CONVERGENCE OF ITERATION METHODS OF MAXIMUM LIKELIHOOD ESTIMATOR AND ITS APPLICATIONS

Iteration methods and their convergences of the maximum likelihoodestimator are discussed in this paper.We study Gauss-Newton method and give a set ofsufficient conditions for the convergence of asymptotic numerical stability.The modifiedGauss-Newton method is also studied and the sufficient conditions of the convergence arepresented.Two numerical examples are given to illustrate our results.

A METHOD OF ON-LINE MEASUREMENT FOR THE FREQUENCY RESPONSE AND IMPULSE RESPONSE FUNCTIONS OF MULTIVARIATE SYSTEM

In this paper,a method of multipoint pseudorandom combined excita-tion with the orthogonal reciprocal repeated sequences(ORRS)is presented on thebackground of the on-line identification of multivariate system.The capacity of therestraint to the identification error caused by the non-random D.C.drift of the mul-ti-input excitation with the ORRS in the multivariate system is also discussed.Thevalidity of the method described in this paper is proved by the modelling tests of themulti-plate rotor system.

MEASUREMENT AND COMPUTATION OF THE PSEUDO-RESONANCE AND ANTI-RESONANCE

This paper presents a phenomenon of“Pseudo-resonance”of beams androds discovered from experiments and computations,and gives the definition of“Pseudo-resonance”.The relationship of distribution between the frequency of pseu-do-resonance and that of anti-resonance is found,and an analytic solution for thetransfer function between any two points on a beam or rod is established.The law ofdistribution of the anti-resonant frequencies,as well as the relation between the fre-quency distribution and the nodes of vibration is also proposed.

THE MODULUS OF CONVEXITY AND THE EQUIVALENT CONDITIONS OF UNIFORMLY NON-SQUARE SPACES

This paper shows that X is uniformly non-square iff P(η_o)】0 for someη_o∈(0,2).Thus X is super-reflexive if and only if for X there exists an equivalent normwhich meets the above condition.By virtue of the before mentioned result,the author derives the necessary,and suffi-cient conditions for X and l^p(X_j)being uniformly non-square,respectively,and gives acharacterization of finite-dimensional spaces which are uniformly non-square.

MODELING AND ANALYSIS OF HUMAN PULSE

Pulse diagnosis is a special method of diagnosing patient’s disease.Amathematical model of the pulse is presented in this paper.The feature parameters ofthe sphygmogram are extracted based on the signal model.The discrimination andprincipal analysis are employed to identify the pulses.The results are matching withthose of traditional methods.

Theory and Applications of Discontinuous State Feedback Generating Chaos for Linear Systems

我们调查由在一个不连续的状态下面增加反馈控制项目在 n 维的线性微分系统的一种类型上产生技术的一种混乱。这个方法与数字模拟的一些例子被检查。一条建设性的定理为与上述混乱系统有关的概括同步被建议。

STUDY ON DYNAMICS, STABILITY AND CONTROL OF MULTI-BODY FLEXIBLE STRUCTURE SYSTEM IN FUNCTIONAL SPACE

The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern Mathematics. First, the dynamical control model of the distributed parameter system with multi-body flexible and multi-topological structure was established which has damping, gyroscopic parts and constrained damping. Secondly, the necessary and sufficient condition of controllability and observability, the stability theory and asymptotic property of the system were obtained. These results expand the theory of the field about the dynamics and control of the system with multi-body flexible structure, and have important engineering significance.

Approximate analytical solutions and approximate value of skin friction coeffcient for boundary layer of power law fluids

This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained. The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms. Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature. Moreover, the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.

Flow of a Viscoelastic Fluid through a Porous Channel with Expanding or Contracting Walls

The flow of a viscoelastic fluid in porous channels with expanding or contracting walls is investigated.Using a similar transformation,the governing equations are reduced to a nonlinear fifth-order differential equation.The homotopy analysis method is employed to obtain the expression for velocity fields.The analytical solutions are influenced by the permeation Reynolds number Re,the wall expansion ratio a and viscoelastic parameter w.Graphs are sketched and the effects of some values of parameters,especially the expansion ratio,on the velocity fields are discussed in detail.

MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP

In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.

Multiple Solutions of Laminar Flow in Channels with a Transverse Magnetic Field

We present a numerical investigation for steady laminar flow of a viscous incompressible electrically conducting fluid through a channel of a rectangular cross-section with a transverse magnetic field and suction or injection wails. Multiple solutions are presented for values of suction Reynolds number R and velocity coefficients of accelerating walls. Additionally, the associated transfer characteristics are discussed in detail.

Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space

It is well known that the problem on the stability of the solutions for Fredholm integral equation of the first kind is an ill-posed problem in C[a, b] or L2 [a, b]. In this paper, the representation of the solution for Fredholm integral equation of the first kind is given if it has a unique solution. The stability of the solution is proved in the reproducing kernel space, namely, the measurement errors of the experimental data cannot result in unbounded errors of the true solution. The computation of approximate solution is also stable with respect to ｜｜· ｜｜c or ｜｜L2· A numerical experiment shows that the method given in this paper is stable in the reproducing kernel space.

Analytical solution to stagnation-point flow and heat transfer over a stretching sheet based on homotopy analysis

This paper is concerned with two-dimensional stagnation-point steady flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit. The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. Analytical solutions of the velocity distribution and dimensionless temperature profiles are obtained for different ratios of free stream velocity and stretching velocity, Prandtl number, Eckert number and dimensionality index in series forms using homotopy analysis method（HAM）. It is shown that a boundary layer is formed when the free stream velocity exceeds the stretching velocity, and an inverted boundary layer is formed when the free stream velocity is less than the stretching velocity. Graphs are presented to show the effects of different parameters.

MHD Boundary Layer Flow of a Non-Newtonian Fluid on a Moving Surface with a Power-Law Velocity

为有幂定律速度的动人的表面上的 MHD 边界层流动的理论分析被介绍。皮肤磨擦系数的精确表情被导出。分析近似答案借助于 Adomian 分解方法被获得。近似答案的可靠性和效率被数字的在文学验证。

Analysis of cavitation problem of heated elastic composite ball

The cavitation problem of a composite ball under a uniform temperature is investigated, and the ball is composed of two elastic solid materials. The nonlinear mathematical model of the problem is established with the finite logarithmic strain measure for a large geometric deformation and by the Hooke law for elastic materials. The analytic solutions in a parametric form are derived for the thermal dilatation of the composite ball with a large elastic deformation. Solution curves are given to describe the variations of the critical temperature in the cavitation with the geometric and material parameters. The bifurcation curve is also given to reveal the cavity growth after void nucleation. The numerical results for a computational example indicate that the radius of the cavity will rapidly grow above the critical temperature, and the loop stress will become infinite when void nucleation. ＂This means that the materials near the cavity will produce a plastic deformation leading to local failure and fracture if the material of the internal ball is elastoplastic. In addition, the cavitation of the composite ball appears at a low temperature if the elastic property of the material of the internal ball is nearly uncompressible.

NONPARAMETRIC ESTIMATION OF BIVARIATE SURVIVAL FUNCTION UNDER THE COMPETING RISKS CASE

Estimation of the bivariate survival function under the competing risks caseis considered.We give an explicit formula for the estimator from a decomposition of thebivariate survival function based on competing risks,which is almost sure consistent.

ON EXISTENCE OF WEAK SOLUTION TO A KIND OF SEMICONDUCTOR EQUATION AFFECTED BY A MAGNETIC FIELD

The semiconductor basic equation system under the influence of magneticfield is considered in this paper.The system is a parabolic-elliptic coupled system with themixed initial-boundary value conditions.The existence result of the weak solution to theproblem is obtained by using the regularizing method and Moser’s technique,and the con-ditions proposed by the authors in another paper are then reduced.

THE DYNAMIC CHARACTERISTICS OF LONG SPAN ARCH STRUCTURE

This paper presents a method for isolatedly solving the normal mode of vi-bration according to the uncoupling condition of vibrations inside and outside the archplane.The finite element method for curved beam elements is adopted to analyse the dy-namic characteristics of arch structures and the calculating program is made.The resultsobtained from Apple II microcomputer are compared with those from SAP5 program byan example,and are in good agreement.

ON A PROBLEM OF N.SALINAS

This paper presents a discussion on a problem suggested by N.Salinas（J.Operator Theory,Vol.10,1983）,i.e.,if T=（T1,T2,…,Tn）is a commuting n-tuple ofhyponormal operators on a complex Hilbert space,do we have（1）（2）δ（T-μ）=dist（μ,σl（T））,μ∈Cn?It is proved that the problems（1）and（2）are both true for some commuting n-tuples ofsemihyponormal operators.In general case,problem（1）has a negative answer.As an ap-plication,we point out that there exists a commuting n-tuple of hyponormal operatorsT（n≥2）,such that|λ|【,where σT（T）denotes J.L.Taylor’sjoint spectra of T,even if the condition of Taylor’s joint spectra of T is given.

RECURSIVE PARAMETER ESTIMATION OF LINEAR DELAYED SYSTEM VIA NUMERICAL INTEGRAL OPERATION

In this paper,the problem of Parameter estimation in linear delayedsystems from sampled data is treated.Using numerical integral operation(NIO),anidentification model which is parametrized directly in the linear delayed system pa-rameters is got.With the least square(LS)method or the instrumental variable(Ⅳ)method,the recursive algorithm of parameter estimation is given.The result ofthe illustrated example shows that this algorithm is simple,rapid and accurrate.