Time dependent canonical perturbation theory I: General theory

In this communication, we reanalyze the causes of the singularities of canonical perturbation theory and show that some of these singularities can be removed by using time-dependent canonical perturbation theory. A study of the local and global properties (in terms of the perturbation parameter) is also undertaken.     

A note on correlations between eigenvalues of a random matrix

Dyson's method is adopted here for the so called Gaussian ensembles. Incidently this confirms the long cherished belief that the statistical properties of a small number of eigenvalues is the same for the two kinds of ensembles, the circular and the Gaussian ones.     

Multiparameter study of 1H, 3H and 4He in fast neutron induced fission of 235U

The emission probabilities per fission of α-particles, tritons and protons have been measured in fast neutron induced fission of ²³⁵U. The measurements were carried out at neutron energies of 120, 180, 230 and 550 keV. AΔE-E semiconductor detector telescope was used to identify different light charged particles and the fission fragments were detected with an ionization chamber. The three-parameter data corresponding to the pulse heights from the ΔE-E detectors and the ion-chamber were recorded event by event on magnetic tape and were analyzed off-line by computer. No significant variation in the most probable energy ($\text{E}$) and the standard deviation (σ_E) of the energy spectra of different light charged particles with incident neutron energy was observed, although $\text{E}{}_{\mathrm{\alpha }}$ was seen to have a slightly higher value beyond E_n = 230 keV. The yield of α-particles in fission induced by neutrons of E_n ～ 200 keV was found to be higher by about 20 % than that in thermal neutron induced fission. The yields of tritons and protons were found to increase significantly with neutron energy.     

Effects of Hall Currents and Gyroviscosity on the Instability of a Self-Gravitating Stratified Plasma

The instability in a horizontal layer of a partially ionized self gravitating plasma has been studied to include simultaneously the effects of Hall currents, viscosity and finiteness of Larmor radius (FLR). The ambient magnetic field is assumed to be uniform and vertical. Proper solutions have been obtained through the variational methods for a semi-infinite plasma in which the density has an exponential gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that the growth rate of unstable perturbations decreases with the effects of viscosity, neutral gas friction and FLR. The influence of effects of viscosity, neutral gas friction and FLR are consequently stabilizing. It is found that the Hall currents have a destabilizing influence as the growth rate is found to increase with this effect.     

A new synthesis of homoisoflavanones (3-benzyl-4-chromanones)

Two 7-hydroxyhomoisoflavanones ( / ) have been synthesized from corresponding 2'-hydroxydihydrochalcones ( / ) in about 33% overall yields. The stages are : (1) selective protection of C₄'-hydroxyl in ( / ) with EtO.CH₂Cl (1 molar equiv.) In the presence of dry K₂C0₃ and acetone at r.t.; (ii) reaction with one more molar equiv. of EtO.CH₂Cl at 60–70° without Isolating products ( / ) (iii) cyclizatlon of resulting α-hydroxymethyl derivatives ( / ) with 4% aq. aIc. Na₂C0₃ and (iv) deprotection of resulting 7-ethoxymethoxy homoisoflavanones ( / ) with 10% CH₃0H-HC1. The explanations for the formation of ( / ) and ( / ) are given.     

Cumulant functions in optical coherence theory

Cumulant functions are introduced to describe the statistical state of a radiation field. These functions are simply related to the optical coherence functions but have some interesting features. It is shown that if the cumulant functions of all orders greater than some numberN ₀ vanish then they also vanish for all orders greater than 2. Thermal field is the only field having this property. This property holds whether the field is described by a classical stochastic process or by a quantum density operator. Further the particular operator ordering used in defining these cumulant functions for the quantized field affects only the second order cumulant function. To describe the statistical state of a vector field such as partially polarized or unpolarized radiation, one would need to introduce cumulant tensors.     

Long-range alpha emission inP-wave neutron induced fission of235U

The yield and energy distribution of long-range alpha-particles (lra) emitted from neutron-induced fission of²³⁵U have been measured at neutron energies; thermal, 125±12, 155±11, 185±10, 210±9, 240±9, 365±50 and 480±45 keV. The long-range alpha-particles were detected in cellulose nitrate track detector foils. Results showed an increase of about 50% in the yield at neutron energies in the region 150 keV≤E _n≤220 keV as compared to that of thermal neutrons. A calculation has been carried out to extract thelra to binary fission ratio forp-wave neutron induced fission.     

Reaction48Ca (p,n)48Sc fromE p =1.885 to 5.1 MeV

The total (p, n) reaction cross section for⁴⁸Ca has been measured as a function of proton energy in the energy range 1.885 to 5.100 MeV with an overall resolution of ∼ 2 keV and in ∼ 5 keV energy steps. The fluctutions in fine resolution data have been analysed to determine the average coherence width 〈Γ〉. The excitation function averaged over large energy intervals has been analyzed in terms of the optical model. The isobaric analogue resonances atE _p ∼ 1.95 and 4 MeV have been shape-analyzed to extract the proton partial width and the spectroscopic factorS _n . A comparison of the gross structures observed in ∼ 55 keV averaged excitation function with the predictions of Izumo’s partial equilibrium model has also been made.     

Dilatometric studies of Leh clay Part II

Clay from the Leh area of J&K State (India) was separated into various size fractions by the method of sedimentation and with Sharpie's supercentrifuge process. The results of dilatometric studies of the fractions are discussed in detail.

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Zusammenfassung Ton aus dem Leh-Gebiet des J&K Staates (Indien) wurde mittels Sedimentation und nach dem Ultrazentrifugenverfahren nach Sharple in Fraktionen unterschiedlicher Grösse zerlegt. Die Ergebnisse von dilatometrischen Untersuchungen dieser Fraktionen werden detailliert diskutiert.

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The authors are grateful to the Director, Regional Research Laboratory, Jammu, for his kind permission to publish this paper. Thanks are also due to Professor G. Mandal, Department of Chemical Engineering, IIT, Bombay, for his suggestions during the study.