Higher order Ito product formula and generators of evolutions and flows

A simple combinatorial formula is found for the product of two iterated quantum stochastic integrals, and used to find conditions that such an integral represent a unitary-valued or^*-algebra homomorphism-valued process.     

Pattern recognition display methods for the analysis of computed molecular properties

Summary Pattern recognition methods, particularly the unsupervised learning techniques, are well suited for the preliminary analysis of the large data sets produced by computer chemistry. The use of linear and non-linear display methods for such exploratory analysis are exemplified with the aid of two data sets of biologically active molecules. Advantages and disadvantages of these techniques are discussed.     

Ultraviolet absorption and luminescence properties of some cannabis constituents

The characteristics of the absorption, fluorescence and phosphorescence spectra of the cannabinols have been determined. The data provide a basis for the detection of these compounds at concentrations down to 10 ng ml .     

Novel mercury(II) complexes of meso-tetraphenylporphyrin and N-methylporphyrins

Treatment of meso-tetraphenylporphyrin, H₂TPP, with just over one equivalent of mercury(II) acetate in methylene chloride-THF gives mercury(II) meso-tetraphenylporphyrin, HgTPP. With excess of mercury(II) acetate, H₂TPP and HgTPP afford a novel dimetallic mononuclear porphyrin, AcOHgTPPHgOAc. In contrast, HgTPP reacts with mercury(II) chloride to give the chloro-analogue, ClHgTPPHgCl, but there is no reaction between H₂TPP and mercury(II) chloride. Demetallation of HgTPP in methylene chloride containing small amounts of hydrogen chloride proceeds via the dimetallic compound, ClHgTPPHgCl, to give free base HTPP. The reaction rate is dependent upon acid concentration suggesting that the rate determining step is protonation, but dilution causes no decrease in the rate; a mechanism which invokes the intermediacy of monohydrogen-meso-tetraphenylporphyrinatomercury(II) chloride, H(TPP)HgCl, in the formation of ClHgTPPHgCl and in its subsequent decomposition into H₂TPP, is proposed.N-Methylporphyrins react with mercury(II) acetate in methylene chloride-tetrahydrofuran to give the corresponding N-methylporphyrinatomercury(II) acetates, Me(P)HgOAc.     

Peptides—XXXX: Synthesis of the 68–75 fragment of a lysozyme analogue

The 68–75 subfragment has been prepared by a 4+4 fragment condensation using DCCI/HOBt. The constituent 68–71 and 72–75 fragments being prepared stepwise by the pivalic mixed anhydride method. The octapeptide prepared by this approach was shown to be identical with that synthesised by a solid phase method using a phenolic polymer as the support.     

Intercalates of α-Sn(HP04)2·H2O with aromatic and heterocyclic bases and some comments on their orientation in the interlayer region

The intercalation of amines into -tin(IV) hydrogen phosphate, -Sn(HP0₄)₂·H₂0, (-SnP) can occur to give mono- or bilayers of the guest molecule. The distribution and orientation of the amines is influenced by geometrical factors, acidity of the guest molecule and moreover, the degree of charge localisation of the guest organic cations. Regarding the monolayer formation, there are two possibilities. The first is that aromatic amines form monolayers with parallel orientation of the amine with respect to the phosphate layer, when the charge is delocalised over the aromatic ring. Monolayer formation with perpendicular orientation occurs when the positive charge is localised in opposite parts of the aromatic ring molecule. Bilayer formation occurs when the positive charge is localised in one part of the molecule and simultaneous interaction with two adjacent layers is not possible.     

Translation-invariant integrals,and Fourier analysis on Clifford and Grassmann algebras

The generalization of Berezin's Grassmann algebra integral to a Clifford algebra is shown to be translation-invariant in a certain sense. This enables the construction of analogs of twisted convolutions of Grassmann algebra elements and of the Fourier-Weyl transformation, which is an isomorphism from a Clifford algebra to the Grassmann algebra over the dual space, equipped with a twisted convolution product. As an application a noncommutative central limit theorem for states of a Clifford algebra is proved.     

Observation of weak impact of a stochastic magnetic field on fast-ion confinement

Fast ions are observed to be very well confined in the Madison Symmetric Torus reversed field pinch despite the presence of stochastic magnetic field. The fast-ion energy loss is consistent with the classical slowing down rate, and their confinement time is longer than expected by stochastic estimates. Fast-ion confinement is measured from the decay of d-d neutrons following a short pulse of a 20 keV atomic deuterium beam. Ion confinement agrees with computation of particle trajectories in the stochastic magnetic field, and is understood through consideration of ion guiding center islands.