A study of the weak coupling limit of the pseudo SU(3) scheme

The usefulness of the pseudo SU(3) weak coupling limit for the study of even-even nuclei for which the protons and neutrons fill different major oscillator shells is examined. The content of proton and neutron configurations in the total wave function of the coupled space is estimated in order to understand their relative importance. The structure of ¹⁴⁴Ba is investigated in detail. Our calculations show that both proton and neutron configurations are important to study the collective excitations in nuclei and perhaps the strong coupling limit is more appropriate for nuclei such as those considered in this work.     

Titrimetric determination of gold by precipitation with hydroquinone

A rapid method for the volumetric determination of gold is described. Gold(III) is reduced to metal with excess of hydroquinone at room temperature and the excess is titrated with ceric sulphate. The effect of chloride ion on the reducibility of gold(III) to the metal is discussed. This method can be successfully employed for the determination of gold in presence of certain base and noble metals. The method was successfully adopted for the determination of gold in a commercial sample.     

Triangle anomaly free weak interaction with two neutral currents

Considering that the neutral interaction is free of triangle anomalies we derive an expression for the most general neutral interaction with two neutral currents. We show that the Bargers version is a special case. We also determine the interaction wheneverZ, D are mass eigen states and show that this differs from the Barger’s version in an essential way.     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

Effect of longitudinal or inplane deformation and inertia on the large amplitude flexural vibrations of slender beams and thin plates

Large amplitude flexural vibrations of slender beams, and thin circular and rectangular plates have been studied when a compatible longitudinal or inplane mode is coupled with the fundamental flexural mode. It is shown that the effect of longitudinal or inplane deformation and inertia is to reduce the non-linearity in the flexural frequency-amplitude relationship. Further, for slender beams and thin plates, the effect of longitudinal or inplane inertia is negligible.     

Studies on W–Re Mixed-Matrix Cathodes

The performance of tungsten-rhenium (W-Re) mixed-matrix cathodes of varying compositions was studied. The work function, when the tungsten percentage is 50 plusmn 25%, is close to that of a Re-coated cathode. The I-V characteristics show an emission anomaly. It was found that the patch fields are not the main reason; rather, it is the field enhancement which is responsible for this anomaly. The emission microscopic results show that the work function distribution does not greatly differ from that of a B-Type cathode. Auger electron spectroscopy, in conjunction with scanning electron microscope studies, supports the presence of a thick active layer. The cathodes exhibited decay and heating effects with pulsed-current emission. The nonmetallic behavior is attributed to the presence of an appreciable amount of unreduced BaO. Poisoning studies show that the resistance to oxygen poisoning is better than that of a conventional B-Type cathode. A chemical technique was developed to prepare a finely divided powder of W-Re sigma-phase alloy. The cathodes made out of this alloy powder showed better emission and uniformity compared to those of simply mixed cathodes.     

A Note on Existence and Convergence of Best Proximity Points for Pointwise Cyclic Contractions

We introduce a notion of pointwise cyclic contraction T satisfying TA ? B and TB ? A to obtain the existence of a point x ∈ A, such that d(x, Tx) = dist(A, B), known as a best proximity point for such a map. We also prove that for any x ∈ A, the Picard iteration {T²ⁿx} converges to a best proximity point.