An invariant trace formula for the universal covering group of SL(2,ℝ)

Automorphic forms of arbitrary real weight can be considered as functions on the universal covering group of SL(2, ). In this situation, we prove an invariant form of the Selberg trace formula for Hecke operators. For this purpose, the Fourier transforms of weightet orbital integrals, obtained by J. Arthur, R. Herb and P. Sally, jr., are explicitly calculated. Our formula does not follow from Arthur's invariant trace formula, since the group has infinite centre, and vector-valued automorphic forms with respect to non-congruence lattices are considered.     

Complete solutions of a family of quartic Thue and index form equations

Continuing the recent work of the second author, we prove that the diophantine equation

for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .

     

Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

Basic differential forms for actions of Lie groups

A section of a Riemannian -manifold is a closed submanifold which meets each orbit orthogonally. It is shown that the algebra of -invariant differential forms on which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on which are invariant with respect to the generalized Weyl group of , under some condition.

     

On quadratic forms of height two and a theorem of Wadsworth

Let and be anisotropic quadratic forms over a field of characteristic not . Their function fields and are said to be equivalent (over ) if and are isotropic. We consider the case where and is divisible by an -fold Pfister form. We determine those forms for which becomes isotropic over if , and provide partial results for . These results imply that if and are equivalent and , then is similar to over . This together with already known results yields that if is of height and degree or , and if , then and are equivalent iff and are isomorphic over .

     

Some remarks on R-contact flows

Let (M, ) be an R-contact manifold, then the set of periodic points of the characteristic vector field is a nonempty union of closed, totally geodesic odd-dimensional submanifolds. Moreover, the R-metric cannot have nonpositive sectional curvature. We also prove that no R-contact form can exist on any torus.     

Ketu and the second invariant of a quadratic space

Using the Chern classes defined by Grothendieck, we map aK-theoretic invariant of invertible symmetric matrices defined by Giffen to the Clifford invariant.According to Herrmann Graßman'sWörterbuch zum Rig-veda, Ketu may not be connected with K₂ but es bezeichnet das, was sich sichtbar oder kenntlich macht ...     

Polarographic behaviour and determination of azintamide

Azintamide was found to be reduced at the dropping mercury electrode over the pH range 1.8–9.4 in Britton Robinson buffers containing 20% methanol. At pH 7.42 a well defined diffusion-controlled cathodic wave was produced. The limiting current versus concentration plot was linear over the range 0.025–1.0 mM and 0.005–1.0 mM in the DC_t and DPP modes, respectively, with a lower detection limit of 1 × 10^–7 M by the latter technique. A mechanism for the electrode reaction has been proposed. The method has been applied to the determination of azintamide in tablets, and the results obtained were in agreement with those obtained by a reference method.AvH Scholar 1989–1991.     

Determination of pefloxacin in serum and pharmaceutical forms by derivative spectrophotometry

A method for the direct determination of pefloxacin in serum and pharmaceutical forms (tablets and ampoules) has been developed, based on the use of second-order derivative ultraviolet spectra. Spectrophotometric assay of pefloxacin in tablets and ampoules was carried out in 0.1 mol/L NaOH, while in serum it was performed in 0.1 mol/L NaOH with the addition of sodium dodecylsulfate, in 337–347 nm wavelength range. Linear calibration curves were obtained in the concentration ranges 2–30g/mL pefloxacin for tablets and ampoules and 0.12–5 g/ mL for serum samples. Relative error of determination, as criterion for accuracy, was less than 1%, while the precision was better than 4 ng/ml. The minimum detectable concentration of pefloxacin in serum was 15 ng/mL.     

Alkylation of cobalt and lutetium tetra(3,5-di-tert-butyl-4-hydroxyphenyl)dodecachlorophthalocyanine complexes initiated with current

Electrochemical properties of tetra(3,5-di-tert-butyl-4-hydroxyphenyl)dodecachlorophthalocyanine complexes of cobalt(II) and lutetium(III) in DMF solutions have been studied. It was suggested that in the presence ofn-butyl bromide, the electrochemically generated monoanionic complexes undergo alkylation at the metal atom. The geometries of the neutral and anionic complexes were calculated by the ZINDO/I semiempirical method. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 289–293, February, 1998.