Para primal varieties: A study of finite axiomatizability and definable principal congruences in locally finite varieties

We introduce new sufficient conditions for a finite algebraU to possess a finite basis of identities. The conditions are that the variety generated byU possess essentially only finitely many subdirectly irreducible algebras, and have definable principal congruences. Both conditions are satisfied if this variety is directly representable by a finite set of finite algebras. One task of the paper is to show that virtually no lattice varieties possess definable principal congruences. However, the main purpose of the paper is to apply the new criterion in proving that every para primal variety (congruence permutable variety generated by finitely many para primal algebras) is finitely axiomatizable. The paper also contains a completely new approach to the structure theory of para primal varieties which complements and extends somewhat the recent work of Clark and Krauss.     

Synthesis and characterization of fluorinated poly(aryl ether ketone)s containing 1,4-naphthalene moieties

The new monomer 2,2-bis[4-(4-{4-fluorobenzoyl}-1-naphthoxy)phenyl]hexafluoropropane ( 2 ) was synthesized in a two-step reaction sequence. 2,2-his[4-(1-naphthoxy)phenyl]-hexafluoropropane ( 1 ) was prepared using the Ullmann ether synthesis reaction of 4,4-(hex-afluoroisopropylidiene)diphenol with 1-bromonaphthalene. Friedel-Crafts acylation of 1 with 4-fluorobenzoyl chloride in methylene chloride containing dimethylsulfone selectively afforded 2 in 82% yield. The polycondensation of 2 with various bisphenols in DMAc in the presence of an excess of potassium carbonate as a condensation reagent was carried out at 165°C to quantitatively afford the corresponding fluorinated poly(aryl ether ketone)s containing 1,4-naphthalene moieties. Thermal analysis of the polymers showed them to have T_gs ranging from 194 to 230°C and to be thermally stable in air up with initial weight losses at about 500°C. In addition, these novel polymers exhibited excellent solubility in organic solvents including NMP, DMAc, and chloroform. © 1997 John Wiley & Sons, Inc.     

Defect-induced dimer pinning on the Si(0 0 1) surface

Room-temperature STM images frequently show regions of antisymmetric dimer ordering surrounding certain types of defect on the Si(0 0 1) surface. While it has been generally believed that any defect asymmetric with respect to the dimer row would induce this dimer pinning effect, recent experimental results have shown that this is not the case. We present a model, based on a nearest-neighbour Ising treatment of the surface, which allows the extent of pinning caused by a dimer to be predicted from ab initio calculations. We use this model to predict the pinning extent for three phosphorus-containing structures important in a proposed silicon-based quantum computer fabrication scheme, and identify one of these asymmetric features as causing no appreciable pinning. In addition, we use ab initio calculations to identify the effects governing the interaction between neighbouring dimers.     

Phase-constrained parallel MR image reconstruction

A generalized method for phase-constrained parallel MR image reconstruction is presented that combines and extends the concepts of partial-Fourier reconstruction and parallel imaging. It provides a framework for reconstructing images employing either or both techniques and for comparing image quality achieved by varying k-space sampling schemes. The method can be used as a parallel image reconstruction with a partial-Fourier reconstruction built in. It can also be used with trajectories not readily handled by straightforward combinations of partial-Fourier and SENSE-like parallel reconstructions, including variable-density, and non-Cartesian trajectories. The phase constraint specifies a better-conditioned inverse problem compared to unconstrained parallel MR reconstruction alone. This phase-constrained parallel MRI reconstruction offers a one-step alternative to the standard combination of homodyne and SENSE reconstructions with the added benefit of flexibility of sampling trajectory. The theory of the phase-constrained approach is outlined, and its calibration requirements and limitations are discussed. Simulations, phantom experiments, and in vivo experiments are presented.     

Electrostatic and optical resonances of arrays of cylinders

The solutions of the electrostatic potential problem for the square and hexagonal arrays of circular cylinders with zero applied field (homogeneous or resonant solutions) are studied. We show that for non-touching cylinders, the set of resonances is discrete except in the neighbourhood of one point, at which the dielectric constant of the array has an essential singularity. For arrays of touching cylinders, the set is well represented by a continuous distribution. This representation enables the derivation of the asymptotic form of the expansion for the dielectric constant of the array when the dielectric constant of the cylinders is large. The known value of the first term in the expansion enables us to derive the second term. The physical characteristics of the resonant solutions are studied. Metals achieve values of dielectric constant which are close to the resonant values (real and negative) for certain wavelengths. Curves are given which enable the prediction of those wavelengths at which the optical resonances of both arrays occur, for any area fraction and composition of a columnar cerment film.     

Extraction of structural information from measured transport properties of composites

We describe clearly Milton's bounds on the scalar transport properties of composite materials in the case when no geometrical information is known about the composite, but when a set of measured values of a transport property is available. We consider how the measured values may be used when they are subject to known errors. In this case, a statistical analysis is employed. We illustrate the various conclusions which may result from this analysis by considering six cases involving both two-and three-dimensional composites. In four of the six cases, estimates of the volume fraction of the composite in agreement with the known value are obtained. In the fifth case, the analysis pointed out a possible error in the experimental data, while in the sixth it revealed a critical dependence of transport properties on composite geometry due to filamentary linking between particles.