The $$\overline \partial $$-Neumann operator on Lipschitz q-pseudoconvex domains

On a bounded q-pseudoconvex domain Ω in ? ⁿ with a Lipschitz boundary, we prove that the \(\overline \partial \)-Neumann operator N satisfies a subelliptic (1/2)-estimate on Ω and N can be extended as a bounded operator from Sobolev (?1/2)-spaces to Sobolev (1/2)-spaces.     

Stabilizing the pull-in instability of an electro-statically actuated micro-beam using piezoelectric actuation

In the present article an investigation is presented into the stability of an electro-statically deflected clamped–clamped micro-beam sandwiched by two piezoelectric layers undergoing a parametric excitation applying an AC voltage to these layers. Applying an electrostatic actuation not only deflects the micro-beam but also decreases the bending stiffness of the structure, which can lead the structure to an unstable position by undergoing a saddle node bifurcation. Utilizing an appropriate AC actuation voltage to the piezoelectric layers produces a time varying axial force, which can play the role of a stabilizer exciting the system parameter. The governing equation of the motion is a nonlinear electro-mechanically coupled type PDE, which is derived using variational principle and discretized, applying Eigen-function expansion method. The resultant is a Mathieu type equation in its damped form. Using Floquet theory for single degree of freedom system the stable and unstable regions of the problem are investigated. The effects of viscous damping and electrostatic actuation on the stable regions of the problem are also studied.     

A facile preparation of trisubstituted amino-furan and -thiophene derivatives

β-Alkylation of amino-furan and -thiophene heterocycles is described through metal-, acid- and base-free carbon-carbon bond formation. The ability of both heterocycles to undergo selective β-alkylation is compared by mean of experimental and theoretical data. The presence of chiral amine substituents induced the diastereoselective generation of the newly formed additional stereocenter.     

Vibrational assignments, normal coordinate analysis, B3LYP calculations and conformational analysis of methyl-5-amino-4-cyano-3-(methylthio)-1H-pyrazole-1-carbodithioate

The Raman and infrared spectra of solid methyl-5-amino-4-cyano-3-(methylthio)-1H-pyrazole-1-carbodithioate (MAMPC, C7H8N4S3) were measured in the spectral range of 3700-100 cm(-1) and 4000-200 cm(-1) with a resolution of 4 and 0.5 cm(-1), respectively. Room temperature 13C NMR and (1)H NMR spectra from room temperature down to -60 °C were also recorded. As a result of internal rotation around C-N and/or C-S bonds, eighteen rotational isomers are suggested for the MAMPC molecule (Cs symmetry). DFT/B3LYP and MP2 calculations were carried out up to 6-311++G(d,p) basis sets to include polarization and diffusion functions. The results favor conformer 1 in the solid (experimentally) and gaseous (theoretically) phases. For conformer 1, the two -CH3 groups are directed towards the nitrogen atoms (pyrazole ring) and CS, while the -NH2 group retains sp2 hybridization and C-CN bond is quasi linear. To support NMR spectral assignments, chemical shifts (δ) were predicted at the B3LYP/6-311+G(2d,p) level using the method of Gauge-Invariant Atomic Orbital (GIAO) method. Moreover, the solvent effect was included via the Polarizable Continuum Model (PCM). Additionally, both infrared and Raman spectra were predicted using B3LYP/6-31G(d) calculations. The recorded vibrational, 1H and 13C NMR spectral data favors conformer 1 in both the solid phase and in solution. Aided by normal coordinate analysis and potential energy distributions, confident vibrational assignments for observed bands have been proposed. Moreover, the CH3 barriers to internal rotations were investigated. The results are discussed herein are compared with similar molecules whenever appropriate.     

Molecular spectroscopic analyses of gelatin

The molecular structure of gelatin was studied using Fourier transform infrared spectroscopy FTIR. The spectrum is subjected to deconvolution in order to elucidate the constituents of the molecular structure. B3LYP/6-31g** was used to study 13 amino acids then the scaled spectrum was compared to those of protein in order to describe the contribution of each amino acid into protein structure. A special interest was paid to the NH and C=O region. The reactivity of each amino acid was studied in terms of some important physical parameters like total dipole moment and HOMO/LUMO which describe the interaction of amino acid with their surrounding molecules. Results indicated that B3LYP/6-31g** model is a suitable and precise method for studying molecular structure of protein.     

Comparative Study of Chromium Biosorption by Mesorhizobium amorphae Strain CCNWGS0123 in Single and Binary Mixtures

The appearance of chromium in the aqueous effluent is a major concern for the modern industry. In this work, Mesorhizobium amorphae strain CCNWGS0123 was investigated as a biosorbent to remove chromium from aqueous solutions. The optimum pH for Cr(III) and Cr(VI) biosorption were 4 and 2, respectively. This isolate showed an experimental maximum Cr(III) adsorption capacity of 53.52 mg?L^?1, while the result was 47.67 mg?L^?1 for Cr(VI), with an initial 100 mg?L^?1 Cr ions and 1.0 g?L^?1 biomass. In terms of time equilibrium, Cr(III) ion was more readily adsorbed than Cr(VI) by this isolate. The biosorption data of both ions fit the Langmuir isotherm better than that of Freundlich model. Meanwhile, this organism exhibited a good capability to release Cr ions, with desorption efficiency of 70 % for Cr(III) and 76 % for Cr(VI). Fourier transform infrared spectroscopy analysis showed that –OH, –COO, –NH, amide I, and C=O were involved in Cr(III) and Cr(VI) binding. The biosorbent was further characterized by scanning electron microscopy and energy-dispersive X-ray spectrometry, which indicated an accumulation of chromium on the cellular level. In the binary mixtures, the removal ratio of total Cr and Cr(III) increased from pH?2 to 4. The highest removal ratio of the total Cr was observed in the 25/25 mg?L^?1 mixture at pH?4. In addition, the removal efficiency of Cr(VI) was closely influenced by Cr(III) in the mixture, decreasing to 23.57 mg?g^?1 in the 100/100 mg?L^?1 mixture system, due to the competition of Cr(III). The potential usage of the chromium-resistant rhizobium for the remediation of chromium-contaminated effluents has been demonstrated based on the above results.     

Nonionic Surfactants from Recycled Poly(ethylene terephthalate) as Corrosion Inhibitors of Steel in 1 M HCl

Recycled poly(ethylene terephthalate) (PET) can be modified to produce nonionic surfactants. Recycling of PET waste was carried out in presence of triethanolamine and manganese acetate as catalyst. The produced oligomers were reacted with stearic acid and polyethylene glycol, PEG, which have different molecular weights 400, 1,000, and 4,000. The inhibition of corrosion of steel in 1 molar hydrochloric acid solution in the presence of the prepared surfactants is studied by weight loss and electrochemical polarization measurements. The polarization curves indicate that these compounds act as mixed‐type inhibitors. The inhibition efficiency increases with the increase of inhibitor concentration to reach their critical micelle concentrations. The temperature effect on the corrosion behavior of steel in 1 M HCl with and without surfactants is studied in the temperature range from 308 to 343 K. The adsorption of inhibitors on the steel surface is found to increase with increasing the temperature. From the adsorption isotherm, some thermodynamic data for the adsorption process are calculated and discussed.     

PREPARATION OF NEW DERIVATIVES OF THIAZOLE,THIAZOLIDINE, AND THIAZOL-2-YLPYRAZOLO[3,4-D]PYRIMIDINE SULFONAMIDO CONJUGATES

Several new thiazoles ( 3–7 ), thiazolylpyrazole carbonitrile ( 10 , 11 ), and Thiazolidine sulfonamido conjugate derivatives ( 19–26 ) were prepared starting with p-Piperidinesulfonylacetophenones ( 1 , 2 ). The structure of these compounds was elucidated on the bases of elemental analysis, IR, PMR, and mass spectra. The antimicrobial activities of some selected compounds are also reported.     

Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation

Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on diffusion-weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (mm(2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology.