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.     

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.     

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.     

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.     

Thermodynamics of binary liquid mixtures

Excess volumes, V^E, of binary liquid mixtures (1) Toluene-Bromo-benzene, (2) Toluene-Nitrobenzene, (3) Toluene-Cyclohexanone, (4) Cyclo-hexane-Nitrobenzene, (5) Cyclohexane-Cyclohexanone were measured at 30° C. The results were analysed in terms of Flory’s theory. It is found that the theory, in general, is applicable to the mixtures studied.     

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.     

Measurements of total electron content over Ahmedabad and Bombay from Beacon satellite data

The paper outlines the method used at Ahmedabad for determining the total electron content in the ionosphere from differential Faraday rotations of plane polarised radio waves on 40.010 and 41.010 Mc./s. transmitted by NASA satellite 64-64A. The observations made during the period October 1964 to April 1965 are utilised to determine the diurnal variation of the total electron content up to the satellite height which was about 1,000 km. over Ahmedabad and Bombay latitudes. The curve of total electron content up to the satellite height shows similarity to the curve of maximum electron density at the F2 peak. The total electron contents over Bombay are in general higher than those over Ahmedabad.     

The Cuboid Lemma and Mal’tsev Categories

We prove that a regular category ? is a Mal’tsev category if and only if a strong form of the denormalised 3 × 3 Lemma holds true in ?. In this version of the 3 × 3 Lemma, the vertical exact forks are replaced by pullbacks of regular epimorphisms along arbitrary morphisms. The shape of the diagram it determines suggests to call it the Cuboid Lemma. This new characterisation of regular categories that are Mal’tsev categories (= 2-permutable) is similar to the one previously obtained for Goursat categories (= 3-permutable). We also analyse the “relative” version of the Cuboid Lemma and extend our results to that context.     

On Green functions inR 2

Conditions which guarantee the validity of the use of Lord Kelvin’s method of electrostatic images to find Green functions of the unbounded Green domains in the plane are examined.     

Integrability properties of the maximal operator on partial sums of Fourier series

In the present work we extend a result ofP. Sjölin on the integrability properties of the maximal operator on partial sums of Fourier Series,S ^*. We actually show that the result is applicable to more general operators and could be considered as an abstract extrapolation principle.     

Effect of UV irradiation on the structure of cotton fiber

The effect of UV irradiation on the structure of 5595-V brand cotton fiber was studied. Photodestruction was shown to be accompanied by a reduction in crystallinity.     

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.     

There exist no Ramanujan congruences mod 6912

Let τ(n) be Ramanujan's function, $$x\prod _{m = 1}^\infty (1 - x^m )^{24} = \sum\nolimits_{n = 1}^\infty {\tau (n)x^n .} $$ In this paper it is shown that the Ramanujan congruence τ(n)=σ_d/nd¹¹ mod 691 cannot be improved mod 691². The following result is proved: for arbitrary r, s mod 691 the set of primes such that p ≡ r mod 691,τ (p) ≡ p¹¹+1+691 · s mod 691² has positive density.     

Solvability of boundary-value problems for nonlinear elliptic equations that are not in the divergence form

One introduces a topological characteristic of general nonlinear elliptic problems, one establishes the solvability of the Dirichlet problem for the Monge-Ampere equations and the solvability of the general nonlinear Dirichlet problem in a thin layer.     

Embedded constant mean curvature surfaces in Euclidean three-space

In this paper we refine the construction and related estimates for complete constant mean curvature surfaces in Euclidean three-space developed in Kapouleas (Ann Math 131:239–330, 1990) by adopting the more precise and powerful version of the methodology which was developed in Kapouleas (Invent Math 119(3):443–518, 1995). As a consequence we remove the severe restrictions in establishing embeddedness for complete Constant Mean Curvature surfaces in Kapouleas (Ann Math 131:239–330, 1990) and we produce a very large class of new embedded examples of finite topology.     

Solas cycle theory of pulsars

The plausibility of the Solar Cycle type of mechanism for pulsar phenomenon is examined. The relevant time scales are found to be within the range of the observed pulsar periods.