Interaction in the geometro-differential conception of extended particles and the Galilei semigroup of trajectories

Along the lines of a previous work, the geometrical structure of Hibert bundles describing extended quantum free particles is repeated with Galilei external and internal independent symmetries. Then, in order to introduce the interaction, this structure is extended by replacing configuration and momentum spaces by the socelled spaces of trajectories and extended velocity boosts, respectively. These provide representations giving the probability amplitudes for the particle to follow certain trajectories. The interaction can be introduced in the transformation law from functions on the space of trajectories (free dynamics) to functions on spacetime (intracting dynamics). This transformation law, which makes use of a universal distribution, is seen as a functional in our work according to a quantum functional theory which generalizes the ideas of de Broglie. Intertwining of induced representations gives the free propagator in the space of trajectories and, henceforth, the propagator with interaction in space-time for the extended particle.     

Separation of unitary representations of connected Lie groups by their moment sets

We show that every unitary representation π of a connected Lie group G is characterized up to quasi-equivalence by its complete moment set.Moreover, irreducible unitary representations π of G are characterized by their moment sets.     

More results on the Ashkin-Teller model

We analyze the low-temperature phase diagram of the Ashkin-Teller model for real values of the quadratic and quartic coupling constants.     

Synthesis,characterization and applications of polysiloxane networks with immobilized pyrogallol ligands

A porous, solid insoluble polysiloxane‐immobilized ligand system bearing pyrogallol active sites of the general formula P? (CH₂)₃? NH(CH₂)₃OC₆H₃(OH)₂ (where P represents [Si? O]_n siloxane network) has been prepared by the reaction of 3‐aminopropylpolysiloxane with 1,3‐dibromopropane followed by the reaction with pyrogallol. ¹³C CP‐MAS NMR and X‐ray photoelectron spectroscopy confirmed that the pyrogallol is chemically bonded to the siloxane backbone. Thermal analysis showed that the ligand system is stable under nitrogen at relatively high temperature. The polysiloxane–pyrogallol ligand system exhibits high potential for the uptake of the metal ions (Fe³⁺, Co²⁺, Ni²⁺ and Cu²⁺). Complexation of the pyrogallol ligand system for the metal ions at the optimum conditions was found to be in the order Fe³⁺ > Cu²⁺ > Ni²⁺ > Co²⁺. Copyright © 2005 John Wiley & Sons, Ltd.     

Triple collisions in the isosceles three body problem with small mass ratio

We use a slightly modified version of McGehee's transformation to study the triple collisions of the isosceles three body problem in a way that allows us to let the mass ratio go to zero. We study the limiting case and show that the collision manifold changes topologically, which affects the behaviour of near collision orbits. We also obtain new information about the flow on the collision manifold when the mass ratio is small.     

Solubility of polycyclic aromatics in binary solvent mixtures using activity coefficient models

Polycyclic aromatic hydrocarbons (PAHs) precipitation is one of the major problems in the hydrocracking units. In this investigation, pyrene and phenanthrene were selected because they were found to be in higher concentrations in the feed to hydrocracking units. Their solubilities were investigated in toluene solvent mixture of iso-octane and heptane over a temperature range from 293 to 323 K. The experimental solubility data were used to predict the interaction parameters for seven different solid–liquid equilibrium models. The following activity coefficient models were used; Wilson, NIBS/Redlich–Kister, UNIQUAC, modified UNIFAC, modified UNIFAC (Dortmund), Flory–Huggins and Sheng. The interaction parameters were expressed as a second-order polynomial function in temperature. In order to test the models, the average absolute deviation percentage (AADP) was used. The overall AADP was found to range from approximately 7 to 14%. The models can be arranged according to their accuracy in a descending order based on AADP as follows: NIBS/Redlich–Kister, Wilson, UNIQUAC, Sheng, Flory–Huggins, modified UNIFAC (Dortmund) and finally modified UNIFAC. All models used in this work gave reasonable results; however, the group contribution models can also be used as a predictive tool for the solubility measurement of pyrene and phenanthrene in other solvents containing the same groups of the solvents used in this study.     

Exploiting the 1,2,3‐Triazole Moiety to Generate Carbazole Molecular Architectures through Click Approach

Reaction of 3,6‐dichlorocarbazole with propargyl bromide in the presence of a basic medium gave an N‐propargylated carbazole. The latter compound was converted into molecular architectures containing 1,2,3‐triazole moiety through Cu(I)‐catalyzed 1,3‐cycloaddition reaction with different azides. Similarly, 2‐azidomethyl benzothiazole was cliched with N‐Boc‐protected N´‐propargyl glutamate to give the biomolecule 2‐triazolylmethyl product.     

Nano ZnO thin films synthesis by sol–gel spin coating method as a transparent layer for solar cell applications

Zinc oxide nano-structured thin films have been synthesized by low-temperature and cost-effective sol–gel spin coating method. Zinc oxide films with good adherence have been deposited on soda lime glass substrates with two thicknesses 250.15 and 311.32?nm. High transmission (>95%) zinc oxide films with proper interference fringes in the visible and near infrared region have been obtained. Film thickness, optical constants and dispersion parameters have been calculated accurately by using Swanepoel method, which basely depends on the interference fringes of the transmission spectra. Zinc oxide films have direct optical band gap, its values slightly change with the annealing temperatures and film thickness. The X-ray diffraction studies indicated the hexagonal wurtzite structure for zinc oxide films with preferred orientation along (002) plane. Raman spectroscopy confirmed the hexagonal structure for the films. The average particle size is in the nano-scale and the crystallinity level increases with the annealing temperatures and film thickness.

     

A Hybrid grey wolf optimizer and genetic algorithm for minimizing potential energy function

In this paper, we propose a new hybrid algorithm between the grey wolf optimizer algorithm and the genetic algorithm in order to minimize a simplified model of the energy function of the molecule. We call the proposed algorithm by Hybrid Grey Wolf Optimizer and Genetic Algorithm (HGWOGA). We employ three procedures in the HGWOGA. In the first procedure, we apply the grey wolf optimizer algorithm to balance between the exploration and the exploitation process in the proposed algorithm. In the second procedure, we utilize the dimensionality reduction and the population partitioning processes by dividing the population into sub-populations and using the arithmetical crossover operator in each sub-population in order to increase the diversity of the search in the algorithm. In the last procedure, we apply the genetic mutation operator in the whole population in order to refrain from the premature convergence and trapping in local minima. We implement the proposed algorithm with various molecule size with up to 200 dimensions and compare the proposed algorithm with 8 benchmark algorithms in order to validate its efficiency for solving molecular potential energy function. The numerical experiment results show that the proposed algorithm is a promising, competent, and capable of finding the global minimum or near global minimum of the molecular energy function faster than the other comparative algorithms.