Effect of high pressure on the nematic–isotropic transition in aerosil–liquid crystal composites

We report the first high pressure investigations of the nematic–isotropic transition in the composites of a liquid crystal compound with hydrophilic aerosil particles. The low concentrations of the aerosil particles used create soft gels of the composites. As expected T_N–Iso, the nematic–isotropic transition at room pressure exhibits a non-monotonic variation with increasing aerosil concentration. This non-monotonic behaviour is seen in the isobaric scans over the wide range of pressures studied, and its “magnitude” is dependent on the pressure applied. The surprising result of the present investigations on these nanocolloidal systems is that the slope of the pressure–temperature boundary also exhibits a non-monotonic dependence with the aerosil concentration, which qualitatively is similar to that of the transition temperature variation. Employing the transition enthalpy values determined at room pressure using differential scanning calorimetric scans collected at low heating rates, we calculate the transition volume dependence on the aerosil concentration. The study adds a new dimension, namely, the influence of pressure on liquid crystalline transitions in restricted geometries.     

Rank preservers of matrices over max algebra

The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We consider the semimodules over max algebra and study the properties of the weak basis and weak dimension of the semi-modules. Moreover, we obtain the characterizations of those linear operators that preserve rank of matrices over max-algebra.     

On functions that preserve M-matrices and inverse M-matrices

In earlier works, authors such as Varga, Micchelli and Willoughby, Ando, and Fiedler and Schneider have studied and characterized functions which preserve the M-matrices or some subclasses of the M-matrices, such as the Stieltjes matrices. Here we characterize functions which either preserve the inverse M-matrices or map the inverse M-matrices to the M-matrices. In one of our results we employ the theory of Pick functions to show that if A and B are inverse M-matrices such that B ^?1 ≤ A ^?1, then (B+tI)?1 ≤ (A+tI)?1, for all t?≥?0.     

Purely sequential bounded-risk point estimation of the negative binomial mean under various loss functions: one-sample problem

A negative binomial (NB) distribution is useful to model over-dispersed count data arising from agriculture, health, and pest control. We design purely sequential bounded-risk methodologies to estimate an unknown NB mean \(\mu (>0)\) under different forms of loss functions including customary and modified Linex loss as well as squared error loss. We handle situations when the thatch parameter \(\tau (>0)\) may be assumed known or unknown. Our proposed methodologies are shown to satisfy properties including first-order asymptotic efficiency and first-order asymptotic risk efficiency. Summaries are provided from extensive sets of simulations showing encouraging performances of the proposed methodologies for small and moderate sample sizes. We follow with illustrations obtained by implementing estimation strategies using real data from statistical ecology: (1) weed count data of different species from a field in Netherlands and (2) count data of migrating woodlarks at the Hanko bird sanctuary in Finland.     

A constructive proof of a permutation-based generalization of Sperner's lemma

In a recent paper, Gale has given an interesting generalization of the KKM lemma in combinatorial topology. We present a similar generalization of Sperner's well-known lemma and give a constructive proof. The argument uses the familiar idea of following simplicial paths in a triangulation. To demonstrate that the algorithm must work, orientation considerations are necessary. Gale's generalized KKM lemma is derived from the main result. A permutation-based generalization of Brouwer's fixed point theorem is also given.     

Temperature dependence of luminescence emission from cerium and europium doped MgO under x-ray excitation

Temperature dependence of luminescence emission from cerium- and europiumdoped MgO is reported. The emission intensity changes with increase in the phosphor temperature. The phosphor showed peaks in the brightness-temperature curves. The intensities at static temperatures were always lower, indicating that temperature quenching occurs in almost all cases. The same is also evident from spectral distribution curves obtained at different temperatures.     

Reactivity of binary mixtures of Cu(II) oxalate and La(III) oxalate

Reactivity of binary mixtures of oxalates of Cu(II) and La(III) was studied by observing their thermal behaviours in decomposition using TG, DTA and XRD techniques to set the temperature conditions for preparations of various composites of oxides of Cu(II) and La(III). In the thermal behaviour it was found that the decomposition of Cu(II) oxalate is not affected while that of La(III) oxalate is drastically affected in the case of all the mixtures. The decomposition temperature at which La(III) oxide is formed is lowered by 250 K in the case of all the mixtures while the complete decomposition occurred at 723 K only in the case of mixtures containing excess Cu(II) oxalate.At 823 K La₂CuO₄ phase is developed in all the mixtures while -La and Cu₂La phases are also detected in mixtures containing excess Cu(II) oxalate. Therefore, the temperature 823 K was found to be suitable to prepare various composites viz. La₂CuO₄, La₂CuO₄·La₂O₃ and La₂CuO₄·CuO to study their electrical properties.Authors are thankful to the authorities of Department of Atomic Energy (DAE), Government of India, for providing the funds for research project and to Professor A. V. Phadke, Department of Geology, University of Poona, for valuable discussion.     

Oxidative determination of thiosulphate by alkaline ferricyanide using osmium tetroxide as a catalyst

Summary The catalytic action of osmium tetroxide has been utilised in the determination of thiosulphate by oxidation to sulphate with alkaline ferricyanide. Both direct and indirect procedures were developed. In the former the titration was carried out either ways using amperometric detection. In the latter, both the excess ferricyanide and ferrocyanide formed, were determined by arsenious oxide or iodometrically with thiosulphate, and by ceric sulphate respectively. The high conversion factor, availability of alternate procedures, use of potassium ferricyanide as a standard oxidant with a high molecular weight are characteristic features of this redox procedure.     

Diphenyl carbazone as an internal indicator in volumetric analysis

Summary A method for the volumetric determination of calcium using diphenyl carbazone as indicator has been described. Calcium is precipitated by excess sodium oxalate, the excess oxalate being determined by standard lead nitrate. A study of the possible interferences of barium and magnesium in the above determination is undertaken and it is shown that the above procedure is applicable to the determination of calcium in the presence of magnesium and barium.Sincere thanks of the authors are due to Professor G. B. Singh for providing the necessary facilities during the course of the above investigation.     

Iodometric determination of potassium permanganate by arsenious oxide following iodide reduction in presence of borax-boric acid buffer and barium chloride

Summary An iodometric method for the determination of potassium permananate is described following its reduction to MnO₂ in presence of boraxboric acid buffer at PH 8–10 by iodide and titration of the liberated iodine with standard arsenious oxide solution. Excess BaCl₂ is added to coagulate the colloidal MnO₂ whose otherwise partial reduction by iodide is prevented thereby.Sincere thanks of the authors are due to Prof. S. S. Joshi, for his kind interest in the work.