Consistency and Asymptotic Property of a Weighted Least Squares Method for Networked Control Systems

In this paper, we study the problems related to parameter estimation of a single-input and single-output networked control system, which contains possible network-induced delays and packet dropout in both of sensor-to-controller path and controller-to-actuator path. A weighted least squares(WLS) method is designed to estimate the parameters of plant, which could overcome the data uncertainty problem caused by delays and dropout. This WLS method is proved to be consistent and has a good asymptotic property. Simulation examples are given to validate the results.

Asymptotic Property of Approximation to x~αsgnx by Newman Type Operators

The approximation of ｜x｜ by rational functions is a classical rationalproblem. This paper deals with the rational approximation of the function xasgnx, which equals ｜x｜ if α=1. We construct a Newman type operator rn（x） and show max｜x｜≤1{｜x^αsgnx-rn（x）｜}-Cn-α/2e-√2nα where C is a constant depending on α.

The Asymptotic Property of Approximation to |x| by Newman Type Rational Operators

Let p(x) =∏k=1n=1((k/n)r+z),0<r≤1,Hn,r(x)=x(p(x)-p(-x))/(p(x)+p(-x)).The present note gives the asymptotic formula of max ||x| - Hn,r(x)|.

Asymptotic Property of Approximation to x~αsgn x by Newman Type Operators

Approximation to the function ｜x｜ plays an important role in approximation theory. This paper studies the approximation to the function xαsgn x, which equals ｜x｜ if α = 1. We construct a Newman Type Operator rn（x） and prove max ｜x｜≤1｜xαsgn x-rn（x）｜～Cn1/4e-π1/2（1/2）αn.

Asymptotic Property for Some Series of Probability

Abstract Let {X, Xn, n ≥ 1} be a sequence of i.i.d.random variables with zero mean, and set Sn = n∑k=1Xk, EX2 = σ2 〉 0, λ（ε） = ∞∑n=1P（1Sn1 ≥ ns）. In this paper, we discuss the rate of the approximation of σ2 by ε2= λ（s） under suitable conditions, and improve the corresponding results of Klesov （1994）.

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,

Global Soultions and Asymptotic Properties for a Class of Partial Differential Equations

This paper is concerned with the generalzed global solution and its asymptotic properties for the initial value problem of the partial differential equationu t+u x 3 =F(u).

ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES

It is well-known that the complete convergence theorem for i.i.d, random vari- ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4] obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever c goes to zero, so it is of interest to investigate the asymptotic behavior of the series as e goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.

Asymptotic Behavior of Global Solutions for Double Degenerate Nonlinear Parabolic Equation

In this paper we study the decay estimate of global solutions to the initial-boundary value problem for double degenerate nonlinear parabolic equation by using a dif-ference inequality.

Spatial Asymptotic Properties of a System Wave Equations with Nonlinear Damping and Source Terms

In this paper,the wave equation defined in a semi-infinite cylinder is considered,in which the nonlinear damping and source terms is included.By setting an arbitrary parameter greater than zero in the energy expression,the fast growth rate or decay rate of the solution with spatial variables is obtained by using energy analysis method and differential inequality technique.Secondly,we obtain the asymptotic behavior of the solution on the external domain of the sphere.In addition,in this paper we also give some useful remarks which show that our results can be extended to more models.

Volume of unit ball in an n-dimensional normed space and its asymptotic properties

Let Bp^n={x∈R^b｜‖x‖p≤1} be the unit ball of p norm in the n-dimensional normed space εp＆n.The formula for the volume of Bp^n was obtained and its asymptotic properties were found out as n→∞and p→∞.

Some Asymptotic Properties for Multivariate Partially Linear Models

The paper considers a multivariate partially linear model under independent errors,and investigates the asymptotic bias and variance-covariance for parametric component βand nonparametric component F（·）by the GJS estimator and Kernel estimation.

Asymptotic and stable properties of general stochastic functional differential equations

The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.

THE ASYMPTOTIC PROPERTIES OF HIGH FREQUENCIES FOR BARS,BEAMS AND MEMBRANES

In this paper, a uniform analysis of the asymptotic properties of high frequencies of non-uniform bars, beams and circular membranes is given by using perturbation method, and the ease of discontinuous physical parameters is also discussed.

ASYMPTOTIC BEHAVIOR OF SOLUTION BRANCHES OF NONLOCAL BOUNDARY VALUE PROBLEMS

In this article, by employing an oscillatory condition on the nonlinear term,a result is proved for the existence of connected component of solutions set of a nonlocal boundary value problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions of the nonlinear problem for all parameter values in that interval.

Binary Bell Polynomials,Bilinear Approach to Exact Periodic Wave Solutions of(2+l)-Dimensional Nonlinear Evolution Equations

In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.

Empirical Likelihood Inference for AR（p） Model

In this article we study the empirical likelihood inference for AR（p） model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parametric, and we also propose an empirical log-likelihood ratio base on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotically standard chi-squared.

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.

Two Notes on Numerical DifFerentiation Formulae

Some new conclusions on asymptotic properties and inverse problems of numerical differentiation formulae have been drawn in this paper.In the first place,several asymptotic properties of intermediate points of numerical differentiation formulae are presented by using Taylor's formula.And then,based on the ideas of algebraic accuracy,several inverse problems of numerical differentiation formulae are given.

Global Existence and Lifespan of Solutions to the Cauchy Problems for the Nonlinear Schrodinger Equations

This paper deals with the global existence,asymptotic property and lifespan of solutions to the Cauchy problems for a class of nonlinear Schrodinger equation.