Two-Parameter Semigroups

In this paper we study compact semigroups that can be written as a product of two one-parameter semigroups. We show that such semigroups admit locally a unique factorization and can locally be embedded into a two-dimensional Lie group. The latter fact allows us to determine their local structure. We show how these results provide generalizations of a number of earlier results of this type.     

Spins and lifetimes of levels in 55Mn

The study of excited ⁵⁵Mn levels with the ⁵²Cr(α, pγ) reaction was extended to levels up to 3161 keV. With a Ge(Li) detector, DSA measurements in gold-backed targets were made, as well as angular correlations; both of these experiments were done in coincidence with protons detected near 180°. A multiple-detector NaI(Tl) array was also used in the same reaction geometry for better γ-ray detection efficiency. Mean lifetimes of 12 levels from 2727 to 3161 keV are reported. Spins and sometimes parities of the following levels were deduced from the angular-correlation analyses and lifetime results: 1885 keV, $\text{7}\text{2}$^?; 2199 keV, $\text{7}\text{2}$(^?); 2311 keV, ($\text{13}\text{2}$); 2366keV, $\text{5}\text{2}$^?; 2727 keV, $\text{7}\text{2}$; 2823 keV, $\text{9}\text{2}$. Multipole mixing ratios and M1 and E2 transition rates of the radiations from these and from the 1292 keV level are presented. The similarity of the low-lying level structure and of interlevel transitions in ⁵⁵Mn to those in certain other f_{$\text{7}\text{2}$}³ nuclei is examined.     

T0-spaces and pointwise convergence

The purpose of this paper is to give several different characterizations of those T₀-spaces E with the property that if F:X × E → Y is separately continuous, then it is jointly continuous. One such is that the lattice 0(E) of open sets of E be a hypercontinuous lattice (i.e. the interval topology on 0(E) is Hausdorff). If E is a sober space, then E must be a quasicontinuous poset endowed with the Scott topology.     

Semigroups in Möbius and Lorentzian Geometry

The Möbius semigroup studied in this paper arises very naturally geometrically as the (compression) subsemigroup of the group of Möbius transformations which carry some fixed open Möbius ball into itself. It is shown, using geometric arguments, that this semigroup is a maximal subsemigroup. A detailed analysis of the semigroup is carried out via the Lorentz representation, in which the semigroup resurfaces as the semigroup carrying a fixed half of a Lorentzian cone into itself. Close ties with the Lie theory of semigroups are established by showing that the semigroup in question admits the structure of an Ol'shanskii semigroup, the most widely studied class of Lie semigroups.     

The isospin forbidden 1− → 0+ transition in 40Ca

The isospin forbidden transition 1^? (6.95 MeV) → 0⁺ (g.s.) in ⁴⁰Ca is explained within a model that mixes isospin through single-particle energy differences and the two-body Coulomb interaction. There is no need to introduce an isospin non-conserving part of the nucleon-nucleon interaction to explain this anomalously fast transition.