Irreducible representations of Virasoro-toroidal Lie algebras

Toroidal Lie algebras and their vertex operator representations were introduced in [MEY] and a class of indecomposable modules were investigated. In this work, we extend the toroidal algebra by the Virasoro algebra thus constructing a semi-direct product algebra containing the toroidal algebra as an ideal and the Virasoro algebra as a subalgebra. With the use of vertex operators and certain oscillator representations of the Virasoro algebra it is proved that the corresponding Fock space gives rise to a class of irreducible modules for the Virasoro-toroidal algebra.To A. John Coleman on the occasion of his 75th birthday     

Regioselectivity in the photochemical ring contraction of 4-diazopyrazolidine-3,5-diones to give aza-β-lactams

The photochemical decomposition of unsymmetrically substituted 4-diazopyrazolidine-3,5-diones leads to aza-β-lactams, and provides some indication of the relative migratory aptitude of nitrogen groups in the Wolff rearrangement.     

Frequency discrimination in the monkey

This study evaluated frequency discrimination ability in 11 monkeys over an extended period of time using a repeating-standard procedure and the method of constant stimuli. The intersubject variability of the difference limens for frequency (delta F) was large, as reported by other investigators, but similar in magnitude to the variability of the difference limens for intensity (delta I) from three of the same subjects in an intensity discrimination experiment. Continued training generally resulted in a rapid decrease in delta F's, followed by a longer-term, slower decrease. For one subject delta F's slowly decreased throughout a 190-week time period. This long-term training effect was specific to frequency discrimination; a similar effect was not observed for the same subject tested in an intensity discrimination experiment. Finally, delta F's from the well-trained monkeys of this study were larger than monkey delta F's from this laboratory reported in an earlier study, and than human delta F's. An anatomical explanation for the human/monkey delta F magnitude difference is explored.     

Approximate forms for SU(2) multi-instanton determinants

An approximate form for SU(2) multi-instanton determinants, in both the 2- and 3-dimensional representations, is obtained which incorporates the correct properties under conformal transformations and also the leading singular behaviour when the multi-instanton solution becomes degenerate, at least for the 't Hooft multi-instanton solution.     

The synthetic challenge of diazonamide A, a macrocyclic indole bis-oxazole marine natural product

The complex structure of the marine metabolic diazonamide A comprises a dichlorinated indole bis-oxazole heteroaromatic fragment, and a [b]-fused dihydrobenzofuran-dihydroindole unit containing an animal carbon, all incorporated within a strained double macrocyclic array. This review details the synthetic studies on this fascinating natural product starting from early studies on the original structure (1991-2001), through the synthesis of the originally proposed structure and the subsequent structural revision, to the eventual successful syntheses of the natural product itself. Throughout we focus on the innovative ways in which synthetic chemists have approached the challenges posed by this natural product.     

A Math Query Language with an Expanded Set of Wildcards

Math search is a new area of research with many enabling technologies but also many challenges. Some of the enabling technologies include XML, XPath, XQuery, and MathML. Some of the challenges involve enabling search systems to recognize mathematical symbols and structures. Several math search projects have made considerable progress in meeting those challenges. One of the remaining challenges is the creation and implementation of a math query language that enables the general users to express their information needs intuitively yet precisely. This paper will present such a language and detail its features. The new math query language offers an alternative way to describe mathematical expressions that is more consistent and less ambiguous than conventional mathematical notation. In addition, the language goes beyond the Boolean and proximity query syntax found in standard text search systems. It defines a powerful set of wildcards that are deemed important for math search. These wildcards provide for more precise structural search and multi-levels of abstractions. Three new sets of wildcards and their implementation details will also be discussed.      

Energy splitting of the ground-state doublet in the nucleus 229Th

The energy splitting of the 229Th ground-state doublet is measured to be 7.6+/-0.5 eV, significantly greater than earlier measurements. Gamma rays produced following the alpha decay of 233U (105 muCi) were counted in the NASA/electron beam ion trap x-ray microcalorimeter spectrometer with an experimental energy resolution of 26 eV (FWHM). A difference technique was applied to the gamma-ray decay of the 71.82 keV level that populates both members of the doublet. A positive correction amounting to 0.6 eV was made for the unobserved interband decay of the 29.19 keV state (29.19-->0 keV).     

The total synthesis of siphonazole, a structurally unusual bis-oxazole natural product

The first synthesis of the unusual bis-oxazole natural product siphonazole is reported, both oxazole rings being constructed using rhodium carbene chemistry.