On Completeness and Minimality of Random Exponential System in a Weighted Banach Space of Functions Continuous on the Real Line

In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin's classical results.     

Radius of locally convex subsets in Alexandrov spaces with curvature ≥1 and radius 〉 π/2

Let X be a complete Alexandrov space with curvature ≥1 and radius 〉 π/2. We prove that any connected, complete, and locally convex subset without boundary in X also has the radius 〉 π/2.     

Completeness of the system {z^λn} in L^2[B,α0]

Let B be an unbounded domain located outside an angle domain with vertex at the origin, A ={λn}（n = 1,2,...） be a sequence of complex numbers satisfying sup ｜ arg（λn）｜ 〈 α 〈 π/2 and denote by M（∧） = {z^λ, λ ∈ ∧} the corresponding system of functions z^λ（λ∈∧）. Let α0（z） be a weight function defined on B. We obtain a completeness theorem for the system M（∧） in the Hilbert space L^2 [B, α0].     

The <Emphasis Type="Italic">D</Emphasis><Subscript>π</Subscript> property of finite groups in the case 2 ∉ π

The characterization of finite simple groups with the D _π property for any set π of odd prime numbers is completed. It was proved earlier that a finite group has the D _π property if and only if each of its composition factors has this property, hence the results of the paper provide an exhaustive characterization of the D _π property for all finite groups with known composition factors in the case 2 ? π.