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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Unique ergodicity of some flows related to axiom a diffeomorphisms

Continuous flows, whose orbits are the unstable manifolds of certain Axiom A attractors, are shown to be uniquely ergodic. The approach used is symbolic dynamics. Equicontinuity (and lack of it) for these flows is also discussed.     

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.     

Electrodeposition of copper on copper single crystal (100) face in presence of chloride ions

Observations of copper electrodeposits on to the (100) plane of copper was made from highly purified solutions of copper sulphate containing known concentration of hydrochloric acid from 10^?10 to 10^?1 m/L. In pure solutions at current densities of 5 and 10 mA/cm.² layers and pyramids were noticed. In the presence of hydrochloric acid of concentration 10^?9 to 10^?5 m/L there is a gradual decrease of distance between successive steps. At 10^?4 m/L of HCl there was the breaking of layers giving rise to ridge type of growth. With the increase of concentration to 3·5×10^?3 m/L pyramids appear again. On increasing the concentration of HCl to 10^?2 m/L there was the formation of triangular pyramids of cuprous chloride and on still increasing the concentration, polycrystalline type of deposit was noticed. The transition from layer to ridge, ridge to pyramids and to polycrystalline deposit occurs at all c.d. studied but the critical concentration of HCl needed for the transition depends upon the current density.     

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.     

Fatigue life of polymethyl methacrylate in stationary and stepped nonisothermal cyclic loading regimes

Rotating cantilever experiments have revealed the heating characteristics of PMMA in multicycle fatigue tests. The effect of heating and damage on the fatigue life under stationary and single-step loading is considered. The statistical characteristics of the fatigue life are presented.