Sharp Sobolev Asymptotics for Critical Anisotropic Equations

We investigate blow-up theory and prove sharp Sobolev asymptotics for a general class of anisotropic critical equations in bounded domains of .     

Fractional order theory in thermoelastic solid with three-phase lag heat transfer

In this work, the field equations of the linear theory of thermoelasticity have been constructed in the context of a new consideration of Fourier law of heat conduction with time-fractional order and three-phase lag. A uniqueness and reciprocity theorems are proved. One-dimensional application for a half-space of elastic material in the presence of heat sources has been solved using Laplace transform and state space techniques Ezzat (Canad J Phys Rev 86:1241–1250, 2008). According to the numerical results and its graphs, conclusion about the new theory has been established.     

State space approach to magnetohydrodynamic flow of perfectly conducting micropolar fluid with stretch

In this work we introduce a model of the boundary layer equations for a perfect conducting micropolar fluid with stretch, bounded by an infinite vertical flat plane surface of a constant temperature. This model is applied to study the effects of free convection currents on the flow of the fluid in the presence of a constant magnetic field. The state space technique is adopted for the solution of a one‐dimensional problem for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Image encryption based on fractional chaotic pseudo-random number generator and DNA encryption method

Nonlinear Dynamics - Nonlinear dynamic systems and chaotic systems have been quite exhaustively researched in the domain of cryptography. However, the possibility of using fractional chaotic...     

Continuum modeling for the modulated vibration modes of large repetitive structuresModèle continu pour les modes de vibrations modulés des longues structures répétitives

By homogenization theory, one can predict the vibrations of long repetitive structures in the low frequency range. Beyond this range, many modes have a modulated shape. Based on a multiple scale analysis, a continuum model is presented, that is able to account for this class of modes. This model involves a real coefficient that can be computed from the finite element resolution of problems defined on a few basic cells. An application in 2D elasticity is presented. To cite this article: E.M. Daya et al., C. R. Mecanique 330 (2002) 333–338.     

Heterocycles from carbohydrate precursors. Part XIX. The X-ray crystal structure determination of the reaction product of 4-(2-acetoxyethylidene)-4-hydroxy-2,3-dioxobutyro-1,4-lactone-2-(p-bromophenylhydrazone) with methylhydrazine

X-ray crystallographic data show that the product obtained in the reaction of 4-(2-acetoxy-ethylidene)-4-hydroxy-2,3-dioxobutyro-1,4-lactone-2-(p-bromophenylhydrazone) with methyl-hydrazine is the bicyclic compound 2,6-dimethyl-3,4-dioxo-2,3,4,6,7,8-hexahydropyridazino-[4,3-c]pyridazine 4-(p-bromophenylhydrazone) ( 10 ) and not as originally suggested 1-methyl-3-(1-methylpyrazolin-3-yl)-4,5-pyrazoledione 4-(p-bromophenylhydrazone) ( 8 ).     

Novel species in the electrochemical reduction of a metalmetal bond bridged by a bidentate fluorophosphine

The purple bridged bimetallic complex [CH₃N(PF₂)₂]₃Co₂(CO)₂ undergoes successive chemically and electrochemically reversible one-electron reductions to the corresponding green radical anion and pale-yellow dianion. The radical anion is relatively unreactive towards oxygen and methyl iodide. The dianion is not only reactive towards oxygen and methyl iodide but also captures small positively charged species (e.g. Li⁺ and H⁺) with significant alteration of its chemical properties.     

Nanosensing of ATP by fluorescence recovery after surface energy transfer between rhodamine B and curcubit[7]uril-capped gold nanoparticles

The authors describe a method for functionalization of gold nanoparticles (AuNPs) with the supramolecular host molecule, curcubit[7]uril (CB[7]) which can bind rhodamine B (RhB). The fluorescence of RhB is quenched by the AuNPs via surface energy transfer. On addition of ATP, a dimeric RhB-ATP complex is formed and RhB is pushed out of CB[7]. Hence, fluorescence increases by a factor of 8. This fluorescence recovery effect has been utilized to develop a new detection scheme for ATP. The assay, measured at fluorescence excitation and emission wavelengths of 500 nm and 574 nm respectively, works in the 0.5–10 μM concentration range and has a 100 nM detection limit. The method is not interfered by UTP, GTP, CTP, TTP, ascorbic acid and glutathione.

Open image in new window

Graphical abstract Schematic of a method for determination of ATP in the 500 nM to 10 μM concentration range by using fluorescence recovery after surface energy transfer (SET) between rhodamine B (RhB) and gold nanoparticles capped with curcubit[7]uril (CB[7]).

     

Biomimetic oxidation of catechol employing complexes formed in situ with heterocyclic ligands and different copper(II) salts

In the present work, catecholase activity is presented. The complexes were prepared by condensation of the organic ligand pyrazolyl L ₁ –L ₄ and copper(II) ion in situ. The pyrazolyl compounds L ₁ –L ₄ used in this study are: L ₁ is (3,5-dimethyl-pyrazol-1-ylmethyl)-(4-methyl-pyridin-2-yl)-pyrazol-1-ylmethyl-amine; L ₂ is 1-{4-[(3,5-dimethyl-pyrazol-1-ylmethyl)-pyrazol-1-ylmethyl-amino]-phenyl}-ethanone; L ₃ is 1-{4-[(3,5-dimethyl-pyrazol-1-ylmethyl)-[1,2,4]triazol-1-ylmethyl-amino]-phenyl}-ethanone, and L ₄ is 2-[(3,5-dimethyl-pyrazol-1-ylmethyl)-[1,2,4]triazol-1-ylmethyl-amino]-6-methyl-pyrimidin-4-ol, and copper ions salts Cu(II) are (Cu(CH₃COO)₂, CuCl₂, Cu(NO₃)₂ and CuSO₄). In order to determine factors influencing the catecholase activity of these complexes, the effect of ligand nature, ligand concentration, nature of solvent and nature of counter anion has been studied. The best activity of catechol oxidation is given by the combination formed by one equivalent of ligand L ₂ and one equivalent of Cu(CH₃COO)₂ in methanol solvent which is equal to 9.09 µmol L^?1 min^?1. The Michaelis–Menten model is applied for the best combination, to obtain the kinetic parameters, and we proposed the mechanism for oxidation reaction of catecholase.