Moment sets and unitary dual for the diamond group

The diamond group G is a solvable group, semi-direct product of R with a (2n+1)-dimensional Heisenberg group Hn. We consider this group as a first example of a semi-direct product with the form R?N where N is nilpotent, connected and simply connected.Computing the moment sets for G, we prove that they separate the coadjoint orbits and its generic unitary irreducible representations.Then we look for the separation of all irreducible representations. First, moment sets separate representations for a quotient group G⁻ of G by a discrete subgroup, then we can extend G to an overgroup G⁺, extend simultaneously each unitary irreducible representation of G to G⁺ and separate the representations of G by moment sets for G⁺.     

Synthesis and characterization of some new cobalt(II) and nickel(II) ternary complexes of <Emphasis Type="Italic">N</Emphasis>-acetyl, <Emphasis Type="Italic">N</Emphasis>-benzoyl and <Emphasis Type="Italic">N</Emphasis>-tosyl derivatives of amino acids

A series of some new cobalt(II) and nickel(II) ternary complexes of N-(acetyl)phenylalaninate (acphe), N-(acetyl)tyrosinate (actyr), N-(benzoyl)leucinate (bzleu), N-(benzoyl)phenylalaninate (bzphe), N-(tosyl)glutamic acid (tsglu), N-(tosyl)arginine (tsarg) with certain N-heterocyclic ligands such as imidazole (imi), methylimidazole (mimi), 2,2′-bipyridyl (bipy) 1,10-phenanthroline (phen) have been synthesized and characterized by elemental analyses, IR and electronic spectra. as well as thermogravimetry. The structure of the cobalt(II) N-phthaloylglycinate complex was also characterized by X-ray single crystal. It was found that the cobalt atom coordinates a 1,10-phenanthroline molecule and four water oxygen atoms, forming a distorted octahedral conformation. A molecule of N-phthaloylglycinate is connected by van der Waals contact and H-bonds.     

Hydrophobicity and Reactivity of Base Hydrolysis of Some Novel Low Spin Fe(II) Amino Acid Schiff Base Complexes in Some Binary Aqueous Solvent Mixtures

Rate constants for base hydrolysis of bis(naphthylidene isoleucinate)iron (II) (nili), bis(naphthylidene leucinate)iron(II) (nli), bis(naphthylidene serinate)iron(II) (nsi), bis(salicylidene isoleucinate)iron(II) (sili), (salicylidene leucinate)iron(II) (sli), bis(salic- ylidene methioninate)iron(II) (smi), and (salicylidene tryptophanate)iron(II) (sti) have been reported in different binary aqueous mixtures at 298 K. The observed reactivity trends are discussed in terms of the hydrophilic and hydrophobic forms of the complexes investigated, as well as the transfer chemical potentials of hydroxide ion and the complex. Both the solvent–solute and solvent–solvent interactions have been considered. The hydrophobic character of the complexes studied was manifested by enhancing the rate of base hydrolysis at the initial addition of the different cosolvents; further addition led mostly to a decrease in reactivity, but, in some cases, the greater destabilization of OH^– ion by added DMSO and acetone increases the rate of base hydrolysis. The modified Savage–Wood equation, based on the principle of group additivity, was applied to estimate the observed kinetic medium effects.     

Reactivity Tracers of the Hydrolysis of Fe(II)‐Bis(salicylidene) Complexes: Initial–Transition States Analysis and Enhanced Impact of Tensides on the Kinetic Trends

The kinetics of the acid hydrolysis reaction of Fe(II)‐bis(salicylidene) complexes were followed under pseudo–first‐order conditions ([H⁺] >> [complex]) at 298 K. The ligands of the studied azomethine complexes were derived from the condensation of salicylaldehyde with different five α‐amino acids. The hydrolysis reactions were studied in acidic medium at different ratios (v/v) of aqua–organic mixtures. The decrease in the dielectric constant values of the reaction mixture enhances the reactivity of the reaction. The transfer chemical potentials of the initial and transition states (IS–TS) from water into mixed solvents were determined from the solubility measurements combined with the kinetic data. Nonlinear plots of logk_obs versus 1/D (the reciprocal of the dielectric constant) suggest the influence of the solvation of IS–TS on the reaction reactivity. Furthermore, the acid hydrolysis reactions were screened in the presence of different concentrations of cationic and anionic tensides. The addition of surfactants to the reaction mixture accelerates the reaction reactivity. The obtained kinetic data were used to determine the values of δ_mΔG^# (the change in the activation barrier) for the studied complexes when transferred from “water to various ratios (v/v) of water–co‐organic binary mixtures” and from “water to water containing different [surfactant].” It was found that the reactivity of the acid hydrolysis reaction was controlled by the hydrophobicity of the studied chelates.     

Development of Microwave-Assisted Extraction of Trigonelline Biomarker from Trigonella foenum-graecum Seeds Followed by High-Performance Thin-Layer Chromatographic and High-Performance Liquid Chromatographic Analyses

JPC – Journal of Planar Chromatography – Modern TLC - An efficient and fast microwave-assisted extraction (MAE) technique was developed for extracting trigonelline as an indicative...     

The variation of heat transfer in a two‐sided lid‐driven differentially heated square cavity with nanofluids containing carbon nanotubes for physical properties of fluid dependent on temperature

The behavior of nanofluids containing cylindrical nanoparticles are investigated numerically inside a two‐sided lid‐driven differentially heated square cavity to gain insight into the convective recirculation and flow processes induced by a nanofluid. The physical properties of the base fluid such as viscosity, thermal conductivity and thermal expansion coefficient are, respectively, assumed to be temperature independent (taking the mean temperature of the left and right walls) and temperature dependent. A model is developed to analyze the behavior of nanofluids taking into account the nanoparticle volume fraction whereas the transport equations are solved numerically with finite volume approach using SIMPLEC algorithm. The left and right moving walls are maintained at different constant temperatures while the upper and bottom walls are thermally insulated. The directions of the moving walls were considered in a way that the force and natural convections aid each other. The governing parameter Richardson number was 0.1<Ri<50.0 but due to space constraints only the results for 0.1<Ri<10.0 from fluid flow are presented. It was found that the temperature dependency of physical properties at different Richardson numbers and nanoparticle volume fractions affects the fluid flow and heat transfer in the cavities. Finally, comparisons between the behaviors of the average Nusselt number at the left wall for two cases are presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Kinetics of base hydrolysis of novel low spin Fe(II) amino acid Schiff base chelates—hydrophobic structural effects

The reactivity against OH^? ion of some novel Fe(II) complexes of Schiff base ligands derived from salicylaldehyde or o‐hydroxynaphth‐aldehyde and some variety of amino acids has been examined in aqueous and aqua‐ethanol mixtures. The rate law and relevant mechanism were assumed. Base hydrolysis kinetics measurements revealed pseudo‐first‐order doubly stage rates because of the presence of mer‐ and fac‐isomers. The evaluated rate constants and activation parameters are consistent with the stability constants of the investigated complexes. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 595–602, 2002     

Reactivity trends of the base hydrolysis of coumarin and thiocoumarin in binary aqueous-methanol mixtures at different temperatures

Rate constants for base hydrolysis of both coumarin and thiocoumarin have been studied in different binary aqueous-methanol mixtures at temperature range from 288 to 313 K. The activation parameters of the reactions were evaluated. Moreover, the change in the activation barrier of the investigated compounds from water to water-methanol mixtures were estimated from the kinetic data.     

Energy of excitons and acceptor-exciton complexes to explain the origin of ultraviolet photoluminescence in ZnO quantum dots embedded in a SiO2 matrix

Assuming finite depth and within the effective mass approximation, the energies of exciton states and of the acceptor-exciton complexes confined in spherical ZnO quantum dots (QDs) embedded in a SiO₂ matrix are calculated using a matrix procedure, including a three-dimensional confinement of carrier in the QDs. This theoretical model has been designed to illustrate the two emission bands in the UV region observed in our experimental Photoluminescence spectrum (PL), with the first emission band observed at 3.04 eV and attributed to the bound ionized acceptor-exciton complexes, and the second one located at 3.5 and assigned to the free exciton. Our calculations have revealed a good agreement between the matrix element calculation method and the experimental results.     

Optical properties of acceptor-exciton complexes in ZnO/SiO2 quantum dots

The binding energy E_b of the acceptor-exciton complex (A⁻,X) as a function of the radius (or of the impurity position of the acceptor) and the normalized oscillator strength of (A⁻,X) in spherical ZnO quantum dots (QDs) embedded in a SiO₂ matrix are calculated using the effective-mass approximation under the diagonalzation matrix technique, including a three-dimensional confinement of the carrier in the QD and assuming a finite depth. Numerical results show that the binding energy of the acceptor-exciton complexes is particularly robust when the impurity position of the acceptor is in the center of the ZnO QDs. It has been clearly shown from our calculations that these physical parameters are very sensitive to the quantum dot size and to the impurity position. These results could be particularly helpful, since they are closely related to experiments performed on such nanoparticles. This may allow us to improve the stability and efficiency of the semiconductor quantum dot luminescence which is considered critical.