We introduce invariant sample measures to nonautonomous random dynamical systems, and consider the behaviors of a stochastic $ p $-Laplacian equation with multiplicative noise on bounded domain. first use asymptotic priori estimate method prove existence (L^2, L^q) $-pullback attractors for generated system. Then, we establish Liouville type theorem in L^2 this equation. Moreover, are carried b...

Let L be a Lie algebra with the universal enveloping algebra U(L). The augmentation ideal ω(L) of U(L) is the associative ideal of U(L) generated by L. Let S be a subalgebra of L and n a positive integer. In this paper we prove that L ∩ ω(L)ω(S) = γn+2(S) + γn+1(S∩γ2(L)), where γn+2(S) is the (n+2) term of the lower central series of S.

An avirulent clone of Leishmania major was used to immunize susceptible BALB/c mice against challenge with virulent L. major. By using the immunized animals as a source of cells, CD4+ parasite-specific T-cell lines could be generated in vitro which, when adoptively transferred to naive BALB/c recipients, conferred marked protection against challenge with virulent L. major. Compared with CD4+ pa...

Calculations for constrained (one-dimensional) diffusion of current carriers in an external field are made, which concern the spectral density of fluctuations resulting from the relaxation of spatial concentration perturbations. Two different model calculations are presented: First diffusion in an infinite medium. In this case the spectral density of concentration fluctuations shows a 1// behav...

Let S be a shift-invariant subspace of L2(Rn) defined by N generators and suppose that its length L, the minimal number of generators of S, is smaller than N . Then we show that at least one reduced family of generators can always be obtained by a linear combination of the original generators, without using translations. In fact, we prove that almost every such combination yields a new generato...

In the present paper we introduce analogs of almost periodic functions on the unit circle. We study certain uniform algebras generated by such functions, prove corona theorems for them and describe their maximal ideal spaces. 1. Formulation of Main Results 1.1. The classical almost periodic functions on the real line first introduced by H. Bohr in the 1920s play an important role in various are...

Let S be a finite nonabelian simple group, and let H be a subgroup of S . In this work, the dominion (in the sense of Isbell) of H in S in Var(S) is determined, generalizing an example of B.H. Neumann. A necessary and sufficient condition for H to be epimorphically embedded in S is obtained. These results are then extended to a variety generated by a family of finite nonabelian simple groups. S...