Spectrophotometric Determination of Ternary Mixtures by the Derivative Ratio Spectrum-Zero Crossing Method

Abstract

A new spectrophotometric method is introduced for the assay of ternary mixtures with overlapping spectra. The method is based on the use of the first derivative of the ratio spectra and measurements of zero-crossing wavelengths. The ratio spectra were obtained by dividing the absorption spectrum of the mixture by that of one of the components. The concentration of the other components are then determined from their respective calibration graphs treated similarly. The method has been applied for the resolution of two ternary mixtures, namely, dipyridamole, aspirin and salicylic acid (I) and dipyridamole, oxazepam and 2-amino-5-chlorobenzophenone (II). Salicylic acid and benzo-phenone derivative are the degradation products of aspirin and oxazepam, respectively. The proposed method was applied for the assay of these combinations in synthetic mixtures and in commercial dosage forms. The results obtained were precise and accurate.     

Stabilité de la Cohomologie LP au Voisinage de 2 pour les Espaces Localement Symétriques

We give a sufficient condition for stability around 2 of L^p cohomology of a system over locally symmetric space.     

Approximation to the Sobolev classesW q r of functions of several variables by bilinear forms inL p for 2≤q≤p≤∞

We study the approximation of functions of several variables by bilinear forms that are the pairwise products of functions of fewer variables. The order of approximation of Sobolev classesW _q ^r by bilinear forms inL _p for 2≤q≤p≤∞ is found. Translated by N. K. Kulman Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 18–34, July, 1997.     

A Statistic for Testing the Null Hypothesis of Elliptical Symmetry

We present and study a procedure for testing the null hypothesis of multivariate elliptical symmetry. The procedure is based on the averages of some spherical harmonics over the projections of the scaled residual (1978, N. J. H. Small, Biometrika65, 657–658) of the d-dimensional data on the unit sphere of ^d. We find, under mild hypothesis, the limiting null distribution of the statistic presented, showing that, for an appropriate choice of the spherical harmonics included in the statistic, this distribution does not depend on the parameters that characterize the underlying elliptically symmetric law. We describe a bivariate simulation study that shows that the finite sample quantiles of our statistic converge fairly rapidly, with sample size, to the theoretical limiting quantiles and that our procedure enjoys good power against several alternatives.     

Gauge fixing procedure in the extended BRST theory. The example of the abelian 2‐forms

The paper proposes a general procedure to find the form of the gauge fixing term in the extended BRST quantization of the gauge theories, a difficult problem in the standard approach. Our proposal is based on the many level structure of the extended spaces and leads to a simple form of the gauge fixing term. The abelian 2‐form model is completely analyzed as an example.     

On the Stability of Equilibria in Two-Degrees-of- Freedom Hamiltonian Systems Under Resonances

We consider the problem of stability of equilibrium points in Hamiltonian systems of two degrees of freedom under resonances. Determining the stability or instability is based on a geometrical criterion based on how two surfaces, related with the normal form, intersect one another. The equivalence of this criterion with a result of Cabral and Meyer is proved. With this geometrical procedure, the hypothesis may be extended to more general cases.     

A proof of Selberg's orthogonality for automorphic L-functions

Let π and π′ be automorphic irreducible cuspidal representations of GL_m(Q_A) and GL_m′(Q_A), respectively. Assume that π and π′ are unitary and at least one of them is self-contragredient. In this article we will give an unconditional proof of an orthogonality for π and π′, weighted by the von Mangoldt function Λ(n) and 1−n/x. We then remove the weighting factor 1−n/x and prove the Selberg orthogonality conjecture for automorphic L-functions L(s,π) and L(s,π′), unconditionally for m≤4 and m′≤4, and under the Hypothesis H of Rudnick and Sarnak [20] in other cases. This proof of Selberg's orthogonality removes such an assumption in the computation of superposition distribution of normalized nontrivial zeros of distinct automorphic L-functions by Liu and Ye [12].     

On length and product of harmonic forms in Kähler geometry

Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as Kähler and hyperbolic geometries are concerned. In the second part of the paper, we give algebraic and topological obstructions to the existence of a geometrically 2-formal Kähler metric, at the level of the second cohomology group. A strong interaction with almost Kähler geometry is to be noted. In complex dimension 3, we list all the possible values of the second Betti number of a geometrically 2-formal Kähler metric.     

Modular lattices over cyclotomic fields

This paper is concerned with modular lattices over cyclotomic fields. In particular, the notion of Arakelov modular ideal lattice is introduced. All the cyclotomic fields over which there exists an Arakelov modular lattice of given level are characterised.