New characterizations of digraphs represented by intervals

We present new characterizations of interval digraphs, interval graphs, and indifference digraphs, using linear orderings of edges and vertices. © 1996 John Wiley & Sons, Inc.     

Quantum black hole and the modified uncertainty principle

Recently Ali et al. (2009) [13] proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Planck length). Inspired by this idea we examine the Wheeler-DeWitt equation for a Schwarzschild black hole with a modified Heisenberg algebra which has a linear term in momentum. We found that the leading contribution to mass comes from the square root of the quantum number n which coincides with Bekenstein?s proposal. We also found that the mass of the black hole is directly proportional to the quantum number n when quantum gravity effects are taken into consideration via the modified uncertainty relation but it reduces the value of mass for a particular value of the quantum number.     

Unprecedented hydrothermal reaction of o-phenylaniline and related derivatives with cyclic ketones. A novel approach to the construction of phenanthridine and quinoline ring systems

[reaction: see text] A new method for synthesizing phenanthridine and its related compounds was developed using the condensation of o-phenylaniline and its homologues with cyclic ketones under hydrothermal conditions.     

A transportation problem with fuzzy-stochastic cost

In this paper, we consider some transportation problems (TPs) with different types of fuzzy-stochastic unit transportation costs and budget constraints. These fuzzy stochastic costs are reduced to corresponding crisp ones in two different ways. For the first method, using the definition of α$\alpha$-cut of the fuzzy numbers, expectation is taken separately on both lower and upper α$\alpha$-cuts and then mean expectation is calculated with the help of signed distance. In the second procedure, we realize fuzzy random events (ξ?r)$(\xi ?r)$ and (ξ?r)$(\xi ?r)$ for the fuzzy random variable (ξ)$(\xi )$. Using credibility measure of these events, mean chances for the above fuzzy random events are calculated and then expectation is taken to get the crisp expressions. The reduced deterministic problems of the fuzzy stochastic TP are solved using a real coded genetic algorithm with Roulette wheel selection, arithmetic crossover and random mutation. Few numerical examples are demonstrated to find the optimal solutions of the proposed models.     

Synthesis of monomeric Fe(II) and Ru(II) complexes of tetradentate phosphines

rac-Bis[{(diphenylphosphino)ethyl}-phenylphosphino]methane (DPPEPM) reacts with iron(II) and ruthenium(II) halides to generate complexes with folded DPPEPM coordination. The paramagnetic, five-coordinate Fe(DPPEPM)Cl(2) (1) in CD(2)Cl(2) features a tridentate binding mode as established by (31)P{(1)H} NMR spectroscopy. Crystal structure analysis of the analogous bromo complex, Fe(DPPEPM)Br(2) (2) revealed a pseudo-octahedral, cis-α geometry at iron with DPPEPM coordinated in a tetradentate fashion. However, in CD(2)Cl(2) solution, the coordination of DPPEPM in 2 is similar to that of 1 in that one of the external phosphorus atoms is dissociated resulting in a mixture of three tridentate complexes. The chloro ruthenium complex cis-Ru(κ(4)-DPPEPM)Cl(2) (3) is obtained from rac-DPPEPM and either [RuCl(2)(COD)](2) [COD = 1,5-cyclooctadiene] or RuCl(2)(PPh(3))(4). The structure of 3 in both the solid state and in CD(2)Cl(2) solution features a folded κ(4)-DPPEPM. This binding mode was also observed in cis-[Fe(κ(4)-DPPEPM)(CH(3)CN)(2)](CF(3)SO(3))(2) (4). Addition of an excess of CO to a methanolic solution of 1 results in the replacement of one of the chloride ions by CO to yield cis-[Fe(κ(4)-DPPEPM)Cl(CO)](Cl) (5). The same reaction in CH(2)Cl(2) produces a mixture of 5 and [Fe(κ(3)-DPPEPM)Cl(2)(CO)] (6) in which one of the internal phosphines has been substituted by CO. Complexes 2, 3, 4, and 5 appear to be the first structurally characterized monometallic complexes of κ(4)-DPPEPM.     

Modeling of optimal conditions for oxyhemoglobin photodissociation in laser-irradiated biotissue

Based on the theory of radiation transfer and a model that describes the structure and optical properties of biotissues, we have found spectral conditions of irradiation of the skin surface that ensure efficient generation of molecular oxygen O₂ in the dermis due to the photodissociation of blood oxyhemoglobin. We show that, for maximal local O₂ formation at depths z ≤ 0.2 mm, 0.2 mm < z ≤ 0.9 mm, 0.9 mm < z ≤ 2.5 mm, and z > 2.5 mm, it is more effective to use wavelengths in the intervals 418 ± 5, 575 ± 5, 585 ± 5, and 600 ± 5 nm, respectively. Physical reasons for the shift of optimal wavelengths toward the red range of the spectrum are described. We show that they are based on the selectivity of optical properties of the skin biotissue, which acts as of a kind of spectral filter the transmission curve of which depends on the depth. It is found that irradiation at a wavelength near 575 nm is optimal for the generation of a maximal amount of O₂ in the intire bulk of the dermis.