A weak law for normed weighted sums of random elements in rademacher type p banach spaces

For weighted sums Σ_{j = 1}ⁿa_jV_j of independent random elements {V_n, n ≥ 1} in real separable, Rademacher type p (1 ≤ p ≤ 2) Banach spaces, a general weak law of large numbers of the form (Σ_{j = 1}ⁿa_jV_j − v_n)/b_n →^p 0 is established, where {v_n, n ≥ 1} and b_n → ∞ are suitable sequences. It is assumed that {V_n, n ≥ 1} is stochastically dominated by a random element V, and the hypotheses involve both the behavior of the tail of the distribution of |V| and the growth behaviors of the constants {a_n, n ≥ 1} and {b_n, n ≥ 1}. No assumption is made concerning the existence of expected values or absolute moments of the {V_n, n >- 1}.     

一类奇异非线性多重调和方程存在正整解的充分必要条件

研究一类奇异非线性多重调和方程?~mu=f(|x|,u,|▽u|)u~(-β),给出了方程存在正的径向对称整体解的充分必要条件和解的性质.     

An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.     

Asymptotic tail probability of randomly weighted sums of dependent random variables with dominated variation

This paper investigates the asymptotic behavior of tail probability of randomly weighted sums of dependent and real-valued random variables with dominated variation, where the weights form another sequence of nonnegative random variables. The result we obtain extends the corresponding result of Wang and Tang[7].     

一类推广的控制收敛定理及其应用

本文研究了一类推广的控制收敛定理及其应用,利用对控制函数满足条件的修改,建立了推广的控制收敛定理,获得其在弱奇异性积分算子中的应用,简化了经典结论的证明.     

关于高维非线性椭圆型方程的正整解

建立一类高维二阶非线性椭圆型方程正整解的存在性定理，并给出解的有关性质．     

Dominated splitting versus small angles

In this paper, we give a partial answer to the problem proposed by Lan Wen. Roughly speaking, we prove that for a fixed i, f has C^1 persistently no small angles if and only if f has a dominated splitting of index i on the C^1 i-preperiodic set P＊^1（f）. To prove this, we mainly use some important conceptions and techniques developed by Christian Bonatti. In the last section, we also give a characterization of the finest dominated splitting for linear cocvcles.     

Anisotropic equipartition state in a charged particle beam

The purpose of this Letter is to conjecture a characterization of the anisotropic equipartition state. The anisotropic equipartition state is defined through a phase space density which is uniform on the invariant surface of ξ, where ξ is the ratio between the oscillation energies in the x- and y-directions. It is a version of the ergodic hypothesis where the invariant surface of ξ plays the role of the conserved energy. We show that the anisotropic equipartition state is characterized by the following properties: the development of an elliptical shape with increasing size along the x-direction, the presence of a coupling between transversal emittances, halo formation along a preferential direction, stationarity of the temperature and a growth of the entropy in the cascade form.     

关于任意随机序列的一个强大数定理

This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained.