Ground state of liquid helium-3: off-shell effects due to non-local potentials

It is shown that by incorporating the off-shell effects through the introduction of phase equivalent nonlocal potentials, (that are essentially equivalent so far as two-body properties are concerned) one could obtain a much better agreement regarding the important properties of the ground state of liquid helium-3, in lowest order Brueckner-Goldstone theory. The binding energy, equilibruim density and the convergence character of Brueckner-Goldstone series improve drastically.     

Thermal expansion of zirconium—II

The generalised Gruneisen parameters γ′ = ?? log ω/??′ and γ″ = ?? log ω/??″ have been calculated for various normal mode frequencies using the force model for Zirconium obtained on Keating's approach. There is a general agreement between the normalised frequency distribution curve of Zirconium obtained on the present model and that of Bezdek et al. The temperature dependence of the effective Gruneisen functions $\text{γ}\text{?}{}_{\mathrm{\perp }}\text{(T)}$ and $\text{γ}\text{?}{}_{\mathrm{|}}\text{(T)}$ has been calculated using the procedure of Blackman. The high temperature limits of $\text{γ}\text{?}{}_{\mathrm{\perp }}\text{(T)}$, $\text{γ}\text{?}{}_{\mathrm{|}}\text{(T)}$ and $\text{γ}\text{?}{}_{\mathrm{v}}$ are in good agreement with those obtained by Goldak et al. from an analysis of the thermal expansion data of Zirconium.     

Isotopic sum rules and compliance scheme

It is known that compliance scheme does not provide simple linear isotopic sum rules in λ^?1 similar to the ones in λ in the force constant scheme. The advantage of not having such sum rules in the compliance scheme is discussed in relation to the uniqueness problem of the molecular force field.Incidentally, for the molecules H₂O, D₂O, and HDO, two quadratic relations in terms of the inverse frequency parameters λ^?1 are obtained. These supplement the three obvious product rule relations.     

4He and soft-core radial function

The suitability of a soft-core radial wave function in⁴He calculations is tested by computing the charge form factor of the alpha particle. The free parameter in the radial function is fixed in a photo-disintegration calculation. The results show that the soft-core function is suitable and the ground state of⁴He may be described reasonably well if a suitable potential model is used with it.     

Solvent influences in the alkaline hydrolysis of esters in aqueous ethanol

The rate data for the alkaline hydrolysis of a number of monoesters, diesters and lactones have been obtained in varying compositions of aqueous ethanol. The application of the Amis and Laidler-Landskroener equations to the data yields reasonable values for the parameters representing the radius of the transition state for the hydrolysis confirming the ion-dipole nature of the reaction. An attempt to explain the rate data on the basis of the solvation requirements of the transition state has been made.     

Solvent extraction of chromium: A review

The separation of chromium by solvent extraction is reviewed.     

Separation theorems for singular values of matrices and their applications in multivariate analysis

Separation theorems for singular values of a matrix, similar to the Poincaré separation theorem for the eigenvalues of a Hermitian matrix, are proved. The results are applied to problems in approximating a given r.v. by an r.v. in a specified class. In particular, problems of canonical correlations, reduced rank regression, fitting an orthogonal random variable (r.v.) to a given r.v., and estimation of residuals in the Gauss-Markoff model are discussed. In each case, a solution is obtained by minimizing a suitable norm. In some cases a common solution is shown to minimize a wide class of norms known as unitarily invariant norms introduced by von Neumann.     

Ultrasound-assisted analyte extraction for the determination of sulfate and elemental sulfur in zinc sulfide by different liquid chromatography techniques

The speciation and determination of sulfate (SO4(2-)) and elemental sulfur (S degree) in zinc sulfide (ZnS) using ion-chromatography (IC) and reversed-phase liquid chromatography (RPLC) respectively is described. Three sample pretreatment approaches were employed with the aim of determining sulfate: (i) conventional water extraction of the analyte; (ii) solid-liquid aqueous extraction with an ultrasonic probe; and (iii) elimination of the zinc sulfide matrix via ion-exchange dissolution (IED). The separation of sulfate was carried out by an anion-exchange column (IonPac AS17), followed by suppressed conductivity detection. Elemental sulfur was extracted ultrasonically from the acid treated sample solution into chloroform and separated on a reversed phase HPLC column equipped with a diode array detector (DAD) at 264 nm. The achievable solid detection limits for sulfate and sulfur were 35 and 10 microg g(-1) respectively.