Limiting distributions of the solutions of the many-dimensional Bürgers equation with random initial data. I

We find Gaussian limiting distributions of the solutions of the many-dimensional Bürgers equation with the initial condition given by a homogeneous isotropic Gaussian random field with strong dependence.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 870–877, July, 1994.     

Time-Changed Processes Governed by Space-Time Fractional Telegraph Equations

We study global and local stabilities of the stationary zero solution to certain infinite-dimensional stochastic differential equations. The stabilities are in terms of fractional powers of the linear part of the drift. The abstract results are applied to semilinear stochastic partial differential equations with non-Lipschitzian drift terms and, in particular, to some specific models of population dynamics. We also expose the stabilizing effect of noise on the otherwise unstable zero solution

As a basic tool we use the Forward Inequality, a generalization of Kolmogorov's forward equation; it is an application of Lyapunov's second method with a sequence of Lyapunov functionals     

A geometric decomposition of spaces into cells of different types II: Homology theory

We develop the homology theory of CW(A)-complexes, generalizing the classical cellular homology theory for CW-complexes. A CW(A)-complex is a topological space which is built up out of cells of a certain core A.     

A note on the spectral characterization of dumbbell graphs

The dumbbell graph, denoted by D_a,b,c, is a bicyclic graph consisting of two vertex-disjoint cycles C_a and C_b joined by a path P_c+3 (c-1) having only its end-vertices in common with the two cycles. By using a new cospectral invariant for (r,r+1)-almost regular graphs, we will show that almost all dumbbell graphs (without cycle C₄ as a subgraph) are determined by the adjacency spectrum.     

New Procedure for the Determination of 3-Nitrotyrosine in Plasma by GC–ECD

A method suitable for the determination of 3-nitrotyrosine, a well known marker of nitro-oxidative stress, in plasma by GC–ECD has been investigated. After deproteinisation, SPE and LC separation, 3-nitrotyrosine was derivatised by a single-step procedure to the corresponding N-heptafluorobutyryl heptafluorobutyl ester and analysed. The precision and reliability of the procedure were assured by using 4-nitrophenylalanine as internal standard and a diverter valve to protect the detector. The method was applied to the analysis of volunteers’ plasma samples.     

Interaction between aspergillic acid and iron(III): A potentiometric,UV–Vis,H NMR and quantum chemical study

The complex formation equilibria of aspergillic acid with iron(III) were studied by potentiometric and spectrophotometric methods. The ligand was prepared by a biosynthetic route and its purity checked by MS and ¹H NMR spectroscopies. Some structural features of the ligand are discussed on the basis of NMR results. The iron(III) coordination model is compared with those of two other cyclic hydroxamates, 1-hydroxy-2-pyridinone and 1,4-dihydroxy-2-pyridinone, and its features are discussed on the basis of quantum chemical calculations.     

Ortho-spirocarbonates and ortho-spirothiocarbonates: synthesis, functionalization and coupling

This paper describes a new efficient synthesis of 2,2′-spirobi-(1,3-benzoxathiole) (1), 2,2′-spirobi-(1,3-benzodithiole) (2) and 2,2′-spirobi-(1,3-benzodioxole) (3). Compound 3 has been functionalized by means of metallation reaction followed by electrophilic quenching to give carboxylic acids, aldehydes and alcohols. Furthermore compound 3 was subjected to homo-coupling and its dimeric structure was determined by XRD analysis.     

Wound Healing Potential of an Oleoresin Essential Oil Chemotype from Canarium schweinfurthii Engl.

This study was conducted to investigate the chemical composition of essential oil (EO) extracted from an oleoresin of Canarium schweinfurthii widespread in the Gabonese tropical forest. A great variability in the chemical composition of EO was observed, among which a chemical profile rich in terpinolene and α-phellandrene (31.2 and 21.8%, respectively), was found and tested as a natural active ingredient for topical applications. After the evaluation of eye and skin irritancy and sensitization potentials of EO on in vitro and in chemico models, the in vitro modulating potential on a model of wound re-epithelialization was assessed. The terpinolene and α-phellandrene-rich chemotype have been proven to accelerate wound healing in a dose-dependent manner (concentration range from 1.8 to 9.0 μg/mL). In addition, the ability of this EO to modulate the pro-inflammatory response in human keratinocytes stimulated by UVB was observed in vitro by the reduction in levels of interleukin 6 (IL-6) and tumour necrosis factor-alpha (TNF-α), suggesting a possible implication during the inflammation phase of wound healing. Despite the high variability in EO composition, a method of solid-phase microextraction (SPME) of the oleoresin headspace is proposed for the in situ identification of the terpinolene and α-phellandrene-rich chemotype instead of conducting hydrodistillation. These results offer interesting perspectives for the development of innovative natural ingredients for the topical route, ingredients obtained in an eco-responsible and non-destructive way.     

Rhamnogalacturonan II: Chemical Synthesis of a Substructure Including α-2,3-Linked Kdo**

The synthesis of a fully deprotected Kdo-containing rhamnogalacturonan II pentasaccharide is described. The strategy relies on the preparation of a suitably protected homogalacturonan tetrasaccharide backbone, through a post-glycosylation oxidation approach, and its stereoselective glycosylation with a Kdo fluoride donor.