Oriented polymer dispersed discotic liquid crystals

Polymer dispersed discotic liquid crystals (PDDLCs) were prepared using the hexa-n-octanoate of rufigallol (RHO) and three polymer matrices: polystyrene (PS), poly(methyl methacrylate) (PMMA) and poly(ethyl methacrylate) (PEMA). The molecular orientation of RHO in stretched PDDLC films was characterized by means of infrared dichroism. It was found that the stretching of films that contain RHO in both the columnar D1 and crystalline phase can effectively align columns of RHO along the stretching direction, with the short axes of the rigid cores lying in the plane of the film. By contrast with stretched polymer dispersed nematic liquid crystals, no orientation of RHO is induced for films stretched with RHO in the isotropic phase, followed by rapid cooling to room temperature. However, if stretched films are cooled under strain into the columnar D1 phase, orientation of RHO can develop with time.     

Quantitative problems in using nuclear reactions and dielectric detectors for the detection of stable isotopes (6Li and10B) in biological samples

The methodology of the detection of (n, ) nuclear reactions by means of cellulose nitrate detectors is discussed with special reference to the reliability of the quantitative estimates. The discrimination of¹⁰B and⁶Li from the other isotopes is possible by using thin coloured detectors. The ratio of the number of tracks found at the level of a¹⁰B or⁵Li-enriched calibrating sample, and the number expected from theoretical calculation, i.e. the detection efficiency, P is generally below 1. P is fairly sensitive to the experimental conditions, and for precise quantitative measurements it must be determined separately for each different experiment. The gelatin, used for solidification of liquid samples is boron contaminated (almost 1 mol natural B per g). It has been observed, especially with¹⁰B-enriched liquid samples, that part of the stable tracer under study is lost during sample preparation.⁶Li extra tracks appear at the rear face of thick, non-plastic-supported detectors. Boron diffuses in the cellulose-nitrate detectors with the diffusion coefficient of the order of 10^–8 cm²·s^–1. Therefore it requires rapid operations for microlocation of boron with high resolving power.     

Detection of stable isotopes with A (n, α) nuclear reaction: Application to the measurement of unidirectional fluxes of borate in a plant

The unidirectional influx of borate has been studied inLemna minor plants with the aid of purified boron isotopes,¹⁰B and¹¹B. Isotope¹⁰B was detected specifically by nuclear reaction¹⁰B(n, α)⁷Li in the presence of “homogeneous” detectors. Despite technical difficulties in performing the¹⁰B-estimations in the plant samples themselves, the results obtained here were consistent with those of efflux experiments, published previously, where the¹⁰B-measurements were performed in the external solution. Kinetic parameters of borate transports inLemna minor have been calculated.     

A family of enneanuclear iron(II) single-molecule magnets

Complexes [Fe₉(X)₂(O₂CMe)₈{(2‐py)₂CO₂}₄] (X^?=OH^? ( 1 ), N₃^? ( 2 ), and NCO^? ( 3 )) have been prepared by a route previously employed for the synthesis of analogous Co₉ and Ni₉ complexes, involving hydroxide substitution by pseudohalides (N₃^?, NCO^?). As indicated by DC magnetic susceptibility measurements, this substitution induced higher ferromagnetic couplings in complexes 2 and 3 , leading to higher ground spin states compared to that of 1 . Variable‐field experiments have shown that the ground state is not well isolated from excited states, as a result of which it cannot be unambiguously determined. AC susceptometry has revealed out‐of‐phase signals, which suggests that these complexes exhibit a slow relaxation of magnetization that follows Arrhenius behavior, as observed in single‐molecule magnets, with energy barriers of 41 K for 2 (τ₀=3.4×10^?12 s) and 44 K for 3 (τ₀=2.0×10^?11 s). Slow magnetic relaxation has also been observed by zero‐field ⁵⁷Fe Mössbauer spectroscopy. Characteristic integer‐spin electron paramagnetic resonance (EPR) signals have been observed at X‐band for 1 , whereas 2 and 3 were found to be EPR‐silent at this frequency. ¹H NMR spectrometry in CD₃CN has shown that complexes 1 – 3 are stable in solution.     

Multifractal analysis of the divergence of Fourier series: The extreme cases

We study the size, in terms of the Hausdorff dimension, of the subsets of T such that the Fourier series of a generic function in L ¹(T), L ^p (T), or C(T) may behave badly. Genericity is related to the Baire Category Theorem or the notion of prevalence. This paper is a continuation of [3].     

The Validity of the Multifractal Formalism: Results and Examples

By obtaining a new sufficient condition for a valid multifractal formalism, we improve in this paper a result developed by L. Olsen (1995, Adv. Math.116, 82-196). In particular, we describe a large class of measures satisfying the multifractal formalism and for which the construction of Gibbs measures is not possible. Some of these measures are not unidimensional but have a nontrivial multifractal spectrum, giving a negative answer to a question asked by S. J. Taylor (1995, J. Fourier Anal. Appl., special issue). We also describe a necessary condition of validity for the formalism which is very close to the sufficient one. This necessary condition allows us to describe a measure μ for which the multifractal packing dimension function B_μ(q) is a nontrivial real analytic function but the multifractal formalism is nowhere satisfied. This example gives also a solution to a problem posed by Taylor (cited above).     

Weierstrass functions with random phases

Consider the function

where 1$">, , and is a non-constant 1-periodic Lipschitz function. The phases are chosen independently with respect to the uniform probability measure on . We prove that with probability one, we can choose a sequence of scales such that for every interval of length , the oscillation of satisfies . Moreover, the inequality is almost surely true at every scale. When is a transcendental number, these results can be improved: the minoration is true for every choice of the phases and at every scale.

     

Boundary Multifractal Behaviour for Harmonic Functions in the Ball

It is well known that if h is a nonnegative harmonic function in the ball of $\mathbb R^{d+1}$ or if h is harmonic in the ball with integrable boundary values, then the radial limit of h exists at almost every point of the boundary. In this paper, we are interested in the exceptional set of points of divergence and in the speed of divergence at these points. In particular, we prove that for generic harmonic functions and for any β?∈?[0,d], the Hausdorff dimension of the set of points ξ on the sphere such that h(rξ) looks like (1???r)^???β is equal to d???β.     

An investigation of the formation of 1,3,5-heterosubstituted benzene rings by cyclo-condensation of acetyl-substituted organometallic complexes

The cyclocondensation of acetylferrocene and acetylcymantrene catalyzed by SiCl₄ in ethanol yields a mixture of 1,3,5-trisubstituted benzenes and the intermediate 3,1-disubstituted (E)-2-buten-1-ones, including all the homo- and heterometallic species, which were separated and quantified by HPLC. The relative yields of these species are determined by the different ability of the organometallic groups to stabilize the cationic intermediates that participate in the reaction mechanism, which is measurable as the basicity of the starting materials. The X-ray crystal structures of 1-cymantrenyl-3,5-diferrocenylbenzene and (E)-3-cymantrenyl-1-ferrocenyl-2-buten-1-one are described within this report.