Large orbits of elements centralized by a Sylow subgroup

If G has a nilpotent normal p-complement and V is a finite, faithful and completely reducible G-module of characteristic p, we prove that there exist ${v_1, v_2 \in V}If G has a nilpotent normal p-complement and V is a finite, faithful and completely reducible G-module of characteristic p, we prove that there exist v₁, v₂ ? V{v_1, v_2 \in V} such that C_G(v₁)?C_G(v₂) = P{{\bf C}_{G}{(v_1)}\cap {\bf C}_{G}{(v_2)} = P} , where P ? Syl_p(G){P \in {\rm Syl}_p(G)} . We hence deduce that, if the normal p-complement K is nontrivial, there exists v ? C_V(P){v \in {\bf C}_{V}(P)} such that |K : C _K (v)|² > |K|.     

Hölder seminorm preserving linear bijections and isometries

Let (X, d) be a compact metric and 0 < α < 1. The space Lip ^α (X) of Hölder functions of order α is the Banach space of all functions ? from X into \(\mathbb{K}\) such that ∥?∥ = max{∥?∥_∞, L(?)} < ∞, where

$L(f) = sup\{ \left| {f(x) - f(y)} \right|/d^\alpha (x,y):x,y \in X, x \ne y\} $

is the Hölder seminorm of ?. The closed subspace of functions ? such that

$\mathop {\lim }\limits_{d(x,y) \to 0} \left| {f(x) - f(y)} \right|/d^\alpha (x,y) = 0$

is denoted by lip ^α (X). We determine the form of all bijective linear maps from lip ^α (X) onto lip ^α (Y) that preserve the Hölder seminorm.

     

The Bochner Integral of Functions with Values in an Orlicz Space

Integration of vector-valued functions is seldom appreciated because of its abstract nature. In this paper, we give a real-valued representation of the Bochner integral of a function with values in an Orlicz space. This is given in the first theorem on the necessary condition for Bochner integrability of such a function. The second theorem gives sufficient conditions for Bochner integrability.AMS Subject Classification (1991) 28Supported by a grant from the Natural Science Research Institute, University of the Philippines, Diliman, Q.C. 1101, Quezon City, Philippines.     

A partition of characters associated to nilpotent subgroups

IfG is a finite solvable group andH is a maximal nilpotent subgroup ofG containingF(G), we show that there is a canonical basisP(G|H) of the space of class functions onG vanishing off anyG-conjugate ofH which consists of characters. ViaP(G|H) it is possible to partition the irreducible characters ofG into “blocks”. These behave like Brauerp-blocks and a Fong theory for them can be developed. Research partially supported by DGICYT and MEC.     

Study of the plume generated by Nd:YAG laser ablation of a hydroxyapatite target

The plume generated by Nd:YAG laser ablation of a hydroxyapatite target has been investigated in vacuum and at 0.1 and 0.2 mbar of water vapor. The investigation has been carried out by means of fast intensified CCD imaging with the aid of bandpass interferential filters that allow the following single species to be isolated: neutral calcium, calcium oxide radicals and neutral oxygen. Results obtained in vacuum reveal that expansion takes place at a constant velocity of about 2᎒⁴ m/s for the atomic species and about 3᎒³ m/s for the molecular ones and that emission is completely dominated by emissive neutral calcium. When ablation is carried out in a water atmosphere, the background gas confines the species in the leading edge of the plume, which results in the formation of a planar shock wave at 0.1 mbar and a spherical shock wave at 0.2 mbar. Comparison of the images with those obtained at 0.1 mbar of Ne has revealed the existence of chemical reactions between the plume and the water atmosphere, leading to the formation of calcium oxide radicals. In that case, plume emission is dominated by these molecular species.     

Erratum to: A three-ranged Gogny interaction in touch with pion exchange: promising results to improve infinite matter properties

The European Physical Journal A - Much of astrophysics is fueled by nuclear physics with observables, such as energy output and elements produced, that are heavily dependent on the masses of the...