Reduction of fuzzy strict order relations

Fuzzy strict order relations and the notion of their reduction are defined. A necessary and sufficient condition is obtained for the transitive closure of the reduction to coincide with the strict order itself. Some possible graph-theoretic significances of these results are discussed in the conclusion.     

On the self-trapping of an electron due to lattice interaction

The problem of the sharpness of the polaron self-trapping transition for a single electron placed in the conduction band of an insulator and interacting with the phonons of the underlying lattice is investigated within the Fröhlich Hamiltonian. It is shown that this phenomenon depends sensitively on the lattice dimensionality, the nature of the electron-phonon coupling, the nature of the phonon dispersion; and on the discrete or the continuum nature of the applicable Hamiltonian.     

On the direct determination of constrained pure state one-electron density matrices: Part I. A new theoretical model for closed-shell systems

A new method based on the penalty-function way of satisfying equality constraints is proposed for the determination of constrained pure state one-electron density matrices for closed-shell many-electron systems. The algorithm suggested can handle many constraints simultaneously. Certain interesting features of the proposed algorithm are discussed with numerical examples.     

Thickness dependence of the phase transition temperature in Ag2Te thin films

Electrical resistance measurements of Ag₂Te thin films of different thicknesses, vacuum deposited on clean glass substrates held at room temperature in a vacuum of 5 × 10^?5 Torr, have been carried out from about 300 to 450 K. A semiconducting-to-metallic-phase transition, which takes place during heating, is indicated by a sharp change in the slope of the resistance-vs-temperature curve. For films of different thicknesses the phase transition is found to occur at different temperatures. The size-dependent phase transition is explained by taking into account the varying surface and intergrain surface (interface) energy contributions to the total energy of the stable phase as a function of thickness and the difference in specific surface and integrain surface energies of the two phases. An order of magnitude of the difference in the function of specific surface and interfacial energies of the two phases is also made.     

De Broglie wave and Compton wave

In contrast to the three-wave hypothesis (TWH) presented earlier [1], it is argued in this letter that a massive particle in motion in a Lorentz frame will actually be associated with only two types of waves: (i) a transformed Compton wave and (ii) a superluminal de Broglie wave (B-wave). The subluminal wave (D-wave or D'-wave [2]) cannot be simultaneously correlated with the particle under consideration.     

Characterization of fatty oils by pattern recognition of triglycerides profiles

The triglyceride profiles for corn, soybean, sunflower, grapestone, olive and olive husks oils were obtained by high temperature capillary gas chromatography on HT-FS capillary columns coated with OV-17-OH. The data were treated by methods of computerized pattern analysis, involving principal component analysis, discriminant analysis, and hierarchical clustering. A graphical representation of results as “star symbol plots” allows prompt visual recognition of the characteristic profiles and straightforward qualitative identification of unknowns as well as recognition of adulterations.