Average potential energy criterion: Force fields of some planar XY3 and tetrahedral XY4 molecules

Minimization of the average potential energy contributions from bending deformations due to zero point vibration serves as a good criterion for fixing the harmonic force fields in planar XY₃ and tetrahedral XY₄ nonhydride molecules. An explanation based on the concept of rehybridization of the orbitals of the central atom during a bending vibration is offered.     

Proposed method of spike suppression in solid-state lasers

A method is proposed to suppress the spikes in the output of solid-state lasers, using passive negative feedback. A saturable absorber, normally used for Q-switching the laser, is used in a modified laser resonator, so that the resonator losses increase with laser intensity. The rate equations of a laser with such a loss mechanism are solved numerically. Numerical results for a ruby laser are presented.     

Metabolites of pyrenomycetes XIII: Structure of (+) hypothemycin,an antibiotic macrolide from Hypomyces trichothecoides

(+) Hypothemycin, an antibiotic metabolite of Hypomyces trichothecoides, has been assigned the macrolide structure I, based on chemical evidence and spectroscopic data.     

Hydrolytic reactions of esters and amides of thiosulphurous acid in a homogeneous medium

The hydrolytic reactions of esters and amides of thiosulphurous acid are investigated in a homogeneous medium. The esters are hydrolysed by alkali to give sulphide, sulphite and thiosulphate whereas the amides are resistant towards alkali. Both the esters and amides are hydrolysed by acids giving hydrogen sulphide, sulphur dioxide, polythionates and elemental sulphur. The hydrolysis of these esters and amides in presence of sulphurous acid and thiosulphuric acid gives tetrathionate and hexathionate, respectively.     

Possible effect of source backing on the backscatter peak in gamma spectra

Backscattering peak is one of the main features of the pulse height spectrum from a gamma ray detector. This arises mainly from materials outside the detector like source backing, photo multiplier tube housing, shielding etc. We have studied the effect of source backing on the relative importance of the back scattered peak for a NaI(I) scintillation detector. Gamma energies in the range from 60 to 1333 keV have been used. The measurements have been carried out for various backing thicknesses and differing source to detector distances. The details of the measurements and the results are presented.     

On the absence of supersymmetry anomalies in gauge theories

It is shown that N = 2 non-abelian gauge theory can be renormalized consistent with gauge invariance, supersymmetry and unitarity. There is no perturbative supersymmetry anomaly: the proof is independent of any specific regulator.     

An Exceptional Set in the Ergodic Theory of Expanding Maps on Manifolds

Under a general hypothesis an expanding map T of a Riemannian manifold M is known to preserve a measure equivalent to the Liouville measure on that manifold. As a consequence of this and Birkhoff’s pointwise ergodic theorem, the orbits of almost all points on the manifold are asymptotically distributed with regard to this Liouville measure. Let T be Lipschitz of class τ for some τ in (0,1], let Ω(x) denote the forward orbit closure of x and for a positive real number δ and let E(x₀, δ) denote the set of points x in M such that the distance from x₀ to Ω is at least δ. Let dim A denote the Hausdorff dimension of the set A. In this paper we prove a result which implies that there is a constant C(T) > 0 such that if τ = 1 and if τ < 1. This gives a quantitative converse to the above asymptotic distribution phenomenon. The result we prove is of sufficient generality that a similar result for expanding hyperbolic rational maps of degree not less than two follows as a special case.