Covering group and graph of discretized volumes

We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L _V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ _v associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.     

On the concept of point value in the infinite-dimensional realization theory

In this article, we study the effect of the chosen representation of a point value (and point evaluation) on the class of periodic signals realizable using a certain type of infinite-dimensional linear system. By suitably representing the point evaluation at the origin in a Hilbert space, we are able to give a complete characterization of its extensions. These extensions involve a new concept called δ-sequence, the use of which as an observation operator of an infinite-dimensional linear system is studied in this article. In particular, we consider their use in the realization of periodic signals. We also investigate how the use of δ-sequences affects the convergence properties of such realizations; we consider the rate and character of convergence and the removal of the Gibbs phenomenon. As still a further demonstration of the significance of the chosen concept of a point value, we discuss the use of distributional point values in the realization of periodic distributions. The possible applications of this work lie in regulator problems of infinite-dimensional control theory, as is indicated by the well-known internal model principle.     

A Tandem Queue with Coupled Processors: Computational Issues

In Resing and Örmeci [16] it is shown that the two-stage tandem queue with coupled processors can be solved using the theory of boundary value problems. In this paper we consider the issues that arise when calculating performance measures like the mean queue length and the fraction of time a station is empty. It is assumed that jobs arrive at the first station according to a Poisson process and require service at both stations before leaving the system. The amount of work that a job requires at each of the stations is an independent, exponentially distributed random variable. When both stations are nonempty, the total service capacity is shared among the stations according to fixed proportions. When one of the stations becomes empty, the total service capacity is given to the nonempty station. We study the two-dimensional Markov process representing the numbers of jobs at the two stations. The problem of finding the generating function of the stationary distribution can be reduced to two different Riemann-Hilbert boundary value problems, where both problems yield a complete analytical solution. We discuss the similarities and differences between the two problems, and relate them to the computational aspects of obtaining performance measures.