Asymptotic equivalence of two systems of differential equations with impulse effect

In this paper we prove an analogue of Levinson's theorem for asymptotic equivalence of linear differential systems with impulse effect.     

THE APPROXIMATE DENSITIES OF SOME QUADRATIC FORMS OF STATIONARY RANDOM VARIABLES

Abstract. First we obtain a convenient way of expressing the determinant of the difference between an identity matrix and some products of Toeplitz matrices. Then, using these results, we show that for a large number of normal processes there exist some quadratic forms whose matrices are of Toeplitz type such that their joint density admits an Edgeworth expansion.     

弯波导的本征模与角传播常数

本文采用严格的本征模表示矩表截面均匀弯曲波导中的场，文中给出了虚阶Ｂｅｓｓｅｌ函数及其导数的计算公式和计算方法，由此完整地解决了任意半径弯波导本征征模及角传播常数的精确计算问题，典型数值计算结果表明，弯波导中的本征模与直波导中的本征模具有一一对应关系，变波导的等效传播常数与直波导的传播常数在数值上相当接近，模场的径向分布则呈衰减的驻波形式。     

Asymptotic approximations and bottleneck analysis in product form queueing networks with large populations

Asymptotic approximations are constructed for the performance measures of product form queueing networks consisting of single server, fixed rate nodes with large populations. The approximations are constructed by applying singular perturbation methods to the recursion equations of Mean Value Analysis. Networks with a single job class are studied first to illustrate the use of perturbation techniques. The leading term in the approximation is related to bottleneck analysis, but fails to be accurate if there is more than one bottleneck node. A uniform approximation is constructed which is valid for networks with many bottleneck nodes. The accuracy of the uniform approximation is demonstrated for both small and large population sizes. Next, multiclass networks are considered. The leading term in the asymptotic approximation is again related to bottleneck analysis but fails to be valid across “switching surfaces”. Across these the bottleneck nodes of the network change as a function of the fraction of jobs in the different job classes. A boundary layer correction is constructed near the switching surfaces which provides an asymptotic connection across the switching surfaces. Numerical examples are presented to demonstrate the accuracy of the results. We illustrate the asymptotic approach on some simple networks and indicate how to treat more complicated problems.     

A new parameter estimate in singular perturbations

A new upper bound is obtained for the singular perturbation parameter of an asymptotically stable singularly perturbed system. General time-invariant systems with a single small parameter are considered. The paper employs a Riccati equation whose solution is known to facilitate the exact decoupling of fast and slow dynamics. An application of the Brouwer fixed point theorem to the Riccati equation and of Liapunov's direct method to the fast and slow subsystems results in the desired upper bound. Computation of the estimate requires only the solution of two Liapunov matrix equations.     

Controller parameterization for SISO and MIMO plants with time delay

Controller parameterization is a very fundamental problem in control theory. It provides an elegant and efficient way towards solving the stabilizing and design problem, with which all stabilizing controllers are characterized and thus a constrained design procedure can be replaced by an unconstrained optimization. In this paper we deal with the problem of characterizing all stabilizing controllers for single-input/single-output (SISO) plants with time delay and multi-input/multi-output (MIMO) plants with multiple time delays. A new parameterization is derived on the basis of the definition of the internal stability. The new parameterization does not depend on the coprime factorization of the plant and has similar form to that of the Youla parameterization for stable plants. An important merit of the proposed parameterization is that it reflects the internal model control (IMC) structure and thus has a very simple relationship to the sensitivity function and complementary sensitivity function. Numerical examples are given to illustrate the proposed parameterization.     

A Decision Procedure for Linear “Big O” Equations

Let F be the set of functions from an infinite set, S, to an ordered ring, R. For f, g, and h in F, the assertion f = g + O(h) means that for some constant C, |f(x) − g(x)| ≤C |h(x)| for every x in S. Let L be the first-order language with variables ranging over such functions, symbols for 0, +, −, min , max , and absolute value, and a ternary relation f = g + O(h). We show that the set of quantifier-free formulas in this language that are valid in the intended class of interpretations is decidable and does not depend on the underlying set, S, or the ordered ring, R. If R is a subfield of the real numbers, we can add a constant 1 function, as well as multiplication by constants from any computable subfield. We obtain further decidability results for certain situations in which one adds symbols denoting the elements of a fixed sequence of functions of strictly increasing rates of growth.     

On the Energy Decay for a Thermoelastic Contact Problem Involving Heat Transfer

A dynamic unilateral contact problem between two thermoelastic beams is considered. Under thermal boundary conditions involving heat transfer, the evolution problem is shown to possess an energy decaying exponentially to zero, as time goes to infinity.     

Control charting and survey sampling techniques in process monitoring

Control charts are widely used for the detection of shifts in process parameters. In this study, we propose some enhanced Shewhart-type control charts using improved estimators based on auxiliary characteristics. A general control charting structure is developed that can be used with different location estimators. Performance of the proposed charts is compared using average run length (ARL), extra quadratic loss (EQL), and relative average run length (RARL) as performance measures. Comparisons are made among different proposals and the existing counterparts. It is observed that the proposed charts offer improved detection abilities depending upon the correlation structures among different variables under consideration. An illustrative example is also included to highlight the applications in practical situations.