具有第二大基指数的本原对称带号有向图的刻画

Recently, the primitive symmetric signed digraphs on n vertices with the maximum base 2n and the primitive symmetric loop-free signed digraphs on n vertices with the maximum base 2n-1 are characterized, respectively. In this paper, the primitive symmetric signed digraphs with loops on n vertices with the base 2n-1 are characterized, and then the primitive symmetric signed digraphs on n vertices with the second maximum base 2n-1 are characterized.     

带有非线性项不可压Navier-Stokes方程整体性吸引子的存在性（英文）

This paper is concerned with the Navier-stokes equations with nonlinear perturbation in R~2,which studies the existence of solution,and gets the existence of the attractors.Finally,we discuss with limit-behavior of the Navier-stokes equation4 with nonlinear perturbation,as α→0.     

带有非线性项不可压Navier-Stokes方程整体性吸引子的存在性

This paper is concerned with the Navier-stokes equations with nonlinear perturbation in R^2,which studies the existence of solution,and gets the existence of the attractors.Finally,we discuss with limit-behavior of the Navier-stokes equation4 with nonlinear per-turbation,asα→0.     

On a nonlinear elliptic problem with critical potential in R~2

Consider the existence of nontrivial solutions of homogeneous Dirichlet problem for a nonlinear elliptic equation with the critical potential in R2. By establishing a weighted inequality with the best constant, determine the critical potential in R2, and study the eigenvalues of Laplace equation with the critical potential. By the Pohozaev identity of a solution with a singular point and the Cauchy-Kovalevskaya theorem, obtain the nonexis tence result of solutions with singular points to the nonlinear elliptic equation. Moreover, for the same problem, the existence results of multiple solutions are proved by the mountain pass theorem.     

GLOBAL STABILITY OF WAVE PATTERNS FOR COMPRESSIBLE NAVIER-STOKES SYSTEM WITH FREE BOUNDARY

In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ 1 with γbeing the adiabatic exponent provided that the wave strength is suitably small.     

UNCONDITIONAL STABLE DIFFERENCE METHODS WITH INTRINSIC PARALLELISM FOR SEMILINEAR PARABOLIC SYSTEMS OF DIVERGENCE TYPE

The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of the discrete functional analysis, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general difference schemes with intrinsic parallelism justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete initial data of the original problems in the discrete W_2~(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original semilinear parabolic problem is proved.     

Existence and Stability of Static Solutions of the Landau-Lifshitz Equation with Multi-direct Effective Field

We prove the existence of solutions of the static Landau-Lifshitz equation with multidirect effective field and with Dirichlet boundary condition, and establish the stability of the solution of Landau-Lifshitz equation with respect to time.     

A Remark on Leray's Problem on Stationary Navier–Stokes Flows with Large Fluxes in Infinite Cylindrical Domains

We consider Leray's problem on stationary Navier–Stokes flows with arbitrary large fluxes in an unbounded cylinder with several exits to infinity. For a stationary Navier–Stokes flow with large fluxes in the unbounded cylinder, we prove that, if the difference between the pressure of the main flow and the pressure of the Poiseuille flow with the same flux in a branch of the cylinder remains bounded at |x| →∞, then the flow behaves at infinity of the branch like the Poiseuille flow.     

STUDY OF THE GLOBAL SOLUTIONS FOR A NONLINEAR HYPERBOLIC SYSTEM

We shall compare the solution of the Cauchy problem with the solution of the corresponding Riemann problem (1.1) with the initial data     

Variational inequalities for the commutators of rough operators with BMO functions

Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the bounded mean oscillation(BMO) functions can be obtained from their weighted variational estimates, we establish the similar variational estimates for the commutators of the BMO functions with rough singular integrals, which do not admit any weighted variational estimates. The proof involves several Littlewood-Paley-type inequalities with the commutators as well as Bony decomposition and related para-product estimates.     

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.     

Simultaneous Identification of Two Parameters on the Reaction Diffusion System from Discrete Measurement Data

This article deals with an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final time space discretized measurement using the optimization method with the help of the smooth interpolation technique. The main objective of the article is to analyse the asymptotic behavior of the solution of the inverse problem for the linearly coupled reaction diffusion system with respect to the homogeneous Dirichlet boundary condition.     

DONSKER''''S WEAK INVARIANCE PRINCIPLE WITH RATES FOR C[0,1] - VALUED, DEPENDENT RANDOM - FUNCTIONS

Ⅰ. Introduction This paper is concerned with the weak invariance principle,namely with the weak convergence of the distribution of the randompolygonal lines     

Shape Analysis of Bounded Traveling Wave Solutions and Solution to the Generalized Whitham-Broer-Kaup Equation with Dissipation Terms

This paper deals with the problem of the bounded traveling wave solutions'shape and the solution to the generalized Whitham-Broer-Kaup equation with the dissipation terms which can be called WBK equati...     

ON THE INTERIOR REGULARITIES OF THE SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

In we discussed the problems of calculus of variations with strong nonlinearity. Its Euler equation is evidently the following elliptic type equation of divergent form with strongly increasing coefficients,We get the interior regularities of the solutions of(1). It is just the Hilbert's 19th problem in the case with strong nonlinearity.     

STUDY OF THE GLOBAL SOLUTIONS FOR A NONLINEAR HYPERBOLIC SYSTEM

§1 Introduction We shall compare the solution of the Caucky problem with the solution of the corresponding Riemann problem (1.1) with the initial data     

Affine planar geodesic immersions with maximal codimension

This work gives a classification theorem for affine immersions with planar geodesics in the case where the codimension is maximal. Vrancken classified parallel affine immersions in this case and obtained, among others, generalized Veronese submanifolds. In this work it is shown that the immersions with planar geodesics are the same as the parallel ones in the considered case. A geometric interpretation of parallel immersions is also given： The affine immersions with pointwise planar normal sections （with respect to the equiaffine transversal bundle） are parallel. This result is verified for surfaces in R4 and for immersions with the maximal codimension.     

Stability of the standing waves for a class of coupled nonlinear Klein-Gordon equations

This paper deals with the standing waves for a class of coupled nonlinear Klein-Gordon equations with space dimension N ≥ 3, 0 〈 p, q 〈 2/N-2 and p ＋ q 〈 4/N. By using the variational calculus and scaling argument, we establish the existence of standing waves with ground state, discuss the behavior of standing waves as a function of the frequency ω and give the sufficient conditions of the stability of the standing waves with the least energy for the equations under study.     

GLOBAL WEAK SOLUTION TO COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY,VACUUM AND GRAVITATIONAL FORCE

Recently,the global existence of weak solutions to the compressible Navier-Stokes equations with vacuum has attracted much attention.In this paper,we study the one-dimension isentropic Navier-Stokes equations with gravitational force and fixed boundary condition when the density connects with vacuum discontinuously.We prove the global existence and the uniqueness of weak solution,requiring less regularity of the initial data.     

Two-scale analysis method for predicting heat transfer performance of composite materials with random grain distribution

A two-scale analysis (TSA) method for predicting the heat transfer performance of composite materials with the random distribution of same-scale grains is presented. First the representation of the materials with the random distribution is briefly described. Then the two-scale analysis formulation of heat transfer behavior of the materials with random grain distribution of small periodicity is formally derived by means of