Representations of Clifford Algebras on Function Spaces on the Cantor Set

We give a representation of the (infinite-dimensional) complex Clifford algebra on the Hilbert space of square-integrable complexvalued functions on the Cantor set.     

Syntheses,spectroscopic and crystallographic characterizations of 4-nitrobenzyloxy derivatives and benzofurans from <Emphasis Type="Italic">ortho</Emphasis>-substituted benzaldehydes and 4-nitrobenzyl bromide

A series of benzyloxybenzaldehyde derivatives (1–3) were prepared by the reactions of 4-nitrobenzyl bromide with 4-hydroxy-3-methoxybenzaldehyde (vanillin), 2-hydroxy-3-methoxybenzaldehyde (o-vanillin) and 2-hydroxy-4-methoxybenzaldehyde. When the reaction time is quite long, benzofuran derivatives (4 and 5) were obtained by the reactions of ortho-hydroxyaldehydes with the 4-nitrobenzyl bromide. Condensation reactions among the three benzyloxybenzaldehyde derivatives (1–3) with 2-aminomethylfuran (furfurylamine) yielded the new imine compounds (6–8). The structures of these aldehydes (1–3), benzofuran derivatives (4 and 5) and imine compounds (6–8) were confirmed on the basis of elemental analyses, IR, ¹H NMR and ¹³C NMR and mass spectroscopy. The solid-state structures of compounds 4–6 were determined by single-crystal X-ray crystallography.     

A quantum chemical investigation on methylated pyridines

The structural features of the methylated pyridine series have been studied by quantum chemical methods. The aromatic character of these molecules is derived from the frontier molecular orbital energies, harmonic oscillator model of aromaticity (HOMA), and nucleus independent chemical shift (NICS) values. Hybrid density functional theory with 6-311++G(d,p) basis set was employed for all calculations.     

Quantum-chemical,spectroscopic and X-ray diffraction studies on nickel complex of 2-hydroxyacetophenone thiosemicarbazone with triphenylphospine

Reaction of 2-hydroxyacetophenone thiosemicarbazone with [Ni(PPh₃)₂Cl₂] in optimized conditions afforded a mixed ligand complex with an isolated triphenylphosphine molecule. The structure was characterized by elemental analysis, IR, NMR and UV–Vis. spectroscopies and single crystal X-ray diffraction technique. In addition, the molecular geometry, vibrational frequencies and gauge including atomic orbital (GIAO) ¹H and ¹³C NMR chemical shift values of the title compound in the ground state have been calculated using the density functional theory (DFT/B3LYP) method with the 6-31G(d,p) basis set for the C, N, O, S, P, H atoms and LANL2DZ pseudo-potential for the Ni atom, and compared with the experimental data. Besides, atomic charge distributions, molecular electrostatic potential and frontier molecular orbitals (FMO) analysis of the title compound were investigated by theoretical calculations. The thermodynamic properties of the compound at different temperatures have been calculated and corresponding relations between the properties and temperature have also been obtained. Atomic charge distributions indicate that during forming the title compound, the free ligand of thiosemicarbazone ion transfers their negative charges to central Ni(II) ion. The effect of different solvents (chloroform, methanol and water) on the geometry, vibrational frequencies, total energies and dipole moments was studied using the density functional theory (DFT/B3LYP) method by applying the Onsager and the Polarizable Continuum Model (PCM).     

Activity,exposure rate and spectrum prediction with Java programming

In order to envision the radiation exposure during Neutron Activation Analysis (NAA) experiments, a software called Activity Predictor is developed using Java^TM programming language. The Activity Predictor calculates activities, exposure rates and gamma spectra of activated samples for NAA experiments performed at Radiation Science and Engineering Center (RSEC), Penn State Breazeale Reactor (PSBR). The calculation procedure for predictions involves both analytical and Monte Carlo methods. The Activity Predictor software is validated with a series of activation experiments. It has been found that Activity Predictor software calculates the activities and exposure rates precisely. The software also predicts gamma spectrum for each measurement. The predicted spectra agreed partially with measured spectra. The error in net photo peak areas varied from 4.8 to 51.29%, which is considered to be due to simplistic modeling, statistical fluctuations and unknown contaminants in the samples.     

On normalized Ricci flow and smooth structures on four-manifolds with b + = 1

We find an obstruction to the existence of non-singular solutions to the normalized Ricci flow on four-manifolds with b⁺ = 1. By using this obstruction, we study the relationship between the existence or non-existence of non-singular solutions of the normalized Ricci flow and exotic smooth structures on the topological 4-manifolds , where . Received: 13 November 2008     

On the regularity condition in a convex feasibility problem

The regularity properties of a family of closed convex sets with nonempty intersection are investigated in the frame of a real Hilbert space. The significant role of these properties in solving convex feasibility problems with projection algorithms is pointed out.     

Synthesis, interface (Au/M2Pc2/p-Si), electrochemical and electrocatalytic properties of novel ball-type phthalocyanines

The phthalodinitrile derivative (3) was prepared by the reaction of 4,4'-(octahydro-4,7-methano-5H-inden-5-ylidene)bisphenol (1) and 4-nitrophthalonitrile (2) with dry DMF as the solvent in the presence of the base K(2)CO(3) by the method of nucleophilic substitution of an activated nitro group in an aromatic ring. The template reaction of 3 with the corresponding metal salts gave the novel bi-nuclear ball-type metallophthalocyanines, MPcs {M = Co (4), Cu (5), Zn (6)}. Newly synthesized compounds were characterized by elemental analysis, UV-vis, FT-IR (ATR), MALDI-TOF mass and (1)H-NMR spectroscopy techniques. The electronic spectra exhibit an intense π→π* transition of characteristic Q and B bands of the Pc core. The dielectric properties and interface between the spin coated films of 4-6 and a p-type silicon substrate have been studied by fabricating metal-insulator-semiconductor capacitors. The results indicated that the frequency dependence of the dielectric permittivity, ε'(ω), exhibits non-Debye type relaxation for all the temperatures investigated. The ac conductivity results indicated that the conduction mechanism can be explained by a hopping model at low temperatures (<430 K) and a free band conduction mechanism at high temperatures (≥430 K). The density of interface state calculations on these novel compounds showed that the combination of Au/4/p-Si is a promising structure with a high dielectric constant and a low interface trap density suitable for metal-oxide-semiconductor devices. The electrochemical properties of the Pc complexes were examined by cyclic voltammetry, differential voltammetry and controlled potential coulometry on platinum in non-aqueous media. The complexes showed ring-based and/or metal-based mixed-valence behaviours as a result of the remarkable interaction between the two Pc rings and/or metal centres. The mixed-valence splitting values for the complexes suggested that the mixed valence species are considerably stable. The Vulcan XC-72(VC)/Nafion(Nf)/4 modified glassy carbon electrode showed much a higher catalytic performance towards oxygen reduction than those of VC/Nf/5 and VC/Nf/6 modified ones.     

Effects of gamma and electron beam irradiation on the properties of calendered cord fabrics

The effects of gamma and e-beam irradiation on mechanical and structural properties of nylon 66 (Ny 66), nylon 6 (Ny 6) and poly(ethylene terephthalate) (PET) fabrics used in tyres were investigated. The untreated (greige), treated cords and calendered fabrics were irradiated at different doses. It is found that the effects of high energy irradiation on greige, treated cords and calendered fabrics are similar. No protective effect of compounds used in calendering was observed against radiation-induced oxidative degradation. The deterioration effect of gamma irradiation on mechanical properties is much higher than that of e-beam irradiation for all types of samples. Limiting viscosity numbers of both gamma and e-beam irradiated nylon 6 and nylon 66 cords were found to decrease with increasing dose. It is concluded that PET calendered fabric has higher resistance to ionizing radiation. Ny 6 and Ny 66 calendered fabrics are more sensitive even at low doses. Therefore, the effects of high energy irradiation on tyre cords have to be taken into consideration during tyre design reinforced with particularly Ny fabrics if pre-vulcanization with high energy radiation is to be applied.     

Determination of Milnacipran in Human Plasma Using GC–MS

A new, simple, and fully validated gas chromatography–mass spectrometry (GC–MS) method was presented for quantitative analysis of milnacipran (MNP) in human plasma. MNP was efficiently derivatized with N-methyl-N-trimethylsilyltrifluoroacetamide (MSTFA) before analysis. The role of catalyst, temperature, time, solvent on the trimethylsilylation reaction were evaluated. The proposed method was fully validated by assessment of the following parameters: limits of detection and quantitation, precision, accuracy, linearity, specificity, stability, extraction recovery and robustness/ruggedness. The limit of quantitation (LOQ) was 30 ng mL^?1. The calibration curve was linear (r ² > 0.9988) in the range 30–500 ng mL^?1. The method was found specific, precise, accurate, selective and reliable according to validation data. This developed method was successfully applied to determine the steady state concentration of MNP in patients.