This paper is devoted to the ergodicity of generalized long-range exclusion processes with positive recurrent transition probabilities. The set of invariant probability measures and the corresponding domain of attraction for each invariant probability measure are described.
Three dimensional initial boundary value problem of the Navier-Stokes equation is considered. The equation is split in an Euler equation and a non-stationary Stokes equation within each time step. Unlike the conventional approach, we apply a non-homogeneous Stokes equation instead of homogeneous one. Under the hypothesis that the original problem possesses a smooth solution, the estimate of the Hs+1 norm, 0≦s<3/2, of the approximate solutions and the order of the L2 norm of the errors is obtained.
In this paper a theorem of Main Boundedness Type is established and then used to study automatic continuity of derivations and module derivations on Banach algebras.
The present paper is the continuation of [1]. Some further generalizations of the fixed point theorems in [2] are obtained by means of the results in [1].
In [1] Homer introduced the honest polynomial reducibility and proved that under this new reducibility a set of minimal degree below O" is constructed under the assumption that P=NP. In this paper we will prove that under the same assumption a set of minimal degree can be constructed below any recursively enumerable degrees. So under the honest polynomial reducibility a set of low minimal degree does exist.
In this paper, the Dirichlet problem for the Monge-Ampére equation det(uij)= F(x,u,Δu) on a convex bounded domain Ω⊂R" is considered. The author establishes a new Co-estimate and gives some new existence results. He also presents a new proof for the C3,α-estimates of solutions, which not only weakens the smooth assumptions for F but also applies to more general nonlinear elliptic systems.
There are a few results of Welch (1967) and O. Moreno (1980) that count the number of solutions of Tr(yl)=0 in GF(2m), for certain values of l. This paper counts the number of solutions of Tr(yl)=h in GF(pm), for further values of l. Then O. Moreno's question is answered.
Cowen-Douglas operators are important Fredholm operators of positive index, for which we can calculate the complete unitary invariants. On the other hand, the cyclicity of an operator is an important property, which provides a useful tool for studing this operator. This paper is devoted to prove: Every Cowen-Douglas operator is cyclic.