Self-assembling properties of lactic acid derivative with several ester linkages in the molecular core

The effect of several polar ester linkage groups incorporated in the molecular core of a chiral lactic acid derivative on self-assembling properties has been investigated by polarizing optical microscopy, small angle X-ray diffraction, differential scanning calorimetry, optical and electro--optical studies. The compound possesses the paraelectric smectic A* (SmA*) and ferroelectric smectic C* (SmC*) phases over a broad temperature range. Mesomorphic behaviour, spontaneous polarization, birefringence, optical transmission, dielectric anisotropy and structural properties of the self-assembled chiral material have been determined. The obtained results are discussed and compared with that of other liquid crystalline materials. Experimentally determined spontaneous polarization and tilt angle values are also used to elucidate the nature of SmC* to SmA* phase transition. The effect of polar ester linkages in the molecular core has also been discussed.     

Hydrovinylation of norbornene. Ligand-dependent selectivity and asymmetric variations

[reaction: see text] Norbornene undergoes Ni-catalyzed (1-2 mol% allylnickel bromide/phosphine/NaBARF or AgSbF(6), 1 bar ethylene, -50 degrees C) hydrovinylation (>97% yield), giving either a 1:1 or a 2:1 (norbornene/ethylene) adduct depending on the size of the phosphine. Use of binaphthol-derived phosphoramidite ligand results in up to 80% ee for the 1:1 adduct. The course of the reaction is highly dependent on the ligand (size and configuration of the appendages) and the counteranion present.     

Estimation, prediction and the Stein phenomenon under divergence loss

We consider two problems: (1) estimate a normal mean under a general divergence loss introduced in [S. Amari, Differential geometry of curved exponential families — curvatures and information loss, Ann. Statist. 10 (1982) 357-387] and [N. Cressie, T.R.C. Read, Multinomial goodness-of-fit tests, J. Roy. Statist. Soc. Ser. B. 46 (1984) 440-464] and (2) find a predictive density of a new observation drawn independently of observations sampled from a normal distribution with the same mean but possibly with a different variance under the same loss. The general divergence loss includes as special cases both the Kullback-Leibler and Bhattacharyya-Hellinger losses. The sample mean, which is a Bayes estimator of the population mean under this loss and the improper uniform prior, is shown to be minimax in any arbitrary dimension. A counterpart of this result for predictive density is also proved in any arbitrary dimension. The admissibility of these rules holds in one dimension, and we conjecture that the result is true in two dimensions as well. However, the general Baranchick [A.J. Baranchick, a family of minimax estimators of the mean of a multivariate normal distribution, Ann. Math. Statist. 41 (1970) 642-645] class of estimators, which includes the James-Stein estimator and the Strawderman [W.E. Strawderman, Proper Bayes minimax estimators of the multivariate normal mean, Ann. Math. Statist. 42 (1971) 385-388] class of estimators, dominates the sample mean in three or higher dimensions for the estimation problem. An analogous class of predictive densities is defined and any member of this class is shown to dominate the predictive density corresponding to a uniform prior in three or higher dimensions. For the prediction problem, in the special case of Kullback-Leibler loss, our results complement to a certain extent some of the recent important work of Komaki [F. Komaki, A shrinkage predictive distribution for multivariate normal observations, Biometrika 88 (2001) 859-864] and George, Liang and Xu [E.I. George, F. Liang, X. Xu, Improved minimax predictive densities under Kullbak-Leibler loss, Ann. Statist. 34 (2006) 78-92]. While our proposed approach produces a general class of predictive densities (not necessarily Bayes, but not excluding Bayes predictors) dominating the predictive density under a uniform prior. We show also that various modifications of the James-Stein estimator continue to dominate the sample mean, and by the duality of estimation and predictive density results which we will show, similar results continue to hold for the prediction problem as well.     

On some sequential simultaneous confidence intervals procedures

Summary The purpose of this paper is two-fold: (i) to extend the simultaneous confidence intervals procedures (SCIP) of Healy [7] along the lines of Chow and Robbins [3] and (ii) to develop certain robust non-parametric SCIP based on the results of Sen [10] and Sen and Ghosh [11]; the allied efficiency results are also presented. Work supported by the National Institutes of Health, Grant GM-12868.     

A “Thermodynamically Stable” 2D Nickel Metal–Organic Framework over a Wide pH Range with Scalable Preparation for Efficient C2s over C1 Hydrocarbon Separations

The design and construction of “thermodynamically stable” metal–organic frameworks (MOFs) that can survive in liquid water, boiling water, and acidic/basic solutions over a wide pH range is highly desirable for many practical applications, especially adsorption-based gas separations with obvious scalable preparations. Herein, a new thermodynamically stable Ni MOF, {[Ni(L)(1,4-NDC)(H₂O)₂]}_n (IITKGP-20; L=4,4′-azobispyridine; 1,4-NDC=1,4-naphthalene dicarboxylic acid; IITKGP stands for the Indian Institute of Technology Kharagpur), has been designed that displays moderate porosity with a BET surface area of 218 m² g⁻¹ and micropores along the [10−1] direction. As an alternative to a cost-intensive, cryogenic, high-pressure distillation process for the separation of hydrocarbons, MOFs have recently shown promise for such separations. Thus, towards an application standpoint, this MOF exhibits a higher uptake of C₂ hydrocarbons over that of C₁ hydrocarbon under ambient conditions, with one of the highest selectivities based on the ideal adsorbed solution theory (IAST) method. A combination of two strategies (the presence of stronger metal–N coordination of the spacer and the hydrophobicity of the aromatic moiety of the organic ligand) possibly makes the framework highly robust, even stable in boiling water and over a wide range of pH 2–10, and represents the first example of a thermodynamically stable MOF displaying a 2D structural network. Moreover, this material is easily scalable by heating the reaction mixture at reflux overnight. Because such separations are performed in the presence of water vapor and acidic gases, there is a great need to explore thermodynamically stable MOFs that retain not only structural integrity, but also the porosity of the frameworks.     

Phase transition and some physical properties of binary mixtures of two nematogenic compounds showing induced smectic phase

The binary mixtures of nematogenic compounds 4-n-pentyl phenyl 4-n′-hexyloxy benzoate (ME6O.5) and 4-cyanophenyl 4-pentyl benzoate (CPPB) show the presence of induced smectic phase. In this article, we report the phase diagram and the results of refractive index, density, static dielectric permittivity and X-ray diffraction measurements of different binary mixtures of (ME6O.5?+?CPPB) throughout the entire composition range. The density and refractive index values have been analysed to obtain orientational order parameters. The various physical properties of the system have been discussed on the basis of the phase diagram.     

Effect of internal heat evolution on the motion of a solid particle in a viscous fluid

The problem of the effect of internal heat evolution on the motion of a heated solid spherical particle in a viscous fluid is analytically solved in the Stokes approximation at small Reynolds and Peclet numbers. The temperature drop between the surface of the particle and the area away from it is assumed to be arbitrary. In solving hydrodynamic equations, the thermal conductivity of the particle is set to be a power function of temperature and the viscosity of the fluid, an exponential-power function of temperature. The observability of this effect is discussed.     

Existence, uniqueness and stability analysis of allelopathic stimulatory phytoplankton model

In this paper we consider the two species competitive delay plankton allelopathy stimulatory model system. We show the existence and uniqueness of the solution of the deterministic model. Moreover, we study the persistence of the model and the stability properties of its equilibrium points. We illustrate the theoretical results by some numerical simulations.