Optimal markovian couplings and applications

This paper is devoted to studying a new topic: optimal Markovian couplings, mainly for time-continuous Markov processes. The study emphasizes the analysis of the coupling operators rather than the processes. Some constructions of optimal Markovian couplings for Markov chains and diffusions are presented, which are often unexpected. Then, the results are applied to study theL ²-convergence for Markov chains and for a diffusion on compact manifold. The estimate of the convergent rate provided by this method can be sharp. Supported in part by NSFC, the State Education Commission of China, the NSERC operating grant of D.A. Dawson and Centro Vito Volterra.     

Global Attractors for a Nonclassical Diffusion Equation

We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of arbitrary order.     

两类高斯过程的局部连续性模型

Abstract. In this article,local continuity moduli for the fractional Wiener process and l^∞-valued Gaussian processes is discussed.     

Dynamic programming for multidimensional stochastic control problems

In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem, singular control problem and impulse control problem as special cases. Using a unified treatment of dynamic programming, we show that the value function of the problem is a viscosity solution of certain Hamilton-Jacobi-Bellman (HJB) quasivariational inequality. The uniqueness of such a quasi-variational inequality is proved. Supported in part by USA Office of Naval Research grant #N00014-96-1-0262. Supported in part by the NSFC Grant #79790130, the National Distinguished Youth Science Foundation of China Grant #19725106 and the Chinese Education Ministry Science Foundation.     

Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions

A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional excursions. Supported by an NSERC Research Grant and a Max Planck Award.Supported by the NSFC (No. 10121101 and No. 10131040).Mathematics Subject Classification (2000): Primary 60J80; Secondary 60G57 60H20     

A Note on <Emphasis Type="Italic">k</Emphasis>-walks in Bridgeless Graphs

We show that every bridgeless graph of maximum degree has a spanning -walk. The bound is optimal. Supported by project 1M0545 and Research Plan MSM 4977751301 of the Czech Ministry of Education. Supported by the NSFC (60673047 and 10471078), SRSDP (20040422004) and PDSF (2004036402) of China.     

Hypersurfaces which are equiaffine extremal and centroaffine extremal

For a centroaffine hypersurface, we use the relations between equiaffine and centroaffine invariants to find many newexamples of equiaffine extremal hypersurfaces. *Supported by NSFC No. 10371013; Joint Research of NSFC and KOSEF; NEU. **Supported by ABRL No. R14-2002-003-01002-0 from KRF; No. F01-2005-000-100024-0 from KOSEF.     

Local Existence of the Shock Front Solution to the Axi-symmetrical Piston Problem in Compressible Flow

In this paper, we study a kind of 2-dimensional axi-symmetrical piston problem in compressible flow. The corresponding mathematical model is the well-known Euler system. With the Newton iteration procedure and energy estimate, we give the local existence of the shock front solution to this problem.     

Constrained continuous-time Markov decision processes with average criteria

In this paper, we study constrained continuous-time Markov decision processes with a denumerable state space and unbounded reward/cost and transition rates. The criterion to be maximized is the expected average reward, and a constraint is imposed on an expected average cost. We give suitable conditions that ensure the existence of a constrained-optimal policy. Moreover, we show that the constrained-optimal policy randomizes between two stationary policies differing in at most one state. Finally, we use a controlled queueing system to illustrate our conditions. Supported by NSFC, NCET and RFDP.     

The approximation on locally convex spaces

In this paper, we give some properties of f-approximation, f-Chebyshev centers and f-farthest points in locally convex spaces. Supported by NSFC     

The π1 of self-maps of nonzero degree on 3-manifolds

Supported by NSFC and AvH     

Convergence of the Cesàro mean for rational orthonormal bases

This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided.     

Representation of Integers by Ternary Quadric Forms

In this paper we give a formula for the number of representations of some square-free integers by certain ternary quadratic forms and estimate the lower bound of the 2-power appearing in this number. Supported by NSFC and RFDP.     

On the Linear Fractional Self-attracting Diffusion

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized self-intersection local time exists in L ² if 1/2<H<3/4. The Project-sponsored by NSFC (10571025) and the Key Project of Chinese Ministry of Education (No.106076).     

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.     

The coapproximation in linear spaces

In this paper, we investigate the properties of strongly coapproximation in normed linear spaces and locally convex spaces. The relations between strongly coapproximation and strongly unique approximation and of the f-coapproximation and f-approximation are also considered. Supported by NSFC     

On the linear representations of circle expanding maps

In this paper, it is proved that the two real analytic expanding endomorphisms of the unit circle are equivalent if and only if they have equal eigenvalues along corresponding cycles. A sufficient and necessary condition that a real analytic solution of Cvitanovic-Feigenbaum equation induces a real analytic expanding map is given. Supported by the NSFC.     

The Hadamard Theorem and Borel–Carathéodory Theorem on Riemann Surfaces

In this paper, we first define a kind of pseudo–distance function and annulus domain on Riemann surfaces, then prove the Hadamard Theorem and the Borel–Carathéodory Theorem on any Riemann surfaces. Supported by NSFC 10501052     

Nonlinear Internal Damping of Wave Equations with Variable Coefficients

For wave equations with variable coefficients on regions which are not necessarily smooth, we study the energy decay rate when a nonlinear damping is applied on a suitable subrigion.     

An interpolation method by bivariate cubic splines with <Emphasis Type="Italic">c</Emphasis><Superscript>2</Superscript>-join on type-II triangulars at a rectangular domain

In this paper, an interpolating method for bivariate cubic splines with C ²-join on type-II triangular at a rectangular domain is given, and the approximation degree, interpolating existence and uniqueness of the cubic splines are studied. Supported by NSFC General Projects(60473130).