Nonnegative solutions to reaction–diffusion system with cross-diffusion and nonstandard growth conditions

We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.     

A critical investigation of smoothed particle hydrodynamics applied to problems with free‐surfaces

In this paper, an in‐depth study of SPH method, in its original weakly compressible version, is achieved on dedicated 2D and 3D free‐surface flow test cases. These rather critical prototype problems shall constitute suitable test cases to get through when building a free‐surface SPH model. The present work aims at investigating various numerical aspects of this method, often little mentioned in literature. In particular, a great care is paid to the dynamic part of the solution, which is critical to the local hydrodynamic load prediction. The role of numerical errors in the development of acoustic frequencies in the pressure signals is discussed, as well as the influence of the choice of the sound velocity. On the shown test problems, it is also evidenced that some numerical tools are crucial to ensure the robustness and accuracy of the standard SPH method. The convergence of our model is heuristically proved on these nonlinear prototype tests, showing at the same time the very satisfactory level of accuracy reached. Through these tests, some other numerical specificities of the SPH method are discussed, such as the self‐redistribution of the particles occurring during the Lagrangian evolution. A higher order model is also proposed, and its advantages and drawbacks are discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Infra-Red Study of Tautomerism in Some Schiff Bases.

Infra-Red spectra of a series of substituted salicylaldehyde and 2-hydroxy-naphthaldehyde Schiff bases were used to investigate enol-keto tautomeric equilibrium. Two model compounds, namely, salicylidinaniline and naphthylidinequinolineamine Schiff bases were used to represent the enol and keto forms, respectively. From the IR spectra of the model compounds it was possible to assign the IR absorption for the C=O and the C=N groups in both the keto and the enol form. It was also possible to assign other absorptions which were either specific to the keto or the enol forms. Specific pattern were observed for all the studied compounds.     

On the solution of stochastic ordinary differential equations via small delays

dx(t)=g(x{t))dW(t) is proved using an approximating sequence of stochastic delay equationsGeneralizations of the approximation scheme are indicated for the Stratonovich case and when the Brownian motion W is replaced by a continuous semi-martingale.     

SYNTHESIS AND NMR SPECTROSCOPIC STUDY OF NEW 5-METHYLFURYL-CONTAINING SCHIFF BASES AND RELATED BIS(AMINOPHOSPHONATES)

The synthesis of three novel 5-methylfuryl-containing Schiff bases: N,N′-bis(5-methylfurfurylidene)-4,4′-diaminodiphenylmethane, N,N′-bis(5-methylfurfurylidene)-1,4-phenylenediamine, and N,N′-bis(5methylfurfurylidene)benzidine and the corresponding bis(aminophosphonates) derived from them, 4,4′-bis{N-methyl(diethoxyphosphonyl)-1-[(5-methyl)-2-furyl]} diaminodiphenylmethane, 1,4-bis { N-methyl(diethoxyphosphonyl)-1-[(5-methyl)-2-furyl]} diaminobenzene, and bis{N-methyl(diethoxyphosphonyl)-1-[(5-methyl)-2-furyl]}- benzidine, is reported. The compounds have been characterized by elemental analysis, TLC, IR, and NMR ( ¹ H, ¹³ C, and ³¹ P) spectra. For comparison, new ¹³ C and ³¹ P NMR data of three furyl-containing analogues of the above bis(aminophosphonates) are also regarded. The NMR studies of the two series of bis(aminophosphonates) reveal the presence of one diastereomer (meso or racemic form).     

Syntheses and molecular structures of four inorganic–organic hybrid compounds from N-containing aromatic bases and perchlorometallates of Zn,Cu, Sn,and Fe

Four organic–inorganic crystals, [(HL1)₂(ZnCl₄)]·H₂O (1) (L1?=?2-methylquinoline), [(HL1)₂(CuCl₄)] (2), [(HL2)₂SnCl₆] (3) (L2?=?6-bromobenzo[d]thiazol-2-amine), and [(HL3)FeCl₄] (4) (L3?=?5,7-dimethyl-1,8-naphthyridine-2-amine), derived from N-containing aromatic Brønsted bases and metal(II) chlorides (zinc(II) chloride, copper(II) chloride dihydrate, tin(II) chloride dihydrate, and iron(III) chloride hexahydrate) were prepared at room temperature and characterized by IR, X-ray structure analysis, elemental analysis, and TG analysis. The crystals are built up by perchlorometallates (Zn, Cu, Sn, and Fe) associated with organic cations through multiple non-covalent associations. X-ray diffraction analysis reveals that 1 and 2 have 3-D network structures built from hydrogen bonds between the cations and chlorometallates. Water molecules play an important role in structure extension in 1. Anhydrous 3 and 4 produced from 2-aminoheterocyclic derivatives display 2-D sheet structures. Arrangements of anions and cations are dominated by shape and size of cations, and also by the different structures of the chlorometallates as well as non-bonding interactions in the crystal structures. Except for 1, the other compounds are thermally stable below 240°C.     

Preparation of Chiral Amino Esters by Asymmetric Phase‐Transfer Catalyzed Alkylations of Schiff Bases in a Ball Mill

The asymmetric alkylation of Schiff bases under basic conditions in a ball mill was performed. The starting Schiff bases of glycine were prepared beforehand by milling protected glycine hydrochloride and benzophenone imine, in the absence of solvent. The Schiff base was then reacted with a halogenated derivative in a ball mill in the presence of KOH. By adding a chiral ammonium salt derived from cinchonidine, the reaction proceeded asymmetrically under phase‐transfer catalysis conditions, giving excellent yields and enantiomeric excesses up to 75 %. Because an equimolar amount of starting material was used, purification was greatly simplified.     

Determination of ß-Diketones by Oscillometric Titration

Abstract

An oscillometric titration technique has been applied to the determination of ß-diketones. Typical accuracies of about ± 1.5% were obtained for the compounds studied. The technique is rapid and simple, and should be suitable to the serial analyses of many compounds of pharmaceutical interest.     

Synthesis,structural characterization and biological studies of neodymium(III) and samarium(III) complexes with mercaptotriazole Schiff bases

A series of neodymium(III) and samarium(III) complexes of type [Ln(L)Cl(H₂O)₃] have been synthesized with Schiff bases (LH₂) derived from 3‐(phenyl/substituted phenyl)‐4‐amino‐5‐mercapto‐1,2,4‐triazoles and isatin. The structures of the complexes were established using elemental analysis, molar conductivities, magnetic moments, infrared, NMR (¹H, ¹³C) and UV–visible spectra, X‐ray diffraction and mass spectrometry. The thermal behaviour of these compounds under non‐isothermal conditions was investigated using thermogravimetry and differential thermogravimetry. The intermediates obtained at the end of various thermal decomposition steps were identified from elemental analysis and infrared spectral studies. All the ligands and their complexes were also screened for their antibacterial activity against Staphylococcus aureus and Bacillus subtilis and antifungal activity against Aspergillus niger, Aspergillus flavus and Colletotrichum capsici. The screening results were correlated with the structural features of the compounds. Copyright © 2015 John Wiley & Sons, Ltd.     

Liquid–liquid extraction of copper(II) with substituted salicylideneanilines from sulfate media

The liquid–liquid extraction of copper(II) with Schiff bases in chloroform from sulfate media is studied for pH and concentration of the extractant. Stoichiometry coefficients of the extracted species are determined by the slope analysis method. With salicylideneaniline, the copper(II) is extracted as a mixed chelate complex, CuL₂HL. In the presence of substituent, the copper is extracted as simple chelates, CuL₂. The trends in the values of extraction constants were explained in terms of the nature of the substituents.