ON ALGEBRAIC VOLUME DENSITY PROPERTY

A smooth affine algebraic variety X equipped with an algebraic volume form ω has the algebraic volume density property (AVDP) if the Lie algebra generated by complete algebraic vector fields of ω-divergence zero coincides with the space of all algebraic vector fields of ω-divergence zero. We develop an effective criterion of verifying whether a given X has AVDP. As an application of this method we establish AVDP for any homogeneous space X = G/R that admits a G-invariant algebraic volume form where G is a linear algebraic group and R is a closed reductive subgroup of G.     

Reaction of Dimethyl Acetylene-Dicarobxylate With Triazinone

Abstract

The addition of dimethyl acetylenedicarboxylate (DMAD) to 6-menthy-1, 2,4-triazlne-3(2H)thione-5(4H)-one afforded 2-methoxylcarboxy-7-methyl-1,3-thiazino[3,2-b][1,2,4]triazine-4,8-dione.     

Influence of anionic substitutions on hyperfine interactions and ionic ordering in ferrites

Hyperfine Interactions -     

Examples of asymptotic completeness in translation invariant systems with an unbounded number of particles

A tagged particle interacting with a finite but unbounded number of particles is considered. Some examples of asymptotic completeness are given which are uniform in the number of particles.     

A Relation Between Closure Operators on a Small Category and Its Category of Presheaves

In this paper we show that each factorization structure on a small category , satisfying certain conditions, yields a presheaf on and a morphism of presheaves . We then give connections, and set up one to one correspondences, between subclasses of the following classes: (a) closure operators on (b) subobjects of (c) morphisms from to (d) weak Lawvere–Tierney topologies (e) weak Grothendieck topologies (f) closure operators on .