The power of adaptive algorithms for functions with singularities

This is an overview of recent results on complexity and optimality of adaptive algorithms for integrating and approximating scalar piecewise r-smooth functions with unknown singular points. We provide adaptive algorithms that use at most n function samples and have the worst case errors proportional to n^−r for functions with at most one unknown singularity. This is a tremendous improvement over nonadaptive algorithms whose worst case errors are at best proportional to n⁻¹ for integration and n^−1/p for the L^p approximation problem. For functions with multiple singular points the adaptive algorithms cease to dominate the nonadaptive ones in the worst case setting. Fortunately, they regain their superiority in the asymptotic setting. Indeed, they yield convergence of order n^−r for piecewise r-smooth functions with an arbitrary (unknown but finite) number of singularities. None of these results hold for the L^∞ approximation. However, they hold for the Skorohodmetric, which we argue to be more appropriate than L^∞ for dealing with discontinuous functions. Numerical test results and possible extensions are also discussed.     

A Study of the Activity of Recombinant Mn-Superoxide Dismutase in the Presence of Gold and Silver Nanoparticles

Applied Biochemistry and Biotechnology - Superoxide dismutase (SOD) is one of the best characterized enzyme maintaining the redox state in the cell. A bacterial expression system was used to...     

An alternative approach to controlled release of oxprenolol from the implantable delivery system based on biodegradable copolymer and genistein

This paper describes the development of covalent star-shaped poly(L-lactide/?-caprolactone) random copolymer-oxprenolol (OXP) conjugates as a potential approach to controlling drug release from implantable delivery systems. We prepared synthesized materials containing 14–17 mol% OXP, which were conjugated via an ester bond. The conjugates, which were composed of biodegradable copolyester chains, natural genistein as a central core and drug, were characterized by hydrogen nuclear magnetic resonance (¹H-NMR), Fourier transform infrared spectroscopy (FTIR) and viscosity methods. We evaluated the cyto- and genotoxicity of the synthesized copolymeric matrices, followed by the conjugates, with bacterial luminescence, protozoan and Salmonella typhimurium TA1535 assays. Furthermore, we performed in vitro mammalian assays of the obtained products with V79 cells. We found that the in vitro release of OXP from the obtained star-shaped conjugates was dependent on the structure of the synthesized biodegradable matrices.     

STM studies of fusion of cholesterol suspensions and mixed 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC)/cholesterol vesicles onto a Au(111) electrode surface

Electrochemical scanning tunneling microscopy (EC-STM) has been applied to study the structure of the film formed by fusion of cholesterol suspensions and mixed dimyristoylphosphatidylcholine (DMPC)/cholesterol vesicles on a Au(111) electrode surface. It has been demonstrated that cholesterol molecules assemble at the gold support into several structures templated by the crystallography of the metal surface and involving flat or edge-on adsorbed molecules. Studies of the film formed by fusion of mixed DMPC/cholesterol vesicles revealed that ordered domains of either pure DMPC or pure cholesterol were formed. These results indicate that, at the metal surface, the molecules released by the rupture of a vesicle initially self-assemble into a well-ordered monolayer. The self-assembly is controlled by the hydrocarbon skeleton-metal surface interaction. In the case of mixed DMPC/cholesterol vesicles, the molecule-metal interactions induce segregation of the two components into single component domains. However, the molecule-metal interaction induced monolayer is a transient phenomenon. When more molecules accumulate at the surface, the molecule-molecule interactions dominate the assembly, and the monolayer is transformed into a bilayer.     

Electron paramagnetic resonance (EPR) and stable isotope records of paleoenvironmental conditions during peat formation

EPR spectroscopy was performed on four peat cores (1-2.5 m depth) collected from Yellowstone National Park (USA), Scotland (UK) and Lower Silesia (Poland) to study peat formation process. The stable free radicals identified in all investigated samples are semiquinone type and g-parameters range from 2.0030 to 2.0048. The highest g-values are characteristic of upper well-aerated peat layers and gradually decrease with depth. The lowest g-values are typical of relatively old fens and bogs where anaerobic conditions are expected and carbonization processes are advanced. The decrease in g-parameter value is connected with conjugation of semiquinone units with gradually augmented polyaromatic units in the peat substance. Generally the radical concentration increases with depth (0.05-5x10(17) spins/gram). However the g-values, line width parameters, and spin concentrations exhibit strong variations in some peat layers. Variation of these parameters observed for certain peat horizons correlate with the variation of carbon stable isotopic composition. For the old well-conserved peat deposits (e.g. Scotland/UK, approximately 5600 BP), variation of EPR parameters may be used to study paleo redox conditions.     

Structure and electrochemical behaviour of 4,7-diazaheptyl-trimethoxy-silane and vinyl-trialkoxy-silane adsorbed at silver surface

Novel self-assembled monolayers were obtained on silver using 4,7-diazaheptyl-trimethoxy-silane (SiN) and vinyl-trialkoxy-silane (SiVA, where the alkyl group is 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60-eicozaoxa- hexaheptaconan). It was shown that thus modified metal surface was protected against electrooxidation. A densely packed monolayer remained stable and did not desorb from the Ag electrode on the potential cycling. The structure of SiN and SiVA as well as their complexes with Li⁺ cations were calculated and visualised by the AM1d and PM5 semi-empirical methods.     

The synthesis of new potential photosensitizers. 1. Mono-carboxylic acid derivatives of tetraphenylporphyrin

Abstract  

A series of mono-alkylcarboxylic acid derivatives of tetraphenylporphyrin have been prepared. All the porphyrins were completely characterized by use of mass, ¹H NMR, UV–visible, and fluorescence spectroscopy. Experimental log P were determined by use of reversed-phase thin-layer chromatography with use of log P _Rekker. These porphyrins are potential photosensitizers in photodynamic therapy.     

Electron scattering on C6F6 and SF6 molecules

Total absolute cross sections for electron scattering on hexafluorobenzene, C₆F₆, and sulfur hexafluoride, SF₆, molecules, have been measured as a function of impact energy from 0.6 to 250 eV. The total cross section for C₆F₆ exhibits a very broad peak stretching from 10 to 100 eV with some weak features near 9.5 and 15 eV superimposed on the peak. Apart from the well-known low-energy resonant structures in the SF6 total cross section function, a new weak resonant feature close to 25 eV has been noticed in the present experiment, in accordance with earlier theoretical calculations.     

Autocatalytic modification of the prosthetic heme of horseradish but not lactoperoxidase by thiocyanate oxidation products. A role for heme-protein covalent cross-linking

The mammalian peroxidases eosinophil peroxidase, lactoperoxidase (LPO), and myeloperoxidase oxidize thiocyanate to the antimicrobial agents hypothiocyanous acid (HOSCN) and (SCN)2 and are part of a defense system that protects the host from infections. Horseradish peroxidase (HRP), a plant enzyme, also oxidizes thiocyanate. We report here that the prosthetic heme vinyl groups of HRP react with the catalytically generated HOSCN and (SCN)2 to form at least nine vinyl-modified heme adducts. Mass spectrometry combined with analysis of the equivalent reactions of HRP reconstituted with 2- or 4-cyclopropylheme, or mesoheme-d4, shows that all of the prosthetic heme modifications result from addition of oxidized thiocyanate to the heme vinyl groups. No delta-meso-substitution of the heme was observed, in contrast to what is observed with radical agents. Model studies show that incubation of either HRP with preformed HOSCN or a solution of heme with preformed (SCN)2 gives rise to the same products obtained in the HRP-catalyzed reaction. Model studies also demonstrate that the SCN* radical, if formed, should add to a meso-carbon. These findings implicate an electrophilic addition mechanism. In contrast, oxidation by LPO of thiocyanate, the normal substrate of this enzyme, does not result in heme modification. In view of the demonstrated intrinsic reactivity of the heme group, LPO must actively suppress heme modification. As the key difference between LPO (and other mammalian peroxidases) and HRP is the presence of two covalent ester links between the heme and the protein, we propose that these links contribute to steric protection of the adjacent heme vinyl groups.