On the domain dependence of solutions to the compressible Navier–Stokes equations of a barotropic fluid

We prove a general compactness result for the solution set of the compressible Navier–Stokes equations with respect to the variation of the underlying spatial domain. Among various corollaries, we then prove a general existence theorem for the system in question with no restrictions on smoothness of the spatial domain. Copyright © 2002 John Wiley & Sons, Ltd.     

Magnetic poly(N‐isopropylacrylamide) microspheres by dispersion and inverse emulsion polymerization

The aim of this study was to develop novel thermally responsive polymer microspheres with magnetic properties. Dispersion and inverse emulsion copolymerization of N‐isopropylacrylamide (NIPAAm) and N,N′‐methylenebisacrylamide (MBAAm) was investigated in the presence of γ‐Fe₂O₃ nanoparticles. The resulting microspheres were characterized in terms of morphology, size, polydispersity, iron content, and temperature‐dependent swelling using optical microscopy, transmission electron microscopy, scanning electron microscopy, QELS, and AAS. The effects of several variables, such as the concentration of γ‐Fe₂O₃, MBAAm crosslinking agent, Span 80 surfactant, 2,2′‐azobis(2‐methyloctanenitrile) (AMON) initiator, and polymerization temperature on the properties of the microspheres were studied. Swelling and thermoresponsive behavior of the microspheres containing γ‐Fe₂O₃ nanoparticles were also investigated. The microspheres contained about 8 wt % of iron. The presence of magnetic nanoparticles and their concentration changes did not have any significant effect on the temperature sensitivity of the composites. The particles gradually shrink into an increasingly collapsed state when the temperature is raised to 40 °C since the increase in temperature weakens the hydration and PNIPAAm chains gradually become more hydrophobic, which leads to the collapse of the particles. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5884–5898, 2007     

Fermions in Odd Space-Time Dimensions: Back to Basics

It is a well-known feature of odd space-time dimensions d that there exist two inequivalent fundamental representations A and B of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in A and B. As a consequence, a parity-invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long-held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge-conjugation operations. We work explicitly in 2 + 1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions.     

A quasilinearization method for a class of integro-differential equations with mixed nonlinearities

We develop an extended form of the quasilinearization method for an initial value problem involving a nonlinear integro-differential equation with mixed nonlinearities, occurring in distributed-infective and distributed-contact models. In fact, a monotone sequence of iterates converging uniformly and quadratically to a solution of the problem is obtained. Some interesting observations are presented.     

Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

Numerical study of charge ordering in NaxCoO2

A simple microscopic model of charge ordering in the Na_xCoO₂ system is presented. The model takes into account the interplane interactions between the ordered Na ions and d electrons from the CoO₂ layers as well as the nearest-neighbor intraplane Coulomb interactions between d electrons. It is shown that a driving force of charge ordering in the CoO₂ layers is the interplane interaction that alone is able to describe various types of inhomogeneous charge ordering (e.g., the striped phases) as well as to predict correctly the conducting properties of the system.     

The monotone iterative technique for impulsive hybrid set valued integro-differential equations

We develop the monotone method for impulsive hybrid set integro-differential equations in all its generality. Some interesting observations are presented.     

Liquid crystalline behaviour from binary mixtures of non-mesogenic 4-alkyl-N-(4-cyanophenyl) piperidines [1]

A relatively rare phenomenon, the induction of thermotropic mesophases from combinations of homologues of non-mesogenic compounds, is examined in some detail. Thus, monotropic nematic phases have been obtained from binary mixtures of 4-alkyl-N-(4-cyanophenyl)piperidines (I). Except for the hexyl homologue, the compounds I with butyl to nonyl as alkyl groups are non-mesomorphic as neat materials. From phase diagrams, the nematic clearing temperatures of the binary mixtures are found to vary linearly with composition and to increase as the molecular lengths of the components are increased. By introducing a methyl group at the 1-position of the alkyl chain, the melting points of the neat components are depressed, and the nematic clearing temperatures of the binary mixtures are lowered. Factors associated with the induction of this mesomorphism and with the 'kinetic' and thermodynamic stabilities of the monotropic nematic phases are discussed. Among these is the orientation between the rings of the core groups in I and in the more common mesogens, the trans-4-alkyl-1-(4-cyanophenyl) cyclohexanes, II.     

Thermotropic liquid-crystalline behaviour from mixtures of non-mesogenic molecules

A class of non-mesogenic molecules, which as mixtures exhibit monotropic nematic phases, is described.     

On-line coupling of sequential injection extraction with restricted-access materials for sample clean-up and analysis of drugs in biological matrix

In this contribution, the on-line coupling of solid phase extraction (SPE), based on a restricted-access material (RAM), with sequential injection technique (SIA) for the analysis of biological samples, is described. The SIA-RAM system was tested with a new potential antileucotrienic drug (VUFB-19363 (Quinlukast)) for serum analysis. The method is based on SPE with the novel internal-surface reversed-phase column packing material-alkyl-diol silica (ADS). The supports tolerate direct and repetitive injection of proteinaceous fluids (plasma, serum) and allow reversed-phase partitioning at the internal surface. A column packed with a 25 microm C18 alkyl-diol support was used for direct serum injection. Using a 6-port selection valve and the system of three mobile phases, the polar matrix compounds and metabolites are removed by sequentially aspirated mobile phases with lower content of the organic part (methanol-water (2:98) and following acetonitrile-water (20:80)) to the waste, and then, the analyte enriched on the column is eluted by a strong mobile phase (acetonitrile-methanol-water (40:20:40)) to the UV detector without transfer loss. With the fully automated SIA system, a total analysis time of less than 10 min was achieved. The only off-line sample pre-treatment step required to remove particulate matter was centrifugation. The studies showed a range of linearity (2-40 microg ml(-1)) and a high recovery (93.6-96.8%) of drug from the biological matrix with coefficients of variation (RSD) less than 5.0% (n = 6). This paper introduces a new, simple and robust analytical technique suitable for screening determination and direct analysis of drugs in biological materials.