• Classical extreme value index estimators are known to be quite sensitive to the number k of top order statistics used in the estimation. The recently developed second order reduced-bias estimators show much less sensitivity to changes in k. Here, we are interested in the improvement of the performance of reduced-bias extreme value index estimators based on an exponential second order regressi...

A G-Frobenius graph, as defined recently by Fang, Li, and Praeger, is a connected orbital graph of a Frobenius group G = K:H with Frobenius kernel K and Frobenius complement H. Γ is also shown to be a Cayley graph, Γ = Cay(K,S) for K and some subset S of the group G. On the other hand, a network N with a routing function R, written as (N,R), is an undirected graph N together with a routing R wh...

In this paper we show that the standing waves of the form (eu(x), eu(x)), β > 0, u(x) real and positive, are stable for the system i ∂u ∂t + uxx + (|u| + γ|v||u|)u = 0 i ∂v ∂t + vxx + (γ|u||v| + |v|)v = 0 provided 2 ≤ p < 3 and 0 < γ 6= p− 1. The Morse index of such solution is one for γ > p − 1 and two for 0 < γ < p− 1 but it is stable in both cases.

Abstract. Let Γ denote the modular group SL(2, Z) and Cn(Γ) the number of congruence subgroups of Γ of index at most n. We prove that lim n→∞ log Cn(Γ) (log n)2/ log log n = 3−2 √ 2 4 . We also present a very general conjecture giving an asymptotic estimate for Cn(Γ) for general arithmetic groups. The lower bound of the conjecture is proved modulo the generalized Riemann hypothesis for Artin-He...

Abstract. In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ 2 of the group Γ of positive units of the Lorentzian quadratic form x 1 + · · ·+ x 5 − x 6 . We also show that Γ 2 is a reflection group with respect to a 5-dimensional right-angled convex po...

For any countable discrete group Γ (without further assumptions on it) we first construct an explicit morphism from the Left-Hand side of Baum-Connes assembly map, Ktop⁎(Γ), to periodic cyclic homology algebra, HP⁎(CΓ). This morphism, called Chern-Baum-Connes allows in particular give a proper and formulation for Chern-Connes pairingKtop⁎(Γ)×HP⁎(CΓ)⟶C. Several theorems are needed formulate map....

We study a variable exponent model for image restoration in the case that the exponent attains the critical value one. We prove existence and Γ-convergence. The results answer an open question by Li, Li and Pi [Variable exponent functionals in image restoration, Appl. Math. Comput. 216 (2010), no. 3, 870–882].

Received (Day Month Year) Communicated by (xxxxxxxxxx) Let Ω be an open bounded set of R 3 and let W and V be two non-negative continuous functions vanishing at α, β and α ′ , β ′ , respectively. We analyze the asymptotic behavior as ε → 0, in terms of Γ-convergence, of the following functional Fε(u) := ε p−2 Z Ω |Du| p dx + 1 ε p−2 p−1 Z Ω W (u)dx + 1 ε Z ∂Ω V (T u)dH 2 (p > 2), where u is a s...

We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γlimit is also stable under volume constraint and various type of boundary conditions.

We provide an approximation result in the sense of Γ-convergence for energies of the form ˆ Ω Q1(e(u)) dx+ aH(Ju) + b ˆ Ju Q 1/2 0 ([u] νu) dH n−1, where Ω ⊂ Rn is a bounded open set with Lipschitz boundary, Q0 and Q1 are coercive quadratic forms on Mn×n sym , a, b are positive constants, and u runs in the space of fields SBD2(Ω) , i.e., it’s a special field with bounded deformation such that i...