Faraday rotation tensor-extraction of components

This paper reports methods of obtaining the components of Faraday rotation tenser in anisotropic crystals, using longitudinal and transverse Faraday rotation along the optic axis. It is found that in crystals belonging to triclinic, monoclinic and orthorhombic symmetry, one can get 6 out of 9, 3 or 4 out of 5, and 2 out of 3 components respectively. In the case of uniaxial crystals only 1 component can be obtained. By measuring Faraday rotation in a randomly oriented polycrystal one more component in all the above classes can be obtained.     

Vibrational spectra and normal vibrations of acetanilide and N-deuterated acetanilide

The Raman and infra-red spectra of acetanilide and N-methylacetamide and of their N-deuterated compounds have been recorded. The vibrational frequencies of acetanilide have been assigned and the nature of the Amide I, II and III bands in acetanilide and N-methylacetamide has been investigated by the study of the changes in the frequencies of these bands in the spectra of their deuterated compounds. Acetanilide and deuterated acetanilide molecules have been subjected to normal co-ordinate treatment and the mixing up of the skeletal frequencies arising out of the in-plane vibrations has been determined. These results indicate that as in secondary amides, the amide II and amide III bands in acetanilide are due to the combined contribution ofδ (NH) andν (C-N) vibrations, but the contribution ofν (C-N) to the amide II band is less in acetanilide and deuterated acetanilide than in cases of N-methylacetamide and deuterated N-methylacetamide.     

On the polarography of zinc in ethylenediamine medium

Polarography of zinc in ethylenediamine medium has been carried out. The equilibrium potentials have been determined by amalgam polarography. The standard rate constant for the electrode reaction and the stability constants of the complexes have been calculated.     

Sorption-desorption hysteresis in fibrous silica gel (Santocel C) with isomeric monohydric aliphatic alcohols

By employing the quartz fibre spring technique, sorption-desorption hysteresis at 35° has been studied of Iso-propyl, Iso-Butyl, Sec-Butyl, Tert-Butyl, Active Amyl and Iso-Amyl alcohols on fibrous silica gel (Santocel C) activated at 250°. The isotherms of all the alcohols have clearly defined “knees”. By the application of BET theory, the monolayer capacities are determined. Knowing the specific surface area of fibrous silica gel, assuming oriented sorption of the isomeric alcohols with the OH group attached to surface; the cross-sections of the alcohol molecules are calculated. Excepting Iso-Propyl and Sec-Butyl alcohols, all others have cross-sections greater than that of normal aliphatic alcohols. These higher values are to be expected in view of the side CH₃ groups. The exceptional behaviour of Iso-Propyl and Sec-Butyl alcohols is not clear. Permanent and reproducible hysteresis loops have been obtained in all the cases. Cohan’s theory of hysteresis cannot explain the observations satisfactorily. Cavity theory however explains all the cases of hysteresis. The shapes of the isotherms of the different alcohols in the high relative vapour pressure region indicate a variation in contact angles of the alcohols.     

Viscosities of binary solutions of non-electrolytes

Viscosities and molar volumes of binary solutions,viz., Toluene-Nitrobenzene, Toluene-Bromobenzene, Toluene-Cyclohexanone, Cyclohexane-Cyclohexanone, Cyclohexane-Nitrobenzene, Cyclohexane-Acetic acid, Cyclohexane-Propionic acid and Cyclohexane-Butyric acid have been measured. The experimental results have been discussed in terms of viscosity-composition relations developed for binary solutions by Grunberg and Nissan and Katti and Chaudhri.     

Acidity function in dipolar aprotic media

The H₀ acidity function has been determined for hydrochloric and trichloroacetic acids in dimethyl sulphoxide (DMSO) and acetonitrile using three amine class of indicators. The variation of H₀ with solvent composition at a fixed concentration of 0.1 M HCI in DMSO-water, acetonitrile-water and DMSO acetonitrile mixtures was also studied. Approximate medium effects on the proton in all these solvents were computed from the H₀ data and the results are discussed.     

Some Remarks on Perov Type Mappings in Cone Metric Spaces

Let \(\left( E,C,t\right) \) be a real ordered topological vector space and let (X, d) be a tvs-cone metric space over cone C. Using Proposition 19.9 of Deimling (Nonlinear functional analysis, Springer, Berlin, 1985), we show that E can be equipped with a norm such that C is a normal monotone solid cone. Hence, a tvs-cone metric space \(\left( X,d\right) \) over a solid cone C is a normal cone metric space over the same cone C. This assures that tvs-cone metric spaces are not a genuine generalization of cone metric spaces introduced by Huang and Zhang, recently. Further, if the cone C is solid then we have only cone metric spaces over normal solid cone (with coefficient of normality \(K=1\)). Here, we introduce also the notion of Sehgal–Guseman–Perov type mappings and we establish a result of existence and uniqueness of fixed points for this class of mappings.     

A cellular-automata model of population dynamics of three species of organisms in Lake Baikal

A cellular automata model of population dynamics of three species of organisms in Lake Baikal is proposed and investigated. Each species is subdivided into age and prey-predator groups. There are eight groups altogether. The model takes into account the spatial distribution of the organisms, seasonal birth rate variation, possible habitat pollution, and water streams. A computational experiment has been carried out for pollution in a southern area of Lake Baikal. It demonstrates that the population dynamics tends to an oscillating process with a period of one year. The minimum pollution at total extinction and maximum pollution not affecting the population dynamics are estimated. The model has been verified with production-to-biomass and occurrence frequency ratios.     

A Brief Note on the Approach to the Conic Sections of a Right Circular Cone from Dynamic Geometry

Nowadays there are different powerful 3D dynamic geometry systems (DGS) such as GeoGebra 5, Calques 3D and Cabri geometry 3D. An obvious application of this software that has been addressed by several authors is obtaining the conic sections of a right circular cone: the dynamic capabilities of 3D DGS allows to slowly vary the angle of the plane w.r.t. the axis of the cone, thus obtaining the different types of conics. In all the approaches we have found, a cone is firstly constructed and it is cut through variable planes. We propose to perform the construction the other way round: the plane is fixed (in fact it is a very convenient plane: \(z=0\)) and the cone is the moving object. This way the conic is expressed as a function of x and y (instead of as a function of x, y and z). Moreover, if the 3D DGS has algebraic capabilities, it is possible to obtain the implicit equation of the conic.     

Vinyl Polymerisation

The ternary system Poly (methyl methacrylate) Fraction 1/Fraction 2/n-butyl bromide has been studied. A viscometric method is proposed for the estimation of the individual polymer concentration in the two conjugate phases in equilibrium.     

A simple proof of Ramanujan’s summation of the1ψ1

A simple proof by functional equations is given for Ramanujan’s₁ ψ ₁ sum. Ramanujan’s sum is a useful extension of Jacobi's triple product formula, and has recently become important in the treatment of certain orthogonal polynomials defined by basic hypergeometric series.     

Approximation by Linear Combinations of Complex Phillips Operators in Compact Disks

In the present article we find direct quantitative estimate for approximation of complex valued functions by linear combinations of the complex Phillips operators. Here we extend the recent results of Gal and Gupta (Mathematics without boundaries; Surveys in Interdisciplinary Research, 2014). We have been able to achieve the better approximation for the complex Phillips operators.     

A numerical study of an MPI/OpenMP implementation based on asynchronous threads for a three-dimensional splitting scheme in heat transfer problems

We present the results of a study of the parallel algorithms based on MPI and OpenMP for vector splitting schemes in heat transfer problems. We compare the three parallel implementations: MPI, “simple” MPI/OpenMP (#pragma omp directives applied to MPI-based code), and MPI/OpenMP with “postman” threads. The main idea of the last algorithm is to assign one thread within each computational node to perform the data transfer. This approach allows us to implement overlapping of useful computations and data transfer. The results show that the introducing postman threads can significantly improve the performance of an MPI/OpenMP implementation; nevertheless, for the considered class of numerical algorithms, it is more reasonable to use an MPI implementation.     

γ-rays from discrete radio sources

The fluxes of low energy (～100 MeV) and high energy (～5×10¹² eV)γ-rays from intense radio sources have been calculated under the hypothesis that radio electrons are continuously produced through nuclear collisions. The effect of expansion of the source which gives rise to a decrease in production rate with time has been taken into account in these calculations. It is found that the fluxes expected from nuclear collision process are generally higher than the fluxes from other processes like bremstrahlung and inverse compton scattering by factors of 10 or more. While the calculated fluxes ofγ-rays of energy >100 MeV are less than the observed upper limits for all the processes, the fluxes calculated for nuclear collision process for E>5×10¹² eV, exceed the experimental upper limits for Crab, Cas A and the jet in Virgo A. More sensitive experiments should be able to decide whether the nuclear collision process is ruled out for low energies as well: in this respect Cas A seems to be the most promising source.     

Inversive planes with circles determined by tangents

In an inversive planeJ, one derived affine plane is such that every circle is uniquely determined by straight line tangents. The validity of 4-point Pascal conditions on one of the circles then plays a role in coordinatization ofJ.     

Kinetics of Thallium (III) oxidation of aromatic ketones

The kinetics of oxidation of acetophenone and six substituted acetophenones by Thallium (III) acetate have been studied in 95% (v/v) aqueous acetic acid. The reaction is first order with respect to the oxidant as well as the organic substrate and acid catalysed. The probable nature of Tl (III) species in aqueous acetic acid has been indicated. The rate data fitted well with Brown’sσ ⁺ values withρ ⁺ = ?0.70. A mechanism for the Tl (III) oxidation of aromatic ketones has been proposed.     

Spectrophotometric study of the uranyl-streptomycin complex

Spectrophotometric studies of the yellow coloured complex of uranyl ion with streptomycin have been carried out. The complex absorbs maximum at 420 mµ and at a pH value of 3·5. The composition of the complex has been ascertained employing Job’s method, mole ratio method and slope ratio method and found to be 1:1. The apparent stability constant (logK) and free energy of formation (ΔF) of the complex at 40° C have been found to be 3·37 and ?4·83K cal per mole respectively.     

Optimality conditions in nonconical multiple-objective programming

Previous theoretical work in multiple-objective optimization has focused entirely on vector orders representable by positive cones. Here, we treat multiple-objective problems in which solutions are sought which are maximal (efficient, nondominated) under an order which may be nonconical. Compactness conditions under which maximal solutions exist and bound the remaining alternatives are given. First-order necessary conditions and first-order sufficient conditions for maximality in general normed linear spaces are derived, and a scalarization result is given. A small computational example is also presented. Several previous results are special cases of those given here.     

Mixed complexes of iron (III)—thiocyanate with some nitrogen and oxygen donors and their analytical applications

Methods for the determination of iron (III) as thiocyanate complex in the presence of neutral donors like isoquinoline and antipyrine have been developed. The two methods are of equal sensitivity (ε=18,000±100 lit. mole^?1 cm^?1) but operate at widely different hydrogen ion concentrations ranging from 10^?5 N(pH 5·0) to 7N. The interference of various foreign substances has been studied in the two methods. The application of these methods in the analysis of alloys and commercial HCl for iron has been explored and the composition of the extracting species established.     

Electron spin resonance of Cr5+ in CaWO4

Electron Spin Resonance of CaWO₄ with 0·1% of Cr has been investigated at liquid nitrogen and liquid helium temperatures. The observed ESR spectrum is attributed to Cr⁵⁺ ion in the substitutional site of W which has a compressed tetrahedral surroundings. A simple point charge calculation based on this geometry explains the observedg anisotropy and hyperfine anisotropy and places the magnetic electron in a predominantly \(3d_{z^2 } \) orbital. A comparison of these results with those obtained on other isoelectronic systems in similar and different co-ordinations justifies our assignment.