Exploiting non-abelian point group symmetry in direct two-electron integral transformations

Summary A simple and general scheme to exploit any discrete point group symmetry in two-electron integral transformations is introduced. It has been implemented together with integral pre-screening techniques in direct two-electron integral transformations. Its application has also been extended to subsequent MO integral processing steps like MP2 or solution of the coupled-perturbed Hartree-Fock equations (CPHF). Timings for representative applications are presented.     

Synthesis, structural determination and photo-antiproliferative activity of new 3-pyrazolyl or -isoxazolyl substituted 4-hydroxy-2(1H)-quinolinones

A convenient route to new 3-quinolinonyl-pyrazoles and isoxazoles is described through cyclization of 3-[(E)-3-(dimethylamino)-2-propenoyl]-4-hydroxy-1-methyl-2(1H)-quinolinone. The phototoxicity as well as the cytotoxic activities of the title compounds are evaluated against leukemia- and adenocarcinoma-derived cell lines in comparison to the normal human keratinocytes.     

Time-resolved electron paramagnetic resonance of photoinduced ion pairs in blends of polythiophene and fullerene derivatives

Substituted polythiophene and triethylenglycolpyrrolidino-C(60) blends are examined by time-resolved electron paramagnetic resonance (TR-EPR) at different temperatures. TR-EPR spectra recorded on the microsecond time scale after a short laser pulse are assigned to polythiophene and fullerene radical ion pairs, generated by electron transfer from the excited state of polythiophene to fullerene. At low temperatures, TR-EPR spectra show polarized lines with an antiphase emission/absorption pattern. The origin of the polarization pattern is described in the frame of spin correlated radical pair theory, in which two unpaired electron spins (on radical cation and anion, respectively) interact through isotropic spin exchange and anisotropic dipolar interactions. The polarization pattern is accounted for assuming a singlet excited state as the precursor of the charge-separated state. Spectral simulations yield dipolar and spin exchange coupling constants between unpaired electrons of the radical ion pair. Their values correspond to a mean distance between opposite charges of 22 A. When the temperature is increased, the spectra gradually loose their antiphase character and eventually consist of a signal totally in emission. This behavior is explained by a polarization mechanism involving a spin-selective charge recombination (ST(-1) mixing). The polarization pattern at different temperatures is examined in detail, and its generating mechanism is discussed.     

New versatile route to the synthesis of tetrahydro-beta-carbolines and tetrahydro-pyrano[3,4-b]indoles via an intramolecular Michael addition catalyzed by InBr3

A simple multistep synthetic strategy to 4-substituted 1,2,3,4-tetrahydro-beta-carboline and 1,3,4,9-tetrahydro-pyrano[3,4-b]indole derivatives starting from commercially available indole 2-carboxylic acid (5) is described. The final intramolecular Michael addition promoted by catalytic amount of InBr(3) (5-10 mol %) provided the expected polycyclic compounds in excellent yields (up to 97%) both in anhydrous organic and aqueous media.     

On resolvable Golomb rulers,symmetric configurations and progressive dinner parties

Journal of Algebraic Combinatorics - We define a new type of Golomb ruler, which we term a resolvable Golomb ruler. These are Golomb rulers that satisfy an additional “resolvability”...     

Statistical properties of shocks in Burgers turbulence

We consider the statistical properties of solutions of Burgers' equation in the limit of vanishing viscosity, , with Gaussian whitenoise initial data. This system was originally proposed by Burgers^[1] as a crude model of hydrodynamic turbulence, and more recently by Zel'dovichet al..^[12] to describe the evolution of gravitational matter at large spatio-temporal scales, with shocks playing the role of mass clusters. We present here a rigorous proof of the scaling relationP(s)s ^1/2,s1 whereP(s) is the cumulative probability distribution of shock strengths. We also show that the set of spatial locations of shocks is discrete, i.e. has no accumulation points; and establish an upper bound on the tails of the shock-strength distribution, namely 1–P(s)exp{–Cs ³} fors1. Our method draws on a remarkable connection existing between the structure of Burgers turbulence and classical probabilistic work on the convex envelope of Brownian motion and related diffusion processes.Inadvertently the sequel to this article, Statistical Properties of Shocks in Burgers Turbulence, II. Tail Probabilities for Velocities, Shock-Strengths and Rarefaction Intervals has already appeared in an earlier issue of Commun. Math. Phys. (Commun. Math. Phys.169, 45–59 (1995).     

Practical aspects of Mössbauer spectroscopy instrumentation

The setting up and updating of a Mössbauer laboratory imply the acquisition and assembling of different units. Guidelines concerning either the construction or the acquisition of the various parts which compose a Mössbauer spectrometer are given in this paper.     

Iron-57 Mössbauer spectroscopic studies of materials of composition Fe x NbTiP3O12: materials with low concentrations of iron and the effects of treatment in air

The⁵⁷Fe Mössbauer spectrum recorded from the material of composition Fe_0.25NbTiP₃O₁₂ shows the presence of Fe²⁺ in a distribution of approximately octahedral type I sites within the channels of the NbTiP₃O₁₂ structure. A comparison of the results with those recorded from the material Fe_0.33NbTiP₃O₁₂ demonstrates the existence of an upper limit to the occupation by the Fe²⁺ species of the type I sites. Lattice parameter measurements and⁵⁷Fe Mössbauer spectroscopy show that treatment of Fe_0.25NbTiP₃O₁₂ in air induces the migration of the incorporated iron from the channels to form macroscopic -Fe₂O₃.     

The rate difference between the weak decays of t and in supersymmetry

We find that the CP-violating asymmetry

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at the one-loop order within the minimal supersymmetric extension of the standard model is of the order of few percent for maximal CP violation. It could be measured by considering the rate difference in the one-lepton events.     

WKB-type approximations for second-order differential equations in -algebras

Rigorous asymptotic approximations of the WKB (or Liouville-Green) type are obtained for a basis of solutions to in the framework of -algebras. Both cases and are included, thus generalizing the classical theory for scalar equations developed by F.W.J. Olver to matrix as well as to infinite-dimensional equations.