ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS

This paper considers the Calerkin finite element method for the incompressible Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble （RFB） functions. The stability features of the residual-free bubble functions for the linearized Navier-Stokes equations are analyzed in this work. It is shown that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrilateral elements.     

THE LAW OF THE ITERATED LOGARITHM OF THE KAPLAN-MEIER INTEGRAL AND ITS APPLICATION

For right censored data, the law of the iterated logarithm of the Kaplan-Meier integral is established. As an application, the authors prove the law of the iterated logarithm for weighted least square estimates of randomly censored linear regression model.     

ON THE SPACES OF THE MAXIMAL POINTS

For a continuous domain D, some characterization that the convex powerdomain CD is a domain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it is proved that the set of the maximal points Max(CD) of CD with the relative Scott topology is homeomorphic to the set of all Scott compact subsets of Max(.D) with the topology induced by the Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.     

THE DYNAMIC PROPERTIES FOR THE PROTEIN MOLECULAR SYSTEM

In this paper, a new theory for the dynamic properties of protein molecular system have been proposed by means of the analysis of the characteristics of the collective excitations generated under the localized fluctuation and the deformation Of structure of the protein. Some new results obtained from this study show that the Davydov theory is an approximate and disadvantegeous theory.     

ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS

This paper is concerned with the regularity of minimum solution u of the following functional on the restraint Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Hlder continuous.     

THE RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR THE MOISIL-THEODORSCO SYSTEM

This article studies the inhomogeneous Moisil-Theodorsco system in the space R3, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hilbert boundary value problem for the Moisil-Theodorsco system in a cylindrical domain of R3, and gives the solvability conditions and the integral expressions of solutions. The Holder continuity of the solutions is proved.     

ON THE COMPLETENESS OF THE GENERALIZED AXISYMMETRIC STOKES FLOW EQUATION

This paper defines new kinds of functions——the conjugate axisymmetric poteptial functions. With the aid of them, we can prove the completeness of the solutions of the generalized axisymmetric Stokes flow equation without the condition on the convexity of the domain.     

THE CATASTROPHE MODEL FOR THE ACID-BASE PROPERTY OF THE HYDROXIDES OF ELEMENTS IN AQUEOUS SOLUTION

In this paper the acid-base property of various hydroxides of elements has been studied by applying the catastrophe theory. It is indicated that the topological structure of the plane diagrams formed by bond-parameters may be deduced by using the catastrophe theory.The author considers that the application of catastrophe theory may be open a new way of thinking for the theoretical derivation of plane diagrams of bond-parameters.The discussion in this paper is only an illustration     

THE AVERAGE CASE COMPLEXITY OF THE SHIFT-INVARIANT PROBLEM

The present paper deals with the average case, complexity of the shift-invariant problem. The main aim is to give a new proof of the upper bound of average error of finite element method. Our method is based on the techniques proposed by Heinrich(1990). We also point out an essential error regarding the proof of the upper bound in A. G. Werschulz(1991).     

THE RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR THE MOISIL-THEODORSCO SYSTEM

This article studies the inhomogeneous Moisil-Theodorsco system in the space R³, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hilbert boundary value problem for the Moisil-Theodorsco system in a cylindrical domain of R³, and gives the solvability conditions and the integral expressions of solutions. The Holder continuity of the solutions is proved.     

THE SERIES SOLUTION OF THE GEL'FAND-LEVITAN-MARCHENKO EQUATION

The convergence of the Neumann series solution of the Gel'fand-Levitan-Marchenko equation in L~∞[0, ∞), L~1[0, ∞) and L~2[0, ∞) is proved and the explicit expression of the series solution is given.     

ON THE PROBLEMS OF PREVENTING THE BLOWING UP OF THE SOLUTIONS FOR SEMILINEAR PARABOLIC EQUATIONS

§ 1 Introduction The investigating of the existence of globally smooth solutions or the formation of singularities of the solutions for semilinear parabolic equations is of much importance in the theory of partial differential equation as well as in the application. The blowing up of the solutions is an interesting phenomenon and has been pointed out by many authors in various cases, such as by S. Kaplan [1], C. V. pao[2], H. Kawarada[3]etc. In[4], Chen studied the problem of     

THE STRUCTURAL PROPERTIES OF THE DISCRETE POSITIVE REAL MATRIX

In this paper, the structural properties of the discrete positive real matrix (DPRM) are discussed by means of coprime fraction of a rational function matrix. Some structural properties of the DPRM are the same with the continuous positive real matrix (CPRM), but the other properties are unique with the DPRM.     

ON THE EQUIVALENCE OF THE ABEL EQUATION

This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations.     

THE CALCULATION OF THE BILINEAR BOLTZMANN OPERATOR FOR MAXWELLIAN MOLECULES

In this paper, the calculation of the bilinear Boltzmann operator based on the Waldmann's method for Maxwellian molecules has been given. The advantage of our technique lies in the calculation need not operato on the integral of operator. The way of carrying out the calculation is illustrated by several examples containing all proofs of the formulas in the article by Chen Tianquan & others. Moreover, for the linear Boltzmann operator, the calculation is slightly simpler than that of Waldmann.     

THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE

Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space L_a~2 in the case of n > 2.     

THE ASYMPTOTIC FORMULA OF THE ORTHOGONAL RATIONAL FUNCTION ON THE UNIT CIRCLE

In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circlewith respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.     

THE INSTABILITY DEGREE IN THE DIEMNSION OF SPACES OF BIVARIATE SPLINE

In this paper ,the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is consdered.The concept of the instability degree in the dimension of spaces of bivariate spline is presented.The resulats in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.     

THE INSTABILITY DEGREE IN THE DIEMNSION OF SPACES OF BIVARIATE SPLINE

In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.     

A CORRESPONDENCE BETWEEN THE AKNS HIERARCHY AND THE JM HIERARCHY

Reference [1] presented a gauge transformation between the x parts of the AKNS eigenvalue problem and those of the JM(Jaulent-Miedek)eigenvalue problem.In this paper we discuss the correspondence between the t parts of the AKNS eigenvalue problem and the t parts of the JM eigenvalue problem under the gauge transformation,and give a correspondence between the AKNS hierarchy and the JM hierarchy and also three types of Darboux tranaformation for the JM hierarchy.