Multidentate ligands for the synthesis of multi-metallic complexes

The reaction of the Schiff base species tris-((2-hydroxybenzylidene)aminoethyl)-amine (TrenSal) and tris-((2-hydroxy-5-bromobenzylidene)aminoethyl)amine (Tren5BrSal) with the acetates of nickel and zinc are reported. Two trimetallic complexes (M₃L₂) of Tren5BrSal with nickel and zinc have been crystallographically characterised. The attempted crystallisation of bis-(tris-((2-hydroxybenzylidene)aminoethyl)amine nickel) nickel from solutions containing TMEDA lead to the production of two novel complexes: namely a nickel adduct of the partially hydrolysed TrenSal ligand and an interesting nickel bromide–carbonate salt. [(TrenSal)₂Ni₃] is reacted with PbCl₂ to form a novel tetrametallic complex, [{(TrenSal)Ni}Pb(NC₅H₅)Cl]₂, where a Pb₂Cl₂ moiety replaces the nickel at the core of the complex. Extending the study to include the related hexadentate ligand, 1,1,1-tris-((2-hydroxybenzylidene)-aminomethyl)propane (TEtSal), we were able to isolate and characterise both [(TEtSal)₂Ni₃] and [{(TEtSal)Ni}₂Pb].     

Synthesis of new azo compounds based on N-(4-hydroxypheneyl)maleimide and N-(4-methylpheneyl)maleimide

Maleic anhydride was reacted with p-aminophenol and p-toluidine in the presence of di-phosphorus pentoxide (P?O?) as a catalyst to produce two compounds: N-(4-hydroxy-phenyl)maleimide (I) and N-(4-methylphenyl)maleimide (II). The new azo compounds I(a-c) and II(a-c) were prepared by the reaction of I and II with three different aromatic amines, namely aniline, p-aminophenol and p-toluidine. The structures of these compounds were confirmed by CHN, FT-IR, 1H-NMR, 13C-NMR, mass spectrum and UV/Vis spectroscopy.     

On Some Measure Convolution Operators in Neutron Transport Theory

We show how some fundamental spectral properties of neutron transport semigroups in L ^p spaces (1<p<+∞), such as stability of essential spectra or critical spectra and related results, can be inferred from the study of two measure convolution operators on  \(\mathbb{R}^{n}\) .     

Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in a water-in-oil microemulsion

In the limit of a large duffusivity ratio, spotlike solutions in the two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion are studied. It is shown analytically that such spots undergo an instability as the diffusivity ratio is decreased. An instability threshold is derived. For spots of small radius, it is shown that this instability leads to a spot splitting into precisely two spots. For larger spots, it leads to deformation, fingering patterns, and space-filling curves. Numerical simulations are shown to be in close agreement with the analytical predictions.     

Influence of the Metal Ion on the Two‐Photon Absorption Properties of Lanthanide Complexes Including Near‐IR Emitters

The synthesis of tris(2‐thenoyltrifluoroacetonate)lanthanide(III) complexes featuring a diethylaminostyryl‐2,2′‐bipyridine coligand was achieved for lanthanum; the near‐infrared (NIR) emitters neodymium, erbium, and ytterbium; and the transition‐metal yttrium. The photophysical properties were thoroughly studied, and it was demonstrated that the conjugated bipyridine ligand acts as a good antenna for the sensitization of the NIR emitters. The two‐photon absorption (TPA) properties of all five complexes were investigated by using both two‐photon excited fluorescence and the Z‐scan method. We demonstrate that the nature of the rare earth ion has almost no influence on the TPA properties centered on the conjugated bipyridyl ligand. Finally, we show that Yb^III is sensitized by a two‐photon antenna effect, and that Nd^III is mostly sensitized by a one‐photon process involving direct excitation of forbidden f–f transitions.     

A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients

We propose a piecewise-linear, time-stepping discontinuous Galerkin method to solve numerically a time fractional diffusion equation involving Caputo derivative of order μ ∈ (0, 1) with variable coefficients. For the spatial discretization, we apply the standard continuous Galerkin method of total degree ≤ 1 on each spatial mesh elements. Well-posedness of the fully discrete scheme and error analysis will be shown. For a time interval (0, T) and a spatial domain Ω, our analysis suggest that the error in \(L^{2}\left ((0,T),L^{2}({\Omega })\right )\)-norm is \(O(k^{2-\frac {\mu }{2}}+h^{2})\) (that is, short by order \(\frac {\mu }{2}\) from being optimal in time) where k denotes the maximum time step, and h is the maximum diameter of the elements of the (quasi-uniform) spatial mesh. However, our numerical experiments indicate optimal O(k² + h²) error bound in the stronger \(L^{\infty }\left ((0,T),L^{2}({\Omega })\right )\)-norm. Variable time steps are used to compensate the singularity of the continuous solution near t = 0.     

Aromatization of cyclohexadienes by TEMPO electro-mediated oxidation: Kinetic and structural aspects

Cyclohexadienes are easily converted into the corresponding aromatics in excellent yield (>90%) in the presence of 2,2,6,6-tetramethyl-1-oxopiperidinium ion (TEMPO⁺). The TEMPO radical was used in catalytic amount and was electrochemically regenerated in the presence of 2,6-lutidine as a base in hydro-organic medium (AcCN/H₂O 95/5). This work has been focused on the kinetic aspects. We have demonstrated that the reactivity of different cyclohexadienes is strongly dependent on the configuration of the double bonds and on the nature of the substituents. Competition between allylic functionalization and aromatization has been observed during the oxidation of 1,2-dihydro-4-phenylnaphthalene.     

Intelligence Way from Eco-friendly Synthesis Strategy of New Heterocyclic Pyrazolic Carboxylic α-Amino Esters

The α-amino acid derivatives constitute a class of compounds of particular medicinal and synthetic attention and considerable interest has been devoted to their synthesis in recent years. In the present work, we develop the computational study of the synthesis reaction of new pyrazolyl α-amino esters derivatives using the Gaussian 09 based on the DFT/B3LYP density functional theory method, with the base 6-31G(d, p) to ensure the possibility of carrying out these reactions within the laboratory of synthesis. Indeed, this research has encouraged us to establish an economical synthesis strategy of these products in overall yields of 73.5% to 87% to have access to new active biomolecule through the O-alkylation reaction between methyl α-azidoglycinate N-benzoylated and primary pyrazole alcohols[(3,5-dimethyl-1H-pyrazol-1-yl)methanol, (1H-pyrazol-1-yl)methanol and (3-ethoxy-5-methyl-1H-pyrazol-1-yl)methanol] under different operating conditions. The structure of the prepared heterocyclic systems was characterized by conventional spectroscopic techniques, like ¹H NMR, ¹³C NMR, and MS. The results revealed that the experimental study is in good correlation with the computational one.     

Selection criteria for two-parameter solutions to scalar-tensor gravity

We investigate the generic properties of static, spherically symmetric, asymptotically flat solutions to the field equations describing gravity minimally coupled to a nonlinear self-gravitating real scalar field. Five corollaries and a theorem on selection criteria for two- and one-parametric solutions are proven and conditions for obtaining particle-like solutions, black holes or naked singularities are derived. A series of exact solutions in closed forms including different black holes, naked singularities and particle-like solutions, all of which obey the weak energy condition at spatial infinity, are provided. Two further corollaries elaborate on the behavior of solutions at spatial infinity, critical mass, mass density, pressure and energy conditions.     

Solutions analytiques globales de problèmes linéaires avec argument absorbant

The aim of this work is the study of the Cauchy problem for a large class of linear operators, non-necessarily kowalevskian, with shrinking argument. We prove the well posedness of this problem in the space of analytic functions with respect to time and Gevrey class with respect to spatial variable. Our tools are based on formal norms of Leray and Waelbroeck [J. Leray, L. Waelbroeck, Norme formelle d'une fonction composée (Préliminaire à l'étude des systèmes non linéaires, hyperboliques non stricts), in: Colloque de Liège, CBRM, 1964, pp. 145-152. [23]], already used in [Cl. Wagschal, Le problème de Goursat non linéaire, J. Math. Pure Appl. 58 (1979) 309-337; D. Gourdin, M. Mechab, Solution globale d'un problème de Cauchy linéaire, J. Funct. Anal. 202 (2003) 123-146].