Derivations, isomorphisms, and second cohomology of generalized Witt algebras

Generalized Witt algebras, over a field of characteristic , were defined by Kawamoto about 12 years ago. Using different notations from Kawamoto's, we give an essentially equivalent definition of generalized Witt algebras over , where the ingredients are an abelian group , a vector space over , and a map which is linear in the first variable and additive in the second one. In this paper, the derivations of any generalized Witt algebra
, with the right kernel of being , are explicitly described; the isomorphisms between any two simple generalized Witt algebras are completely determined; and the second cohomology group for any simple generalized Witt algebra is computed. The derivations, the automorphisms and the second cohomology groups of some special generalized Witt algebras have been studied by several other authors as indicated in the references.

     

Uniform molecular analysis using femtosecond laser mass spectrometry

The potential of femtosecond laser time-of-flight mass spectrometry (FLMS) for uniform quantitative analysis of molecules has been investigated. Various samples of molecular gases and vapours have been studied, using ultra-fast ( approximately 50 fs) laser pulses with very high intensity (up to 1.6 x 10(16) Wcm(-2)) for non-resonant multiphoton ionisation/tunnel ionisation. Some of these molecules have high ionisation potentials, requiring up to ten photons for non-resonant ionisation. The relative sensitivity factors (RSF) have been determined as a function of the laser intensity and it has been demonstrated that for molecules with very different masses and ionisation potentials, uniform ionisation has been achieved at the highest laser intensities. Quantitative laser mass spectrometry of molecules is therefore a distinct possibility. Copyright 1999 John Wiley & Sons, Ltd.     

FLOG: A system to select ‘quasi-flexible’ ligands complementary to a receptor of known three-dimensional structure

Summary We present a system, FLOG (Flexible Ligands Oriented on Grid), that searches a database of 3D coordinates to find molecules complementary to a macromolecular receptor of known 3D structure. The philosophy of FLOG is similar to that reported for DOCK [Shoichet, B.K. et al., J. Comput. Chem., 13 (1992) 380]. In common with that system, we use a match center representation of the volume of the binding cavity and we use a clique-finding algorithm to generate trial orientations of each candidate ligand in the binding site. Also we use a grid representation of the receptor to assess the fit of each orientation. We have introduced a number of novel features within this paradigm. First, we address ligand flexibility by including up to 25 explicit conformations of each structure in our databases. Nonhydrogen atoms in each database entry are assigned one of seven atom types (anion, cation, donor, acceptor, polar, hydrophobic and other) based on their local bonded chemical environments. Second, we have devised a new grid-based scoring function compatible with this heavy atom representation of the ligands. This includes several potentials (electrostatic, hydrogen bonding, hydrophobic and van der Waals) calculated from the location of the receptor atoms. Third, we have improved the fitting stage of the search. Initial dockings are generated with a more efficient clique-finding algorithm. This new algorithm includes the concept of essential points, match centers that must be paired with a ligand atom. Also, we introduce the use of a rapid simplex-based rigid-body optimizer to refine the orientations. We demonstrate, using dihydrofolate reductase as a sample receptor, that the FLOG system can select known inhibitors from a large database of drug-like compounds.     

Turbulence characteristics from minisodar data

Vertical profiles of atmospheric turbulence characteristics, including spatial and temporal longitudinal and transverse velocity structure functions, velocity structure characteristics, and turbulent kinetic energy dissipation rates retrieved from time series of vertical profiles of the wind velocity vector measured with a minisodar operating at a frequency of 4900 Hz are presented. It is established that the structure functions first increase with the separation distance between the observation points and then are saturated; moreover, the longitudinal structure function is much greater than the transverse one, which is in agreement with the data available from the literature. The velocity structure characteristic is well described by the z^−2/3 altitude dependence predicted theoretically. Calculated values of the turbulent energy dissipation rate are in agreement with the data available from the literature.