The dual of a finitely generated multiplication module

This paper is based on the M. Sc. thesis written by the third author under the supervision of the first two authors. It was submitted to the University of Baghdad in 1986.     

Polarity and steric effect of the lateral substituent on the mesophase behaviour of some newly prepared liquid crystals

Eight homologous series of 2- (or 3-) substituted phenyl 4?-(4?-alkoxy phenylazo) benzoates (In_a–h) were prepared in which, within each homologous series, the length of the terminal alkoxy group varies between 6, 8, 10 and 12 carbons, while the other substituent, X, is a laterally attached polar group that alternatively changed from CH₃, H, F, Br and CN. Compounds prepared were characterised by infrared and ¹H-NMR spectroscopy, and their mesophase behaviour investigated by differential scanning calorimetry and identified by polarised light microscopy. The results were discussed in terms of polarity and steric effects. The stability of the mesophase was correlated once with the dipolar anisotropy of the whole molecule and another with the dipolar anisotropy of the substituent, X. A comparative study was made between the investigated compounds and their previously prepared linear 4-substituted isomers, namely 4-substituted phenyl 4?-(4?-alkoxy phenylazo) benzoates (In_i–k).     

Determination of traces of polychlorinated biphenyls in pigments

PCB patterns in a new pigment brand are characterized using GC-MS in the single ion monitoring (SIM) mode. Specific PCBs are then used as external standards for GC-ECD quantification. The following PCB isomers or groups of isomers have to be determined (CB = chlorobiphenyl): total diCBs, 3,3′ diCB, 2,4,5-triCB, 2,2′,4,4′-tetraCB, 2,2′,5,5′-tetraCB, total pentaCB, total hexaCB. Capillary gas chromatography is performed on preseparated solutions (LC) of pigment. An electron caputure detector (ECD) is used for PCB detection and quantification. Calibration is based on the peak areas of external standards and the PCB isomers in the samples, all normalized for internal standard peak areas. Total concentrations of diCB, hexaCB, or pentaCB in a sample are calculated by summing the individual PCB isomer concentrations within the correcsponding elution ranges. Determination limits lie in the range of 1 mg/PCB-isomer/kg pigment.     

Effect of molecular structure on the phase behaviour of some liquid crystalline compounds and their mixtures XIV. Binary mixtures of 4-(4-substituted phenylazo) phenyl-4-alkoxybenzoates

Binary mixtures formed from components of the five homologous series of the 4-(4-substituted phenylazo)phenyl-4-alkoxybenzoates Ia-e were prepared and their mesophase behaviour characterized. Transition temperatures of the mixtures prepared were measured by differential scanning calorimetry and identified by polarizing optical microscopy. Each binary combination was made from components bearing a terminal alkoxy group with the same number of carbon atoms (kept constant at n = 6, 8, 10, 12, 14 or 16), while the other substituent (X) was different—CH₃O, CH₃, Cl, NO₂, or CN. Phase diagrams were constructed for the various systems in order to investigate the effect of the terminal substituent X, as well as of the alkoxy chain length, on the phase behaviour of mixed systems.     

Mesophase behaviour of azobenzene-based angular supramolecular hydrogen-bonded liquid crystals

New types of angular 1:1 hydrogen-bonded supramolecular complexes via hydrogen-bond formation between 4-alkoxyphenylazo benzoic acids (In) and 4-(3?-pyridylazo)-4??-alkoxybenzoates (IIm) with various alkoxy chains (from 6 to 16 carbons) were prepared and investigated for their mesophase behaviour by differential scanning calorimetry (DSC) and polarised-light microscopy (PLM). All prepared homologues were found to be dimorphic, possessing smectic C and nematic mesophases. The formation of 1:1 hydrogen-bonded supramolecular liquid crystals (LCs) complexes was confirmed by FTIR and UV?visible (UV?vis) absorption spectroscopy. The study revealed that nematic transition enhancement (ΔT) decreases with the increase of the alkoxy chain length on the base complement, while it increases with the increase of the chain attached to the acid complement of the complex, that is the stability of the nematic phase is more dependent on the length of the acid component.     

Effect of molecular structure on the phase behaviour of some liquid crystalline compounds and their mixtures XIII. 4-(4-Substituted phenylazo)phenyl 4-alkoxybenzoates

Five homologous series of 4-(4-substituted phenylazo)phenyl 4-alkoxybenzoates (Ia-e) were prepared in which the substituent (X) was taken from CH₃O, CH₃, Cl, NO₂, and CN, while, within each homologous series, the length of the terminal alkoxy group varied between 6 and 16 carbon atoms. Compounds prepared were characterized by infrared spectroscopy, and their mesophase behaviour investigated by differential scanning calorimetry and polarizing optical microscopy. The results are discussed in terms of mesomeric and polarizability effects. In each group of compounds bearing the same alkoxy group, the mesophase - isotropic transition temperatures (T_c) were successfully correlated with the polarizability anisotropy of bonds to the substituent X.     

Semi-multiplication modules

This paper forms a portion of the Ph.D dissertation written by the first author under the supervision of the second author, and submitted to the University of Baghdad in 1990.     

Coexistence of superconductivity and ferromagnetism in ferromagnetic metals

We address the question of coexistence of superconductivity and ferromagnetism. Using a field theoretical approach we study a one-fermion effective model of a ferromagnetic superconductor in which the quasiparticles responsible for the ferromagnetism form the Cooper pairs as well. For the first time we solve self-consistently the mean-field equations for the superconducting gap and the spontaneous magnetization. We discuss the physical features which are different in this model and the standard BCS model and consider their experimental consequences.