Preparation, structural analysis and dielectric properties of Bi x La1−x FeO3 perovskite

Rare earth element substituted bismuth ferrites (BiFeO₃) are of enormous importance as magnetoelectric materials. The polycrystalline samples of Bi _x La_1−x FeO₃ (x=0, 0.2, 0.4, 0.6, 0.8) were prepared by solid-state reaction using standard ceramic method. The single-phase formation of these compounds was confirmed by X-ray diffraction (XRD) studies. The samples with x=0, 0.2, 0.4, 0.6 are found to be orthorhombic while the sample with x=0.8 is triclinic. The dielectric constant (ε′) and dissipation factor (tan δ) were measured in the frequency range 100 Hz to 1 MHz at room temperature and as a function of temperature at certain fixed frequencies (1 kHz, 10 kHz, 100 kHz, 1 MHz). All the samples showed dielectric dispersion. The dielectric constant with temperature shows a broad peak; the peak temperature shifts with frequency which reflects the relaxor-type behavior. The peak above 600 K in the measured temperature range corresponds to antiferromagnetic ordering temperature (Néel temperature). The broadness of the peak changes with composition. The ac conductivity as well as ε′ are found to be maximum for the sample x=0.2 at room temperature.     

Magnetoelectric effect in cobalt ferrite-barium titanate composites and their electrical properties

CoFe₂O₄-BaTiO₃ composites were prepared using conventional ceramic double sintering process with various compositions. Presence of two phases in the composites was confirmed using X-ray diffraction. The dc resistivity and thermoemf as a function of temperature in the temperature range 300 K to 600 K were measured. Variation of dielectric constant (ɛ′) with frequency in the range 100 Hz to 1 MHz and also with temperature at a fixed frequency of 1 kHz was studied. The ac conductivity was derived from dielectric constant (ɛ′) and loss tangent (tan δ). The nature of conduction is discussed on the basis of small polaron hopping model. The static value of magnetoelectric conversion factor has been studied as a function of magnetic field.     

Lewis acid-aldehyde-solvent interactions. A computational approach for determining the critical amount of THF molecules necessary for achieving a high enantioselection in chiral oxazaborolidinone-promoted asymmetric aldol reactions

The effect of THF as a solvent on the enantioselectivity of oxazaborolidinone-promoted asymmetric aldol reactions of aldehydes with silylketene acetals was investigated. The use of 4-5 M equiv of THF, relative to the chiral borane, was required to achieve a high enantioselectivity. A solvent-modeling study, based on ab initio calculations of intermolecular interactions, revealed the existence of an extended hydrogen bonding network in the resulting assembly, which was composed of THF molecules, the aldehyde, and the oxazaborolidinone. The model rationally provides a spatially suitable active site for controlling the stereochemical outcome of the reaction.     

Terminality,normality, and transversality conditions

The maximum principle distinguishes between two phases of the optimal control problem. Some of the stated conditions are to be satisfied at points other than endpoints and some conditions are to be satisfied specifically at the endpoints. This paper utilizes the first set of conditions from the maximum principle to reexamine the second set. In the process, a new necessary condition to be satisfied at the endpoints is obtained. This condition is for certain cases easier to apply than the transversality conditions, yields additional information which may be of computational advantage, and lends itself quite naturally to an exposition of abnormal solutions. The relationship of the new condition to the transversality conditions and a discussion on normality are included. Several examples are given to illustrate the results.This research was supported in part by NASA under Grant NGR-03-002-224 and NSF Science Faculty Fellowship. The authors are indebted to Professors G. Leitmann, G. Basile, and E. Cliff for their helpful comments and suggestions.     

Characterization of a carbonyl-conjugated polyene precursor in 10-membered enediyne biosynthesis

We have characterized a linear carbonyl-conjugated polyene generated by the iterative polyketide synthase (CalE8) involved in the biosynthesis of the 10-membered enediyne core of calicheamicin. The results provide insight into the mysterious biosynthetic mechanism of the unique enediyne. The carbonyl-conjugated polyene differs from the precursor for 9-membered enediyne, suggesting that the divergence of enediyne biosynthesis starts at the PKS stage.     

Tandem conjugate addition-elimination reaction promoted by chiral pyrrolidinyl sulfonamide (CPS)

Chiral pyrrolidinyl sulfonamides have been found to promote the conjugate addition-elimination reaction between activated allylic bromides and 1,3-dicarbonyl compounds with high enantioselectivities and the highly functionalised products can be used to generate a variety of interesting enantiomerically pure compounds via simple transformations.     

Random partitions with restricted part sizes

For a subset of positive integers let Ω(n, ) be the set of partitions of n into summands that are elements of . For every λ ∈ Ω(n, ), let M _n(λ) be the number of parts, with multiplicity, that λ has. Put a uniform probability distribution on Ω(n, ), and regard M _n as a random variable. In this paper the limiting density of the (suitably normalized) random variable M _n is determined for sets that are sufficiently regular. In particular, our results cover the case = {Q(k) : k ≥ 1}, where Q(x) is a fixed polynomial of degree d ≥ 2. For specific choices of Q, the limiting density has appeared before in rather different contexts such as Kingman's coalescent, and processes associated with the maxima of Brownian bridge and Brownian meander processes. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Structural studies on cycloadducts of furan, 2-methoxyfuran, and 5-trimethylsilylcyclopentadiene with maleic anhydride and N-methylmaleimide

The early stages of the retro-Diels-Alder reaction are clearly apparent in the structures of the cycloadducts formed between furan or 5-trimethylsilylcyclopentadiene with maleic anhydride and N-methylmaleimide. The degree of lengthening of the C-C bonds that break in this reaction is clearly related to the known reactivity of these cycloadducts toward this reaction. In the structures of the cycloadducts 21 and 22 derived from 2-methoxyfuran, the early stages of an alternative fragmentation reaction are apparent, consistent with the reactivity of these compounds in solution.