On Liouville decompositions in local fields

In 1962 Erd\H{o}s proved that every real number may be decomposed into a sum of Liouville numbers. Here we consider more general functions which decompose elements from an arbitrary local field into Liouville numbers. Several examples and applications are given. As an illustration, we prove that for any real numbers , not equal to 0 or 1, there exist uncountably many Liouville numbers such that are all Liouville numbers.

     

Development of a tandem cyclization mediated by samarium(II) iodide: sequential intramolecular conjugate addition/nucleophilic acyl substitution

The development of a one-pot tandem intramolecular conjugate addition/nucleophilic acyl substitution using samarium(II) iodide is reported. The reaction relies on the reagent’s unique ability to mediate both radical and anionic pathways, which are likely integral to the mechanism of this transformation. The tricyclic hemiacetal product was formed in good yield, with excellent diastereoselectivity, and its structure was verified by X-ray crystallographic analysis.     

Unprecedented reversible migration of amide to schiff base ligands attached to tin: latent single-site initiators for lactide polymerization

In an unprecedented transformation, amide ligands are found to attack the imine carbon centers of tridentate Schiff base ligands attached to tin. The process is reversible, and the resultant (masked) amide species can be exploited as latent single-site initiators for the controlled polymerization of rac-lactide.     

Asymmetric [2,3]-rearrangement of glycine-derived allyl ammonium ylids

The first examples of highly enantioselective [2,3]-sigmatropic rearrangements of acyclic allylic ammonium ylids are reported. Thus, a range of N-{2'-[(N'-allyl-N',N'-dialkyl)ammonium]}acetyl camphor sultams undergo rearrangement at 0 degrees C in DME solution with high diastereofacial control (up to 99:1 dr) to give allylglycines in generally high yield. The power of the method has been demonstrated in a rapid and efficient synthesis of (R)-allyl glycine.     

Molecular Replacement Studies of Cucurmosin from Cucurbita Moschata:Structure Homology with Trichosanthin

1 INTRODUCTION Many plants contain proteins that are capable of inactivating ribosomes and therefore are called ribosome-inactivating proteins or RIPs[1]. RIPs are RNA N-glycosidases that inactivate ribosomes through a site-specific deadenylation of the large ribosomal RNA[2, 3]. RIPs are also capable of inactivating many nonribosomal nucleic acid substrates and can be considered as polynucleotide: adenosine glycosidases[4～6]. There are two types of RIPs: type I, single chain pr…     

Synthesis and polymerisation of lipophilic peptide nucleic acids derived from stearic acid and pentacosa-10,12-diynoic acid

The adenine, cytosine and thymine peptide nucleic acid (PNA) monomers and PNA T₁₀ oligomers bearing either a diacetylenic or stearoyl moiety at the N- or C-terminus have been successfully prepared. The resulting thymine monomeric and T₁₀-mer derivatives have been subsequently incorporated into polydiacetylene-containing liposomes.     

Thermal decomposition of RDX from reactive molecular dynamics

We use the recently developed reactive force field ReaxFF with molecular dynamics to study thermal induced chemistry in RDX [cyclic-[CH(2)N(NO(2))](3)] at various temperatures and densities. We find that the time evolution of the potential energy can be described reasonably well with a single exponential function from which we obtain an overall characteristic time of decomposition that increases with decreasing density and shows an Arrhenius temperature dependence. These characteristic timescales are in reasonable quantitative agreement with experimental measurements in a similar energetic material, HMX [cyclic-[CH(2)N(NO(2))](4)]. Our simulations show that the equilibrium population of CO and CO(2) (as well as their time evolution) depend strongly of density: at low density almost all carbon atoms form CO molecules; as the density increases larger aggregates of carbon appear leading to a C deficient gas phase and the appearance of CO(2) molecules. The equilibrium populations of N(2) and H(2)O are more insensitive with respect to density and form in the early stages of the decomposition process with similar timescales.     

Global gravitational anomalies

A general formula for global gauge and gravitational anomalies is derived. It is used to show that the anomaly free supergravity and superstring theories in ten dimensions are all free of global anomalies that might have ruined their consistency. However, it is shown that global anomalies lead to some restrictions on allowed compactifications of these theories. For example, in the case of O(32) superstring theory, it is shown that a global anomaly related to ₇(O(32)) leads to a Dirac-like quantization condition for the field strength of the antisymmetric tensor field.Related to global anomalies is the question of the number of fermion zero modes in an instanton field. It is argued that the relevant gravitational instantons are exotic spheres. It is shown that the number of fermion zero modes in an instanton field is always even in ten dimensional supergravity.Supported in part by NSF Grant No. PHY80-19754