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.     

Quantum yield of Cl* (2P1/2) production in the gas phase photolysis of CCl4 in the ultraviolet

In this paper, we have probed the dynamics of chlorine atom production from the gas phase photodissociation of carbon tetrachloride at 222 and 235 nm. The quantum yield, φ* of Cl* (²P_1/2) production has been determined by probing the nascent concentrations of both excited (²P_1/2) and ground state (²P_3/2) chlorine atoms by suitable resonance-enhanced multiphoton ionization (REMPI) detection schemes. Although at the photolysis wavelengths the absorption of carbon tetrachloride is weak, significant amounts of Cl* are produced. Surprisingly, the quantum yield of Cl* production does not follow the absorption spectrum closely, which gives rise to the possibility of an indirect dissociation mechanism present in CCl₄ along with direct dissociation at these ultraviolet wavelengths     

Calorific study of the smectic A—smectic C transition in TBBA

An a.c. calorimetric technique has been used to measure the heat capacity variation associated with the smectic A—smectic C transition in terephthal-bis-(4n)-butylaniline (TBBA). Contrary to expectations based on the recent observation of petransitional acoustic effects in the semectic-A phase, the heat capacity shows no evidence of critical fluctuations and can be well described by a Landau mean-field model.