A Generalization of the Hilbert Basis Theorem

A generalization of the Hilbert basis theorem in the geometric setting is proposed. It asserts that, for any well-describable (in a certain sense) family of polynomials, there exists a number C such that if P is an everywhere dense (in a certain sense) subfamily of this family, a is an arbitrary point, and the first C polynomials in any sequence from P vanish at the point a, then all polynomials from P vanish at a.     

Dirac Operators on Hypersurfaces of Manifolds with Negative Scalar Curvature

We give a sharp extrinsic lower bound for the first eigenvaluesof the intrinsic Dirac operator of certain hypersurfaces boundinga compact domain in a spin manifold of negative scalar curvature.Limiting-cases are characterized by the existence, on the domain,of imaginary Killing spinors. Some geometrical applications, as anAlexandrov type theorem, are given.     

Representability of Analytic Functions in Terms of Their Boundary Values

Suppose that is an arbitrary finite complex Borel measure on the interval is its Poisson integral, and are the conjugate harmonics of , and is the nontangential limiting value of the analytic function as . In this paper, we consider the problem of representing the analytic function in terms of its boundary values .     

Empirical likelihood for partial linear models

In this paper the empirical likelihood method due to Owen (1988,Biometrika,75, 237–249) is applied to partial linear random models. A nonparametric version of Wilks' theorem is derived. The theorem is then used to construct confidence regions of the parameter vector in the partial linear models, which has correct asymptotic coverage. A simulation study is conducted to compare the empirical likelihood and normal approximation based method. Research supported by NNSF of China and a grant to the first author for his excellent Ph.D. dissertation work in China. Research supported by Hong Kong RGC CERG No. HKUST6162/97P.     

Flow Compactifications of Nondiscrete Monoids, Idempotents and Hindman's Theorem

We describe the extension of the multiplication on a not-necessarily-discrete topological monoid to its flow compactification. We offer two applications. The first is a nondiscrete version of Hindman's Theorem, and the second is a characterization of the projective minimal and elementary flows in terms of idempotents of the flow compactification of the monoid.     

HILBERTIAN INVARIANCE PRINCIPLE FOR EMPIRICAL PROCESS ASSOCIATED WITH A MARKOV PROCESS

The authors establish the Hilbertian invariance principle for the empirical process of a stationary Markov process, by extending the forward-backward martingale decomposition of Lyons-Meyer-Zheng to the Hilbert space valued additive functionals associated with general non-reversible Markov processes.     

BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS

Using non-linear connection of Finsler manifold M, the existence of local coordinates which is normalized at a point x is proved, and the Laplace operator A on 1-form of M is defined by non-linear connection and its curvature tensor. After proving the maximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theorem of Killing vectors and harmonic 1-form are obtained.     

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.     

STURM COMPARISON THEOREM OF SOLUTION FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, we establish some differential identities and obtain some Sturm comparison theorems for the second order nonlinear differential equation by using them.and generalize some classicial Sturm comparison theorems.     

Periodic Solution of a Nonautonomous Diffusive Food Chain System of Three Species with Time Delays

Abstract By using the continuation theorem of coincidence degree theory,the existence of a positive periodicsolution for a nonautonomous diffusive food chain system of three species. dx_1(t)/dt=x_1(t)[r_1(t)-a_(11)(t)x_1(t)-a_(12)(t)x_2(t)]+D_1(t)[y(t)-x_1(t)], dx_2(t)/dt=x_2(t)[-r_2(t)+a_(21)(t)x_1(t-r_1)-a_(22)(t)x_2(t)-a_(23)(t)x_3(t)], dx_3(t)/dt=x_3(t)[-r_3(t)+a_(32)(t)x_2(t-r_2)-a_(33)(t)x_3(t)], dy(t)/dt=y(t)[r_4(t)-a_(44)(t)y(t)]+D_2(t)[x_1(t)-y(t)]+D_2(t)[x_1(t)-y(t)],is established,where,r_i(t),a_(ii)(t)(i=1,2,3,4),D_i(t)(i=1,2),a_(12)(t),a_(21)(t),a_(23)(t)and a_(32)(t) are all positiveperiodic continuous functions with period w>0,T_i(i=1,2)are positive constants.