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.     

A new approach of binary addition and subtraction by non-linear material based switching technique

Here, we refer a new proposal of binary addition as well as subtraction in all-optical domain by exploitation of proper non-linear material-based switching technique. In this communication, the authors extend this technique for both adder and subtractor accommodating the spatial input encoding system.     

Flow-driven voltage generation in carbon nanotubes

The flow of various liquids and gases over single-walled carbon nanotube bundles induces an electrical signal (voltage/current) in the sample along the direction of the flow. The electrical response generated by the flow of liquids is found to be logarithmic in the flow speed over a wide range. In contrast, voltage generated by the flow of gas is quadratically dependent on the gas flow velocity. It was found that the underlying physics for the generation of electrical signals by liquids and gases are different. For the liquid, the Coulombic interaction between the ions in the liquid and the charge carriers in the nanotube plays a key role while electrical signal generation due to gas flow is due to an interplay of Bernoulli’s principle and Seebeck effect. Unlike the liquid case which is specific to the nanotubes, the gas flow effect can be seen for a variety of solids ranging from single and multi-walled carbon nanotubes, graphite and doped semiconductors.     

Expansive self-homeomorphisms on G-spaces

Beginning with examples, the notion ofG-expansiveness over a metric spaceX on which a topological groupG acts is introduced. Some conditions are determined under which expansiveness onX impliesG-expansiveness. A characterization of aG-expansive homeomorphism is obtained which in turn gives a sufficient condition for the homeomorphic extension of aG-expansive homeomorphism to beG-expansive. At the end, some results are stated in the form of concluding remarks.