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.

     

Time-domain electromagnetic scattering by open ended circular waveguide and related structure

The axial electromagnetic backscattering by four objects characterized in part by either a circular aperture or circular conducting surface is studied. Impulse response waveforms for finite and open circular waveguides, a circular loop and a thin circular disc are synthesized from exact and/or approximate frequency domain scattering data. Complex natural resonances of the four objects are compared to illustrate similar and dissimilar features. For the open circular waveguide it is demonstrated that approximate scattering solutions for loaded guides in the resonance region can be obtained by properly combining low and high frequency estimates.     

Unsigned State Models for the Jones Polynomial

It is a well-known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we show that for every diagram of a link in S ³ there exists a diagram of an alternating link in a thickened surface (and an alternating virtual link) with the same Kauffman bracket. We also recover two recent results in the literature relating to the Jones and Bollobás-Riordan polynomials and show they arise from two different interpretations of the same embedded graph.     

H-transfer rates in ion-neutral complexes versus those in intact aliphatic ions

The relative rates of H-transfer between partners in ion-neutral complexes were compared with those in intramolecular rearrangements using results of first differential photoionization mass spectrometry measurements. Complex-mediated H-transfers are inferred to have rates of the same order as those for intramolecular hydrogen rearrangements, suggesting a similar range of motion of the reactive sites in both types of reactions. It is also concluded that at their fastest H-transfers take place between the partners in ion-neutral complexes within at most the time of several rotations of the partners in the complexes. Copyright 1999 John Wiley & Sons, Ltd.     

Comparison of capillary electrochromatography with high-performance liquid chromatography for the analysis of pirimicarb and related compounds.

The applicability of capillary electrochromatography (CEC) to the analysis of pirimicarb and structurally related pyrimidines has been investigated. Methods were developed to improve the separation of closely related compounds. Resolution was achieved both by the use of running buffers containing a mixture of two organic modifiers to increase selectivity and reduce retention times. Solvent composition step gradients were used to separate compounds of widely differing retention factors. A comparison has been made between HPLC and CEC using identical separation parameters and the same stationary phase, from which two important conclusions are drawn. First, it has been shown that values of k' for the compounds analyzed were the same in both techniques. Secondly, although it is evident that CEC produces higher efficiencies than HPLC when running buffers with high organic solvent content are used, as the aqueous content of the running buffer is increased the efficiencies achieved in CEC and HPLC converge until they become equivalent. This is contrary to the theoretical model which predicts efficiencies are inherently higher using electrically rather than pressure driven flow. Disadvantages of the limited control of flow-rate in CEC in comparison with HPLC, are shown.     

Net charge in deep inelastic antineutrino-nucleon scattering

We investigate the net change in the current fragmentation region in antineutrino-nucleon charged current interactions in the Fermilab 15 ft bubble chamber. Support is presented for the d-quark origin of the forward hadrons in the hadron center-of-mass system. An extrapolation of the net charge to infinite center-of-mass energy is performed giving as a result $\text{〈Q〈}{}_{\mathrm{<mtext>v</mtext>}}\text{=? (0.44 ± 0.09)}$. Combining this result with the result obtained using our v events in the same experiment we obtain the value 0.98 ± 0.15 for the charge difference between the fragmenting quarks in $\text{v}\text{and}\text{v}$ charged current events.     

A combined vibrational sum frequency generation spectroscopy and atomic force microscopy study of sphingomyelin-cholesterol monolayers

A combination of vibrational sum frequency generation spectroscopy and atomic force microscopy is used to study the changes in morphology and conformational order in monolayers prepared from three natural sphingomyelin (SM) mixtures as a function of surface pressure and cholesterol concentration. The most homogeneous SM gave monolayers with well-ordered acyl chains and few gauche defects with relatively small effects of either increasing surface pressure or cholesterol addition. Heterogeneous SM mixtures with a mixture of acyl chain lengths or with significant fractions of unsaturated acyl chains had much larger contributions from gauche defects at low surface pressure and gave increasingly well-ordered monolayers as the surface pressure increased. They also showed substantial increases in lipid chain order after cholesterol addition. Overall, these results are consistent with the strong hydrogen bonding capacity of SM leading to well-ordered monolayers over a range of surface pressures. The changes in acyl chain order for natural SMs as a function of cholesterol are relevant to formation of sphingolipid-cholesterol enriched domains in cell membranes.