1,3-Cyclobutandionderivate aus Keten

1,3-Cyclobutanedione derivatives from ketene The dimerisation of ketene leads mainly to the methylidene-β-lactone ‘Diketene’ 2c . It is shown, that also a small amount of the symmetrical dimer, 1,3-cyclobutadione 1c is produced, which under the reaction conditions is acetylated to 3-acetoxycyclo-butenone (5) .     

The He(Iα) Photoelectron Spectra of Substituted 1,2-Dithietes

The He(Iα) photoelectron (PE.) spectra of a series of substituted 1,2-dithietes have been recorded and assigned with respect to the orbital sequence derived from an STO-3G model calculation and by correlation with the PE. spectra of related compounds. The results provide additional support for the presence of a closed, four-membered ring moiety in all the 1,2-dithietes investigated. In all cases the two highest occupied molecular orbitals are b₂(π)= HOMO, a₂(π), with exception of 3,4-bis(trifluoromethyl)-1,2-dithiete where the sequence b₂(π), a₂(π) or a₂(π), b₂(π) is uncertain.     

A New Class of Equations for Rotationally Constrained Flows

The incompressible Navier–Stokes equation is considered in the limit of rapid rotation (small Ekman number). The analysis is limited to horizontal scales small enough so that both horizontal and vertical velocities are comparable, but the horizontal velocity components are still in geostrophic balance. Asymptotic analysis leads to a pair of nonlinear equations for the vertical velocity and vertical vorticity coupled by vertical stretching. Statistically stationary states are maintained against viscous dissipation by boundary forcing or energy injection at larger scales. For thermal forcing direct numerical simulation of the reduced equations reveals the presence of intense vortical structures spanning the layer depth, in excellent agreement with simulations of the Boussinesq equations for rotating convection by Julien et al. (1996). Received 30 May 1997 and accepted 4 January 1998     

Verallgemeinerung eines Satzes von F. Riesz

Let X be a compact Hausdorff space, C(X) the class of all continuous functions f: XR, considered as an ordered vector space over R with respect to its canonical order; furthermore let F be an order complete ordered vector space over R. A linear operator A: C(X)F is called bounded, if it transforms each bounded set of C(X) into a bounded set of F.The purpose of this paper is to represent such a bounded linear operator A: C(X)F as an integral Af= d with respect to some content , defined on the algebraa(X) which is generated by the open sets UX.This representation is unique, if is required to be regular (p. 11).