On spaces in which countably compact sets are closed, and hereditary properties

A space X is called C-closed if every countably compact subset of X is closed in X. We study the properties of C-closed spaces. Among other results, it is shown that countably compact C-closed spaces have countable tightness and under Martin's Axiom or 2^ω0<2^ω1, C-closed is equivalent to sequential for compact Hausdorff spaces. Furthermore, every hereditarily quasi-k Hausdorff space is Fréchet-Urysohn, which generalizes a theorem of Arhangel'sk in [4]. Also every hereditarily q-space is hereditarily of pointwise countable type and contains an open dense first countable subspace.     

Preface

Preface

Preface     

Application of multi-element clustering techniques of five Egyptian industrial sugar products

The concentration of 18 elements in different cane sugar products, i.e., cane sugar plants, crude and syrup juices, molasses, and the end products of the consumer sugar, were analyzed and processed. The samples were collected from five citics, i.e., Kom Ombo, Edfu, Armant, Deshna and Naga Hammady in Upper Egypt where the main Egyptian sugar industry factories are located. INAA was applied for the determination of Al, Ca, Cl, Co, Cr, Fe, Mg, Mn, Na and Sc, while Cu, Li, P, Sn, V and Zn were determined by ICP-AES and Pb and As were determined by AAS. These three analytical methods were applied to optimize the sensitivity and the accuracy of the measurements in order to provide a sound basis for the obtention of reliable clustering results.     

The attractive Coulomb potential polynomials

TheJ matrix method in quantum mechanics developed by Heller, Reinhardt, and Yamani points to a set of orthogonal polynomials having a nonempty continuous spectrum in addition to an infinite discrete spectrum. Asymptotic methods are used to investigate the spectral properties of these polynomials. We also obtain generating functions for both numerator and denominator polynomials. The corresponding continued fraction is computed and the Stieltjes inversion formula is used to determine the distribution function.     

Interaction of monovalent cations with salicylaldehyde: Evidence for excited-state ion-pair dissociation

Interaction of monovalent cations with salicylaldehyde resulted in the formation of tight ion-pairs. In these ion-pairs salicylaldehyde acts as a bidentate anion through the phenolate and the carbonyl oxygen atoms. Para substituted phenols, on the other hand, form less tight ion-pairs with monovalent cations. Red shifts in both absorption and emission spectra of these ion-pairs were observed as the ionic radius of the metal ion is increased. In presence of 18-crown-6, solventseparated ion-pairs are formed at the expense of contact ion-pairs. Evidence for excited-state dissociation of the solvent-separated ion-pairs is reported.     

Application of environmental relaxation model to the transport behavior of glass-forming melts

The environmental relaxation model was applied successfully to explain the temperature dependence of viscosity, conductance, and the Walden product of molten Ca(NO₃)₂.3.91H₂O + NiCl₂ system in the non-Arrhenius region. This model was applied to pure melts, binary molten salt systems with ideal solutions marked by the absence of complex ions, and systems in which octahedral or tetrahedral complexes are formed. The values of the glass transition temperature obtained from the free volume and environmental relaxation models are in good agreement. The values of apparent activation energies for viscous and conductance flows derived from these two models are also comparable.