Second-Order Formulas in Action

This survey article illustrates many important current trends and perspectives for the field and their applications, of interest to researchers in modern algebra, mathematical logic and discrete mathematics. It covers a number of directions, including completeness theorem and compactness theorem for hyperidentities;the characterizations of the Boolean algebra of n-ary Boolean functions and the bounded distributive lattice of n-ary monotone Boolean functions;the functional representations of finitely-generated free algebras of various varieties of lattices via generalized Boolean functions, etc.

A CLASS OF STATIONARY MODELS OF SINGULAR STOCHASTIC CONTROL

A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.

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.

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

A theoretical analysis for MHD boundary layer flow on a moving surface with the power-law velocity is presented. An accurate expression of the skin friction coefficient is derived. The analytical approximate solution is obtained by means of Adomian decomposition methods. The reliability and efficiency of the approximate solutions are verified by numerical ones in the literature.

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.

Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet

The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.

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.

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.

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.

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

We investigate a kind of chaos generating technique on a type of n-dimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system.

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.

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.

DECAY ESTIMATE OF THE SOLUTIONS TO THE MAGNETO-SEMICONDUCTOR EQUATIONS

In this paper,the relationship between the time-dependent solutions andsteady-state solutions of the semiconductor equations affected by magnetic field isconsidered.A decay estimate between the time-dependent solutions and steady-statesolutions is proved by a series of estimetes on the solutions under some conditions.

ASSESSMENT OF INFLUENCE IN CANONICAL CORRELATION ANALYSIS

By expanding the perturbation of covariance matrix in the powers of er-ror term,the influence functions for five canonical measurements in CCA are devel-oped and three sample versions are given.For generalized correlation coefficient p_z,the influence function is a quadratic form of r.v.z,and its distribution is considered.A practical example iUustrates the utility of the proposed influence functions.

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.