Nonlinear programming problems are to minimize general nonlinear functions, possibly subject to some nonlinear constraints. In this paper, we review some recent results on nonlinear optimization.

In this article the author gives a detailed introduction to three basic methods of calculating normal forms of ordinary differential equations, and a brief introduction to a method of getting normal forms of parameter dependent systems. The versa-lity of normal forms with parameters is also discussed.

Very little is known in general about estimating the smallest integer l such that a manifold Mn emheds in Rn+k +l if it immerses in Rn+k. Indeed there are relatively few examples where k and l can be estimated accurately. There are old examples for which l is known to be arbitrarily Iarge; for those examples l can grow like logn and there are recent examples where l can grow linearly with n. The main difficulty in resolving questions of this kind is that the only general methods known for proving non-embedding and non-immersion results involve doing calculations with characteristic classes and the estimates that they give are very similar for the two problems. In this paper an account is given of various methods that can be used to study examples.

Let (M,g) and (N,h)be two Riemannian manifolds. Consider the heat flow for harmonic maps from (M,g) into (N,h).We prove the following results Suppose dim M =3 and is a nontrivial homotopy class in C(M,N).Then there exists a constant ?o such that if and E(u0)Related Articles

Suppose that either the outer mapping function of a domain D has continuous second derivatives or D is a strictly star domain. In this paper we first establish two inequalities concerning polynomials at Fejer's points with multiplicity (3 + 1). Using these two inequalities, we obtain the order of approximation in Lp(dD), 0

In this paper, the winding of stationary diffusions are studied. It is shown that, differently from Brownian motions,stationary diffusions wind up to time t angles in order of t, while Brownian motions wind up angles in order of logt,and the winding rates tend to , where c, an-i c2 are constants and is a Cauchy random variable.Moreover, it is proved that a stationary diffusion is reversible iff c2=0 for the winding around every point.

In this paper,we introduce the lower semicontinuity w.r.t.(with respect to)adecreasing sequence,which can replace the lower semicontinuous condition in somewell-known results. Definition Let X be a topological space,a function φ:X→RU{+∞)is said

We call that λ(x)belongs to Muckenhoupt class A_p if λ(x)≥0 and satisfiesfor all balls in R,where|B_R| denotes the Lebesgue measure of a ball with centerx_0 and radius R,andLet be a bounded domain.Define normHere,denotes the Banach space of all measurable functions defined on

A superprocess is a continuous analogue of an infinite particle branching pro-cess.The branching mechanism of a superprocess is a function ψ(λ)of the form(cf.[3])

M.M.Derriennic discussed the properties of Bernstein-Durrmeyer operators,M. Heilmann solved the saturation situation and the author obtained the characte-rization of their order of approximation.As extending Kantorovich polynomials inL_p[0,1]to Szász-Mirakjan-Kantorovich operators in L_p[0,∞)by V.Totik,We in-troduce a new class of Szász-Mirakjan type operators:

Let{X(m,n)}_(m,m=0,±1,±2…)be a stationary random field.The closed linearspace spanned by all X(m,n):m,n=0,±1,±2,…is denoted by L(X).Throughoutthe following pages L_1(x:s)will denote the subspace generated by all X(m,n):m≤s,-∞Related Articles

Let X(n)be a time series satisfying the following general ARMA(p,d,r,q)model: E(B)U(B)A(B)X(n)=C(B)W(n),whereC(z)is relatively prime with the polynomial E(z)U(z)A(z),B is the backshiftoperator such that BX(n)=X(n-1),and(W(n),F(n),n≥1)is a sequence ofmartingale differences. For simplicity,we shall assume throughout that the initial values(X(-p-d

The thesis is divided into twochapters.In chapter one,we study bycombining topological method with conetheory the nonlinear eigenvalue pro-blem x=f(λ,x),where f:[0,+∞]×P→P is a completely continuous map-ping with f(λ,0)≠0,P is a cone in aBanach space.A detailed description