Fatou Theorem and Its Converse for Positive Eigenfunctions of the Laplace–Beltrami Operator on Harmonic NA Groups

A Fatou-type Theorem for Harmonic Functions on Symmetric Spaces

on the groups satisfying the converse of schur's theorem

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the center of such...

Positive Eigenfunctions of a Schrödinger Operator

The paper considers the eigenvalue problem −∆u − αu + λg(x)u = 0 with u ∈ H(R ), u = 0, where α, λ ∈ R and g(x) ≡ 0 on Ω, g(x) ∈ (0, 1] on R \ Ω and lim |x |→+∞ g(x) = 1 for some bounded open set Ω ∈ RN . Given α > 0, does there exist a value of λ > 0 for which the problem has a positive solution? It is shown that this occurs if and only if α lies in a certain interval (Γ, ξ1) and that in this ...

the geopolitics of afghanistan after september 11, 2001, and its impact on iranian national security

abstract u.s. attack to afghanistan after 9/11 provided opportunities for us who tried to become the dominant power after collapse of ussr and bipolar world. thinkers like fukuyama believed american liberal democrats thought would be universally accepted without resistances. liberal democracy is the best and final model of governance; in this regard, united state has moral responsibilities for...

an investigation of the impact of self monitoring on langauge teachers motivational practice and its effect on learners motivation

the central purpose of this study was to conduct a case study about the role of self monitoring in teacher’s use of motivational strategies. furthermore it focused on how these strategies affected students’ motivational behavior. although many studies have been done to investigate teachers’ motivational strategies use (cheng & d?rnyei, 2007; d?rnyei & csizer, 1998; green, 2001, guilloteaux & d?...