On the epicomplete monoreflection of an archimedean lattice-ordered group

In a category C an object it G is epicomplete if the only epic monics out of G are isomorphisms, epic or monic meant in the categorical sense of right or left cancellable. For each of the categories Arch: archimedean ?-groups with ?-homomorphisms, and its companion category W: Arch-objects with distinguished weak unit and unit-preserving ?-homomorphisms, (and for the corresponding categories of vector lattices) epicompleteness has been characterized as divisible and conditionally and laterally σ-complete, and it has been shown to be monoreflective. Denote the reflecting functors by β and β ^W , respectively. What are they? For W the Yosida representation has been used to realize β ^W A as a certain quotient of B (Y A), the Baire functions on the Yosida space of A. For Arch, very little has been known. Here we give a general representation theorem, Theorem A, for β G as a certain subdirect product of W-epicomplete objects derived from G. That result, some W-theory, and the relation between epicity and relative uniform density are then employed to show Theorem B: β C _K (Y)=B _L (Y), where C _K (Y)is the ?-group of continuous functions on Y with compact support and B _L (Y) is the ?-group of Baire functions on Y having Lindelöf cozero sets.     

A three-level analytic model for alkali metal vapor lasers: part I. Narrowband optical pumping

A three-level analytic model for optically pumped alkali metal vapor lasers is developed by considering the steady-state rate equations for the longitudinally averaged number densities of the ground ²S_1/2 and first excited ²P_3/2, and ²P_1/2 states. The threshold pump intensity includes both the requirements to fully bleach the pump transition and exceed optical losses, typically about 200  W/cm². Slope efficiency depends critically on the fraction of incident photons absorbed and the overlap of pump and resonator modes, approaching the quantum efficiency of 0.95–0.98, depending on the alkali atom. For marginal cavity transmission losses, peak performance is achieved for low output coupling mirror reflectivity. For efficient operation, the collisional relaxation between the two upper levels should be fast to prevent bottlenecking. By assuming a statistical distribution between the upper two levels, the limiting analytic solution for the quasi two-level system is achieved. For properly designed gain conditions, the quasi two-level solution is usually achievable and represents ideal performance.     

An exact algorithm for graph partitioning

An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained by decomposing the objective function into convex and concave parts and replacing the concave part by an affine underestimate. It is shown that the best affine underestimate can be expressed in terms of the center and the radius of the smallest sphere containing the feasible set. The concave term is obtained either by a constant diagonal shift associated with the smallest eigenvalue of the objective function Hessian, or by a diagonal shift obtained by solving a semidefinite programming problem. Numerical results show that the proposed algorithm is competitive with state-of-the-art graph partitioning codes.     

Clean unital ℓ-groups

A ring with identity is said to be clean if every element can be written as a sum of a unit and an idempotent. The study of clean rings has been at the forefront of ring theory over the past decade. The theory of partially-ordered groups has a nice and long history and since there are several ways of relating a ring to a (unital) partially-ordered group it became apparent that there ought to be a notion of a clean partially-ordered group. In this article we define a clean unital lattice-ordered group; we state and prove a theorem which characterizes clean unital ?-groups. We mention the relationship of clean unital ?-groups to algebraic K-theory. In the last section of the article we generalize the notion of clean to the non-unital context and investigate this concept within the framework of W-objects, that is, archimedean ?-groups with distinguished weak order unit.     

Mandel?l

Ohne Zusammenfassung     

Ueber Reactionen auf Solanin

Ohne Zusammenfassung     

Kalkstickstoff

Ohne Zusammenfassung