AN INEQUALITY OF SCHUR''''S TYPE

It is proved that the Chebyshev polynomial _n(x)=T_n (xcos π/2n), has the greatest uniformnorm on [-1, 1] of its third derivative among the real polynomials of degree at most n, whichare bounded by 1 in [-1, 1] and vanish in -1 and 1.     

GENERALIZED ROSENTHAL＇S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES

A generalized Rosenthal＇s inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and characterizes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.     

DOUBLE Φ-FUNCTION INEQUALITY FOR NONNEGATIVE SUBMARTINGALES

The authors establish a kind of inequalities for nonnegative submartingales which depend on two functions Φ and ψ, and obtain the equivalent conditions for Φ and ψ such that this kind of inequalities holds. In the casen Φ =ψ∈Δ2, it is proved that this necessary and sufficient condition is equivalent to qΦ > 1.     

A SOBOLEV-HARDY INEQUALITY WITH APPLICATION TO A NONLINEAR ELLIPTIC EQUATION

In this paper, when μ< 1/4, and 2 0 and q=2(3-σ),the method is coming from the idea of Pohozaev.     

A ROBUST SQP METHOD FOR OPTIMIZATION WITH INEQUALITY CONSTRAINTS

A new algorithm for inequality constrained optimization is presented, which solves a linear programming subproblem and a quadratic subproblem at each iteration. The algorithm can circumvent the difficulties associated with the possible inconsistency of QP subproblem of the original SQP method. Moreover, the algorithm can converge to a point which satisfies a certain first-order necessary condition even if the original problem is itself infeasible. Under certain condition, some global convergence results are proved and local superlinear convergence results are also obtained. Preliminary numerical results are reported.     

A globally and superlinearly convergent trust region method for LC 1 optimization problems

Abstract. A new trust region algorithm for solving convex LC1 optimization problem is present-ed. It is proved that the algorithm is globally convergent and the rate of convergence is superlin-ear under some reasonable assumptions.     

INEQUALITY OF KORN‘S TYPE ON COMPACT SURFACES WITHOUT BOUNDARY

Inequalities of Korn's type on a surface with boundary have been proved in many papers using different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn's type on a compact surface without boundary. The idea is to use a finite number of maps for defining the surface and the inequality of Korn's type without boundary conditions for every map and to recast these in a general functional analysis setting about quotient spaces.     

A FUNDAMENTAL INEQUALITY AND ITS APPLICATION

Let f(z) be meromorphie in |z|k+4+[2/k].In this note,a fundamental inequality is established such that thecharacreristic function T(r,f)can be limibd by N(r,1/f)and _(τ-1)(r,1/(f~(k)-1).As anapplication,the following criterion for normality is also proved:Let be a family ofmeromorphic functions in a region D.If for every f(z)∈ ,f(z)≠0 and all the zeros off~(k)(z)-1 are of multiplicity >k+4+[2/k]in D,then is normal there.     

STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D MAXWELL EQUATIONS IN A LOSSY MEDIUM

Several new energy identities of the two dimensional(2D) Maxwell equations in a lossy medium in the case of the perfectly electric conducting boundary conditions are proposed and proved.These identities show a new kind of energy conservation in the Maxwell system and provide a new energy method to analyze the alternating direction implicit finite difference time domain method for the 2D Maxwell equations(2D-ADI-FDTD).It is proved that 2D-ADI-FDTD is approximately energy conserved,unconditionally stable and second order convergent in the discrete L2 and H1 norms,which implies that 2D-ADI-FDTD is super convergent.By this super convergence,it is simply proved that the error of the divergence of the solution of 2D-ADI-FDTD is second order accurate.It is also proved that the difference scheme of 2D-ADI-FDTD with respect to time t is second order convergent in the discrete H1 norm.Experimental results to confirm the theoretical analysis on stability,convergence and energy conservation are presented.     

A GENERALIZED PROJECTION-SUCCESSIVE LINEAREQUATIONS ALGORITHM FOR NONLINEARLY EQUALITy AND INEQUALITY CONSTRAINED OPTIMIZATION AND ITS RATE OF CONVERGENCE

In this paper, a new superlinearly convergent algorithm is presented for optimization problems with general nonlineer equality and inequality Constraints, Comparing with other methods for these problems, the algorithm has two main advantages. First, it doesn‘t solve anyquadratic programming (QP), and its search directions are determined by the generalized projection technique and the solutions of two systems of linear equations. Second, the sequential points generated by the algoritbh satisfy all inequity constraints and its step-length is computed by the straight line search,The algorithm is proved to possesa global and auperlinear convergence.     

THE OPIAL INEQUALITY IN R~N

Where n is a bounded smooth dornain in RN, A.u = Z k(IVuIp--'e) is the p1aPlacei = 1operator, p 2 2, q E be, ff) are some given real number. By this result, we deduce the famousOpial inequality in RN.As we know, the solvabiliy of problem (1) resuIts from whether the minimumcan be achieved. If (2) is achieved, the attained function W(x) is the nontrivial solution ofproblem (1) corre8ponding to A = A1(p, q, n) and ^ = ^1(p, ql n) is the corresponding ndnimumeigenvalue. Since q i8 8maller …     

GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE DIFFUSIVE CONVECTION IN POROUS MEDIUM

Nonlinear stability of the motionless double-diffusive solution of the problem of an infinite horizontal fluid layer saturated porous medium is studied. The layer is heated and salted from below. By introducing two balance fields and through defining new energy functionals it is proved that for CLe ≥ R, Le ≤ 1 the motionless double-diffusive solution is always stable and for CLe R, Le 1 the solution is globally exponentially and nonlinearly stable whenever R 4π~2+ Le C, where Le, C and R are the Lewis number, Rayleigh number for solute and heat, respectively. Moreover, the nonlinear stability proved here is global and exponential, and the stabilizing effect of the concentration is also proved.     

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0 (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.     

A DELAY DIFFERENTIAL INEQUALITY

In this paper, we obtain a slight generalization of the celebrated Halanay delay differential inequality[1]. Using this inequality, Liapunov function and vector Liapunov function, we show that our result can be applied to the stability behavior of solutions of some delay differential systems. And also, we attempt to relax some restrictions of dv/dt, which is necessary under Liapunov function's method on the delay differential systems.     

THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

In this paper,we first propose a new stabilized finite element method for the Stokes eigenvalue problem.This new method is based on multiscale enrichment,and is derived from the Stokes eigenvalue problem itself.The convergence of this new stabilized method is proved and the optimal priori error estimates for the eigenfunctions and eigenvalues are also obtained.Moreover,we combine this new stabilized finite element method with the two-level method to give a new two-level stabilized finite element method for the Stokes eigenvalue problem.Furthermore,we have proved a priori error estimates for this new two-level stabilized method.Finally,numerical examples confirm our theoretical analysis and validate the high effectiveness of the new methods.     

Partial Regularity of Suitable Weak Solutions to the System of the Incompressible Shear-thinning Flow

This paper is devoted to the partial regularity of suitable weak solutions to the system of the incompressible shear-thinning flow in a bounded domainΩ■Rⁿ,n≥2.It is proved that there exists a suitable weak solution of the shear-thinning fluid in the n-D smooth bounded domain(for n≥2).For 3 D model,it is proved that the singular points are concentrated on a closed set whose 1 dimensional Hausdorff measure is zero.     

1-planar Graphs without 4-cycles or 5-cycles are 5-colorable

A graph is 1-planar if it can be drawn on the Euclidean plane so that each edge is crossed by at most one other edge. A proper vertex k-coloring of a graph G is defined as a vertex coloring from a set of k colors such that no two adjacent vertices have the same color. A graph that can be assigned a proper k-coloring is k-colorable. A cycle is a path of edges and vertices wherein a vertex is reachable from itself. A cycle contains k vertices and k edges is a k-cycle. In this paper, it is proved t...     

The semiclassical limit in the quantum drift-diffusion model

Semiclassical limit to the solution of isentropic quantum drift-diffusion model in semicon- ductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical drift-diffusion model. In addition, we also proved the global existence of weak solutions.     

DEFICIENT FUNCTIONS OF RANDOM DIRICHLET SERIES

In this article, the uniqueness theorem of Dirichlet series is proved. Then the random Dirichlet series in the right half plane is studied, and the result that the random Dirichlet series of finite order has almost surely(a.s.) no deficient functions is proved.     

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation （1） are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.