Solving stochastic convex feasibility problems in hilbert spaces

In a stochastic convex feasibility problem connected with a complete probability space (Ω,A,μ) and a family of closed convex sets (C_ω)_ωεΩ in a real Hilbert space H, one wants to find a point that belongs to C_ω for μ almost all ω ε Ω. We present a projection based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a μ almost common point. We then give a general condition assuring norm convergence of this equation to that μ almost common point     

Lichtbrechung und Dispersion

Ohne Zusammenfassung     

Finding projections onto the intersection of convex sets in Hilbert spaces. II

We present a parallel iterative algorithm to find the shortest distance projection of a given point onto the intersection of a finite number of closed convex sets in a real Hilbert space; the number of sets used at each iteration step, corresponding to the number of available processors, may be smaller than the total number of sets. The relaxation coefficient at each iteraction step is determined by a geometric condition in an associated Hilbert space, while for the weights mild conditions are given to assure norm convergence of the resulting sequence. These mild conditions leave enough flexibility to determine the weights more specifically in order to improve the speed of convergence.     

Triblock Copolymer Based on Poly(propylene oxide) and Poly(1‐[11‐acryloylundecyl]‐3‐methyl‐imidazolium bromide)

The controlled atom transfer radical polymerization of an ionic liquid, 1‐(11‐acryloylundecyl)‐3‐methyl imidazolium bromide (ILBr), from both ends of a telechelic poly(propylene oxide) (PPO) macroinitiator, end‐functionalized with bromoisobutyryloyl is reported. The resulting highly water‐soluble triblock, poly(ILBr‐b‐PO‐b‐ILBr) is multistimuli responsive. This new class of triblocks exhibits classical surface activity in lowering surface tension at the air–water interface and in modifying wetting in waterborne coatings. It also immunizes model colloids against coagulation induced by Debye–Hückel (indifferent electrolyte) electrostatic screening. Further, sol–gel thermoreversibility is unexpectedly found as an additional form of stimuli responsiveness.     

Polymer dewetting via stimuli responsive structural relaxation-contact angle analysis

Thin films of a stimuli-responsive homopolymer dewet as a stimulus response after anion exchange of the imidazolium's counter anion. Contact angle analysis and interfacial energy considerations indicate dewetting goes counter to increasing spreading coefficient. Intrafilm stress arising from structural relaxation drives the dewetting.     

Stimuli responsive poly(1-[11-acryloylundecyl]-3-methyl-imidazolium bromide): dewetting and nanoparticle condensation phenomena

A stimuli-responsive homopolymer poly(ILBr) is fabricated via a "two-phase" atom transfer radical polymerization (ATRP) process, where ILBr stands for the reactive ionic liquid surfactant, 1-[11-acryloylundecyl]-3-methyl-imidazolium bromide. An extraordinarily wide molecular weight distribution (PDI = 6.0) was obtained by introducing the initiator (4-bromomethyl methyl benzoate) in a heterogeneous two-phase process. The molecular weight distribution of poly(ILBr) was characterized by size-exclusion chromatography (SEC). The resulting homopolymer was found to be surface active and stimuli responsive. Poly(ILBr) films coated on quartz exhibit stimuli-responsive dewetting after ion exchange of Br(-) by PF(6)(-). This dewetting phenomenon can be understood in chain segmental terms as a stimuli-induced structural relaxation and appears to be the first such reported stimuli-responsive polymeric dewetting. Titrating aqueous poly(ILBr) with aqueous bis(2-ethylhexyl)sulfosuccinate induces nanophase separation and results in the condensation of nanoparticles 30-60 nm in diameter.     

Quantitative liquid chromatographic determination of cefatrizine in serum and urine by fluorescence detection after post-column derivatization

A fast, specific and sensitive high-performance liquid chromatographic procedure for the determination of cefatrizine, an orally active cephalosporin, in serum and urine is proposed. The drug is determined by the internal standard method, using cephradine as the internal standard. The separation is carried out on a reversed-phase column, filled with octadecylsilane chemically bonded microparticles. The eluent is a mixture of acetonitrile with 0.025 M sodium phosphate buffer (pH 7). Quantitation is effected by fluorescence detection of the fluorophores formed after post-column derivatization with fluorescamine in a packed-bed reactor. The chromatographic conditions and the conditions for the post-column derivatization are discussed. The method has been applied to serum and urine samples, which were analysed after deproteinization with trichloroacetic acid and injection of the clear supernatant. The accuracy and reproducibility of the procedure were investigated by the determination of the cefatrizine content in spiked serum and urine samples.     

On partially orderedf-groupoids

Acta Mathematica Hungarica -