meso-substituted aromatic 34pi core-modified octaphyrins: syntheses,characterization and anion binding properties

Modified octaphyrins with 34pi electrons have been synthesized and characterized following a simple synthetic methodology. An acid-catalyzed alpha,alpha coupling of tetrapyrranes containing furan, thiophene and selenophene rings resulted in the formation of the respective octaphyrins in relatively good yield. Solution studies by (1)H NMR and 2D NMR methods and single crystal Xray structural characterization reveal an almost flat structure with two heterocyclic rings inverted. Specifically, in 14 two selenophene rings (one on each biselenophene unit) are inverted while in 15 two furan rings (one on each bifuran unit) are inverted when the meso substituent are mesityl groups. On changing the mesityl substituent to m-xylyl group as in 19, the location of ring inversion shifts to pyrrole rings (one on each bipyrrole unit) indicating the dependence of structure on the meso substituents. UV/Vis studies, both in freebase and protonated forms reveal typical porphyrinic character and the aromatic nature of the octaphyrins. The Deltadelta values evaluated by (1)H NMR spectroscopy also support their aromatic nature. The protonated forms of octaphyrins bind TFA anion in a 1:2 ratio. The TFA anions are located one above and below the plane of the octaphyrin macrocycle and they are held by weak electrostatic NH-O interactions similar to that observed for protonated rubyrins. However, in the present case, there is an additional non-electrostatic CH-O interaction involving beta-CH of the inverted heterocyclic ring and the carbonyl oxygen of the TFA. Furthermore, inter molecular interactions between the Cbond;H of the meso-mesityl group and the fluorine of CF(3) group of bound TFA leads to the formation of one-dimensional supramolecular arrays with interplanar distance of 13 A between two octaphyrins.     

The left-definite Legendre type boundary problem

The left-definite Legendre type boundary problem concerns the study of a fourth-order singular differential expressionM _k [–] in a weighted Sobolev spaceH generated by a Dirichlet inner product. The fourth-order differential equation

On the polynomial τ-functions for the KP hierarchy and the bispectral property

We show that the -functions obtained from Schur polynomials lead to wave functions w(x ₁, x ₂, ... ; k) that possess the following bispectral property: There exists a differential operator B{k,_k}, independent of x ₁ , such that B{k,_k}w = {x ₁}w, where {x ₁} is independent of k. This extends for the KP hierarchy some earlier results of J. J. Duistermaat and F. A. Grünbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.     

Oscillations of certain second order nonlinear differential equations

A second order nonlinear differential equation

A new method for the determination of the 34S/32S ratio of water-soluble sulphur in soil

A new method for the determination of the ³⁴S/³²S ratio of water-extractable sulphate in soil is described. Soils are extracted directly with deionized water, which is evaporated down. The remaining residue is then rehydrated and transferred to tin cups containing an adsorbent and mixed with an oxygen donor (V₂O₅). Samples are then analysed using a continuous flow isotope ratio mass spectrometer. The new method requires around 10?g soil per determination, compared to much larger amounts (up to kilograms) of soil required for the previous methods. Sample preparation and subsequent analysis is quick and efficient. The method is demonstrated using a number of soils collected from around the world to provide a range of determined δ³⁴S values. The δ³⁴S values of water-extractable sulphur were broadly similar to those of the soil total sulphur.     

Numerical solutions for jump-diffusions with regime switching

This paper is devoted to numerical solutions for a class of jump-diffusions with regime switching. After briefly reviewing the notion of jump-diffusions with regime switching, finite-difference procedures are constructed. Under simple conditions, it is proved that the algorithm converges to the desired limit by means of a martingale problem formulation. Numerical experiments are carried out to demonstrate the performance of the algorithm.     

Oscillatory properties of first order linear functional differential equations

Oscillatory properties of retarded and advanced functional differential equations are investigated.In the first part, the study concerns equations with piecewise constant arguments, which found applications in certain biomedical problems. Then, results of some authors are generalized for general equations with many argument deviations. Finally, applications are given to equations with linear transformations of the argument.     

Square-mean weighted pseudo almost automorphic solutions for non-autonomous stochastic evolution equations

In this paper, we first introduce the concepts and properties of the square-mean weighted pseudo almost automorphy and the square-mean bi-almost automorphy for a stochastic process. With these preliminary settings and by virtue of the theory of the semigroups of the operators, the Banach fixed point theorem and the stochastic analysis techniques, we investigate the well-posedness of the square-mean weighted pseudo almost automorphic solutions for a general class of non-autonomous stochastic evolution equations that satisfy either global or only local Lipschitz condition. Moreover, we estimate the boundedness of attractive domain for the case where the only local Lipschitz condition is taken into account. Finally, we provide two illustrative examples to show the practical usefulness of the analytical results that we establish in the paper.     

Sur les Transformations Simultanées de Deux Équations Différentielles Linéaires du Deuxième Ordre dans Elles-mêmes

AMS (MOS) Classification 34C20     

An integrative in silico approach to the structure of Omp33-36 in Acinetobacter baumannii

Omp33-36 in A. baumannii, a bacterium causing serious nosocomial infections, is a virulence factor associated with the pathogen metabolic fitness as well as its adherence and invasion to human epithelial cells. This protein is also involved in interaction of the bacteria with host cells by binding to fibronectin. Moreover, Omp33-36 renders cytotoxicity to A. baumannii in addition to inducing apoptosis and modulation of autophagy. In the present study, an integrated strategy is launched to pierce into the 3D structure of Omp33-36 protein. The signal peptide within the sequence was determined, then, topology as well as secondary and tertiary structures of the protein were predicted. The mature protein assigned as a 14-stranded barrel in which residues 1–19 is removed as signal peptide. The obtained 3D models were evaluated in terms of quality; and then, served as queries to find similar protein structures. The hits were analyzed regarding topology among which 14-stranded were considered. The most qualified model was refined and then its sequence aligned to its counterpart similar structure protein (CymA from Klebsiella oxytoca). The determined structure of Omp33-36 could justify its porin function and carbapenem-resistance associated with the loss of this protein.