Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

Thermal structure of clean and contaminated free-surfaces subject to an impinging gas jet

The thermal structure of clean and contaminated free-surfaces subject to the transient flow of a gas jet were investigated experimentally. The interface and near-surface flow were examined using optical high-speed (HS) motion analysis, infrared (IR) imagery, and laser-induced fluorescence (LIF). IR imagery revealed an instability in the form of thermal scars on the expanding circular surfactant front. The nature of this instability was explored by performing experiments with both clean and contaminated surfaces. LIF visualization techniques were used to gain insight into the nature of the near-surface flow field. This revealed the presence of a vortex ring that underwent an instability in which ringlets surrounded the primary core. Using simultaneous IR/LIF imaging of a fixed spatial region, it is shown that the thermal scars are spatially and temporally correlated with the near-surface ringlet structures, suggesting that the scars are a surface manifestation of the near-surface structures.

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Where are the GaPs? A rational approach to monomer acquisition and selection

Gridding and partitioning (GaP) is a computational method for the classification and selection of monomers for combinatorial libraries. The molecules are described in terms of the pharmacophoric groups they contain and where those pharmacophoric groups can be located in three-dimensional space. The approach involves a detailed conformational analysis of each molecule. This conformational analysis is done within a common coordinate frame, thus enabling the monomers to be compared. The use of a partitioned space is central to this particular application as it facilitates the identification of regions of space which are not well represented by existing compounds. Several ways to extend the use of partitioned pharmacophore spaces are described. Applications of the approach in monomer acquisition and in library design are outlined.     

Angular-momentum theory and projective geometry

The Desarguesian nature of angular-momentum theory is illustrated by drawing correspondences between relations satisfied by then-j symbols and various collinearity properties of the appropriate diagrams. No examples of Pappus' theorem have been found. A relation is suggested between the operations of angular-momentum theory and Hilbert's constructions for the addition and multiplication of points on a line.     

Lambda spectra in 11.6A GeV/c Au-Au collisions

E896 has measured Lambda production in 11.6A GeV/c Au-Au collisions over virtually the whole rapidity phase space. The midrapidity p(t) distributions have been measured for the first time at this energy and appear to indicate that the Lambda hyperons have different freeze-out conditions than protons. A comparison with the relativistic quantum molecular dynamics model shows that while there is good shape agreement at high rapidity the model predicts significantly different slopes of the m(t) spectra at midrapidity. The data, where overlap occurs, are consistent with previously reported measurements.     

The Symbiotic Relationship Between Drug Discovery and Organic Chemistry

All pharmaceutical products contain organic molecules; the source may be a natural product or a fully synthetic molecule, or a combination of both. Thus, it follows that organic chemistry underpins both existing and upcoming pharmaceutical products. The reverse relationship has also affected organic synthesis, changing its landscape towards increasingly complex targets. This Review article sets out to give a concise appraisal of this symbiotic relationship between organic chemistry and drug discovery, along with a discussion of the design concepts and highlighting key milestones along the journey. In particular, criteria for a high-quality compound library design enabling efficient virtual navigation of chemical space, as well as rise and fall of concepts for its synthetic exploration (such as combinatorial chemistry; diversity-, biology-, lead-, or fragment-oriented syntheses; and DNA-encoded libraries) are critically surveyed.