Note on some s-shaped bifurcation curves

In this article we consider asymptotic behavior of some bifurcation curves of the two-point boundary value problem -u′ (x) =λf(u(x)) for 0 < x < 1; u(0) = u(1) = 0. Infact we prove that λ grows linearly with respective to p(p = u(1/2)) for p large     

Experimental and quantum chemical study on the IR, UV and electrode potential of 6-(2,3-dihydro-1,3-dioxo-2-phenyl-1H-inden-2-yl)-2,3-dihydroxybenzaldehyde

Electrode potential of 6-(2,3-dihydro-1,3-dioxo-2-phenyl-1H-inden-2-yl)-2,3-dihydroxybenzaldehyde (DPDB) in methanol have been calculated theoretically. For the achievement of this task, the density functional theory (B3LYP/6-31G(d)) was employed with the inclusion of the entropic and thermochemical corrections to yield the free energies of the redox reactions. The electrode potential was also obtained experimentally by means of an electrochemical technique (cyclic voltammetry). The geometric parameters, the vibrational frequency values and the UV spectrum of DPDB and 2-(2,3-dihydro-1,3-dioxo-2-phenyl-1H-inden-2-yl)-5,6-dioxocyclohexa-1,3-dienecarbaldehyde (DPDD is the oxidized form of DPDB), were computed using the same methods. The calculated IR spectrum of DPDB, used for the assignment of the IR frequencies, was observed in the experimental FT-IR spectrum. The correlation between the theoretical and experimental DPDB vibrational frequencies was 0.996. This agreement mutually verified the accuracy of the experimental method and the validity of the applied mathematical model.     

Molecular parameterization and determination of the electrode potentials of anticoagulant derivatives: Electrochemical and quantum chemical study

This research presents calculations and computation of two anticoagulant derivatives electrode potentials in methanol. For this purpose, the ab initio molecular orbital calculations (HF) and density functional theory (DFT) together with the 6-31G(d) basis set were utilized. The calculated values were compared with the experimental values obtained by linear sweep voltammetry. The observed and the calculated changes in the reduction potential of the anticoagulant derivatives differed from those of the reference compound (catechol), being less than 20 mV. In this way, a method was provided, by which the reduction potentials of the related molecules could be predicted very accurately. Actually, the resulting data illustrated that the method was likely to be useful for the prediction of biomolecules electrode potentials in different aprotic solvents. The bond lengths, bond angles and dipole moment of the studied compounds were calculated in two different solvents and the solvent effects were discussed.     

Effects of substituents in the beta-position of 1,3-dicarbonyl compounds in bromodimethylsulfonium bromide-catalyzed multicomponent reactions: a facile access to functionalized piperidines

1,3-Dicarbonyl compounds can be converted to Mannich-type products A or highly functionalized piperidines B in the presence of a catalytic amount of bromodimethylsulfonium bromide (BDMS). The combination of aromatic aldehyde, amine, and 1,3-dicarbonyl compounds in the presence of a catalytic amount of BDMS leads to the formation of Mannich-type product A when R is a non-enolizable carbon or an alkoxy group, whereas in cases when R = CH3, the same combination yielded highly functionalized piperidines B. A synthetic study and mechanistic proposal are presented.     

H2TPP organocatalysis in mild and highly regioselective ring opening of epoxides to halo alcohols by means of halogen elements

We found that elemental iodine and bromine are converted to trihalide nucleophiles (triiodine and tribromide anion, respectively) in the presence of catalytic amounts of meso-tetraphenylporphyrins (H2TPP). Therefore a highly regioselective method for the synthesis of beta-haloalcohols through direct ring opening of epoxides with elemental iodine and bromine in the presence of H2TPPs as new catalysts is described. At room temperature a series of epoxide derivatives were converted into the corresponding halohydrins resulting from an attack of trihalide species anion atoms at the less substituted carbon atom. This method occurs under neutral and mild conditions with high yields in various aprotic solvents, even when sensitive functional groups are present.     

Characterization of the Engineering Flow in a Miniaturised Bioreactor by Computational Fluid Dynamics

Three approaches based on computational fluid dynamics(CFD) techniques have been assessed for their ability to describe the engineering flow environment in a miniaturized mechanically agitated bioreactor. The three approaches tested were the source-sink(SS), the multiple reference frames (MRF) and the sliding grids(SG). In all the cases, the predictions of the velocity components agree with reported experimental data. However, the analysis of the results of the turbulent intensities predicted by the three approaches indicates the MRF and the SG techniques under predicted turbulent intensities are comparable to both experimental measurements and the SS method. The predicted power number and pumping number based on the SS ap-proach are closer to typical reported experimental values compared to those obtained from the MRF and SG methods.     

Synthesis, characterization and catalytic oxidation of cyclohexene with molecular oxygen over host (zeolite-Y)/guest (nickel(II) complexes of R2[12]1,3-dieneN2O2 and R2[13]1,4-dieneN2O2; R = H, Me, Ph) nanocatalyst (HGN)

12- and 13-Membered diaza dioxa Schiff-base nickel(II) complexes were successfully prepared in a nanoscale microreactor by the template condensation of (1,8-diamino-3,6-dioxaoctane)nickel(II) complex with bifunctional diketones within the nanodimensional pores of zeolite Y. The host–guest nanocatalyst (HGN); ([Ni((R₂[12]1,3-dieneN₂O₂)]²⁺-NaY, [Ni(R₂[13]1,4-dieneN₂O₂)]²⁺-NaY; R = H, Me and Ph) is catalytically very efficient as compared to other neat complexes for oxidation of cyclohexene with molecular oxygen as oxidant in the absence of solvent at 70 °C, affording 2-cyclohexene-1-ol and 2-cyclohexene-1-one.