Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a C^r diffeomorphism f of a surface, are not C^1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.     

Determination of naphthalene and total methylnaphthalenes in gasoline using direct injection-mass spectrometry

A high-speed determination of naphthalene and total methylnaphthalenes using a non-separative method based on direct injection into the mass spectrometer was performed. The results obtained for total methylnaphthalenes were very similar to those provided with fast gas chromatography-mass spectrometry (GC-MS). However, the non-separative method afforded higher concentrations in the determination of naphthalene than those found when fast GC-MS was used. We propose a correction that removes this error very satisfactorily and allows the same results to be obtained with both methodologies. The non-separative method is rapid, simple and - in view of the results - highly suitable for the determination of naphthalene and total methylnaphthalenes in gasoline samples.     

A nonstandard definition of finite order ultradistributions

Taking into account that finite-order ultradistributions are inverse Fourier transforms of finite-order distributions a nonstandard representation is obtained for one-dimensional finite-order ultradistributions.     

Synthesis of amphiphilic sulfonamide halogenated porphyrins: MALDI-TOFMS characterization and evaluation of 1-octanol/water partition coefficients

Porphyrins are key precursors for development of photosensitizers for photodynamic therapy. A new series of ortho-halogenated tetraarylporphyrins with sulfonamide substituents have been synthesized via chlorosulfonation reaction and characterized by MALDI-TOFMS. To predict their partition properties, log K_OW of a selected range of the synthesized halogenated amphiphilic porphyrins is described. A significant effect of the number and type of halogen group as well as on the number of sulfonamide side chain was observed. The determined 1-octanol/water partition coefficients showed that it is possible to obtain compounds with a wide range of lipophilicities, from log K_OW=−2.71 till log K_OW>4, which are suitable to optimize the biological efficacy of this class of sensitizers.     

Substituted Pyrazolo[3,4‐d]pyrimidines: Microwave‐Assisted,Solvent‐Free Synthesis and Biological Evaluation

A simple and efficient method has been developed for the synthesis of various pyrazolo[3,4‐d]pyrimidines by using microwave irradiation under solvent‐free conditions. The advantages of applying microwave irradiation compared with the classical method were demonstrated. The structures of all the compounds were confirmed by the usual techniques and, in two cases, by X‐ray analysis. The compounds did not display appreciable ability to inhibit xanthine oxidase activity. Screening for antifungal activity showed that some derivatives were active against four fungi, with more significant results for Botrytis.     

Identification of 1‐palmitoyl‐2‐linoleoyl‐phosphatidylethanolamine modifications under oxidative stress conditions by LC‐MS/MS

Phosphatidylethanolamines are a major class of phospholipids found in cellular membranes. Identification of the alterations in these phospholipids, induced by free radicals, could provide new tools for in vivo diagnosis of oxidative stress. In this study, 1‐palmitoyl‐2‐linoleoyl‐phosphatidylethanolamine oxidation products, induced by the hydroxyl radical, were studied using LC‐MS and LC‐MS/MS. Data obtained allowed the identification and separation of isomeric oxidative products with modifications in the sn‐2 acyl chain, attributed to long‐ and short‐chain products. Among long‐chain products keto, keto‐hydroxy, hydroxy, poly‐hydroxy, peroxy and hydroxy–peroxy derivatives were identified. Product ions formed by loss of two H₂O molecules vs loss of HOOH, allowed the identification of, respectively, di‐ (or poli‐) hydroxy vs peroxy derivatives. Location of functional groups was determined by the product ions formed by cleavage of C–C bonds, in the vicinity of the oxidation positions, allowing the identification of C9, C12 and C13 as the predominant substituted positions. Short‐chain products identified comprised aldehydes, hydroxy‐aldehydes and carboxylic derivatives, with modified sn‐2 acyl lengths of C7–C9 and C11, C12. Among the short‐chain products identified, C9 products showed higher relative abundance. Copyright © 2009 John Wiley & Sons, Ltd.     

Hyperfinite representation of distributions

Hyperfinite representation of distributions is studied following the method introduced by Kinoshita [2,3], although we use a different approach much in the vein of [4]. Products and Fourier transforms of representatives of distributions are also analysed.     

Innovative Eco-Friendly Hydrogel Film for Berberine Delivery in Skin Applications

Hydrogel formulations (masks or patches, without tissue support) represent the new frontier for customizable skin beauty and health. The employment of these materials is becoming popular in wound dressing, to speed up the healing process while protecting the affected area, as well as to provide a moisturizing reservoir, control the inflammatory process and the onset of bacterial development. Most of these hydrogels are acrylic-based at present, not biodegradable and potentially toxic, due to acrylic monomers residues. In this work, we selected a new class of cellulose-derived and biodegradable hydrogel films to incorporate and convey an active compound for dermatological issues. Films were obtained from a combination of different polysaccharides and clays, and berberine hydrochloride, a polyphenolic molecule showing anti-inflammatory, immunomodulatory, antibacterial and antioxidant properties, was chosen and then embedded in the hydrogel films. These innovative hydrogel-based systems were characterized in terms of water uptake profile, in vitro cytocompatibility and skin permeation kinetics by Franz diffusion cell. Berberine permeation fitted well to Korsmeyer–Peppas kinetic model and achieved a release higher than 100 µg/cm² within 24 h. The latter study, exploiting a reliable skin model membrane, together with the biological assessment, gained insights into the most promising formulation for future investigations.     

Some Problems of Information Neurodynamics

The goal of neural science is to understand the brain, how we perceive, move, think, and remember. All of these things are dynamical processes which are taking place in a complex, non-stationary and noisy environment. This means that these dynamical processes at all levels from small neural networks to behavior should be stable against perturbations but flexible and adaptive. The goal of neurodynamics is to formulate the main dynamical principles which can be a basis of such behavior and to predict the possible activities of neurons and neural ensembles using the tools of nonlinear dynamics. In this paper we discuss our last results related to the mostly challenging part of neurodynamics: information processing by dynamical neural ensembles.