Two Families of Approximation Schemes for Delay Systems

Based on the Trotter-Kato approximation theorem for strongly continuous semigroups we develop a general framework for the approximation of delay systems. Using this general framework we construct two families of concrete approximation schemes. Approximation of the state is done by functions which are piecewise polynomials on a mesh (m-th order splines of deficiency m). For the two families we also prove convergence of the adjoint semigroups and uniform exponential stability, properties which are essential for approximation of linear quadratic control problems involving delay systems. The characteristic matrix of the delay system is in both cases approximated by matrices of the same structure but with the exponential function replaced by approximations where Padé fractions in the main diagonal resp. in the diagonal below the main diagonal of the Padé table for the exponential function play an essential role.     

[1.1]meta-Stilbenophanes as calixarene analogs: preparation, crystal structure, and cis-trans photoisomerization

Three isomers of [1.1]meta-stilbenophane were synthesized by the McMurry reaction of diarylmethane dialdehyde and their crystal structures and photochemical properties were investigated. X-ray crystallographic analyses of these isomers revealed that they were assigned to a trans-trans (t-t) form with a 1,3-alternate conformation, a cis-trans (c-t) form with a distorted-cone conformation, and a cis-cis (c-c) form with a 1,2-alternate conformation. A ¹H NMR study indicated that a t-t isomer could be completely transformed into a 35:65 mixture of c-t and c-c isomers by photoirradiation at 254 nm.     

Preparation of hexa-, penta- and tetraphenyl-2,6- and -2,7-naphthyridines

Di- and triphenyldibenzoylpyridines ( 1 ) were prepared by the condensation reaction of 3, 4-dibenzoyl-2, 5-diphenylthiophene ( 2 ) with methylamine derivatives 3 and by the subsequent oxidative ring cleavage of the resultant thieno[3, 4-c]pyridines 4 . The reaction of 1 with 3 afforded polyphenyl-2, 6- ( 5 ) and -2, 7-naphthyridines ( 6 ).     

Synthesis of [1]benzothienonaphthyridines

3-Chlorobenzo[b]thiophene-2-carbonyl chloride reacted readily with 2-amino-, 3-amino-, or 4-aminopyridine to give the corresponding amides. Photocyclization of the amides afforded the following lactams: [1]ben-zothieno[2,3-c][1,5]naphthyridin-6(5H)-one ( 14 ), [1]benzothieno[2,3-c][1,6]naphthyridin-6(5H)-one ( 7 ), [1]benzo-thieno[2,3-c][1,7]naphthyridin-6(5H)-one ( 11 ), and [1]benzothieno[2,3-c][1,8]naphthyridin-6(5H)-one ( 3 ). These lactams have been converted to other derivatives including in two instances the unsubstituted ring system.     

Cerebroside Langmuir monolayers originated from the echinoderms: II. Binary systems of cerebrosides and steroids

Two-component Langmuir monolayers formed on a subphase of 0.5M sodium chloride solution were investigated for two different cerebrosides (LMC-1 and LMC-2) with steroids of cholesterol (Ch) and cholesteryl sodium sulfate (Ch-S); i.e. LMC-1/Ch, LMC-1/Ch-S, LMC-2/Ch, and LMC-2/Ch-S were examined in terms of surface pressure (pi), the surface potential (DeltaV) and the dipole moment (mu( perpendicular)) as a function of surface area (A) by employing the Langmuir method, the ionizing electrode method, and the fluorescence microscopy. Surface potentials (DeltaV) of steroids were analyzed using the three-layer model proposed by Demchak and Fort. The miscibility of cerebrosides and steroids in the insoluble monolayers was examined by plotting the variation of the molecular area and the surface potential as a function of the steroid molar fraction (X(steroid)) based upon the additivity rule. From the A-X(steroid) and DeltaV(m)-X(steroid) plots, partial molecular surface area (PMA) and apparent partial molecular surface potential (APSP) were determined at the different surface pressures. The PMA and APSP with the mole fraction were discussed for the miscible system. Judging from the two-dimensional phase diagrams, they can be classified into two types. The first is a completely immiscible type; the combination of cerebrosides with cholesterol. The second is a negative azeotropic type, where cerebrosides and cholesteryl sodium sulfate are completely miscible both in the expanded state and in the condensed state. In addition, a regular surface mixture (the Joos equation for the analysis of the collapse pressure of two-component monolayers) allowed calculation of the interaction parameter (xi) and the interaction energy (-Delta epsilon) between the cerebrosides and Ch-S. The miscibility of cerebroside and steroid components in the monolayer state was also supported by fluorescence microscopy.     

Preparation of single‐walled carbon nanotubes‐induced poly(p‐oxybenzoyl) crystals

Crystallization of oligomers was applied for the preparation of single‐walled carbon nanotubes (SWNTs)/poly(p‐oxybenzoyl) (POB) crystals using SWNTs as a nucleating agent. Polymerization conditions were investigated to induce the crystallization of POB oligomers through SWNTs. SWNTs/POB plate‐like or lozenge‐shaped crystals were successfully prepared by direct polymerization of p‐hydroxybenzoic acid (HBA) in a mixed solvent of DMF/Py with TsCl in the presence of functionalized SWNTs. The size of the plate‐like crystals were ～200 nm to 3 μm. The crystals consisted of some layers, ～3 nm thick plates. Model reactions showed that esterification reactions proceed between functionalized SWNTs and HBA monomers in the polymerization system. The obtained crystals exhibited unique morphology and high crystallinity, producing a novel SWNT/POB hybrid. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1265–1277, 2008     

Semi-smooth Newton methods for the Signorini problem

Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.     

Surface functionalization chemistries on highly sensitive silica-based sensor chips

The surfaces of silica-based sensor chips, designed for evanescent-field-coupled waveguide-mode sensors, were functionalized using various surface chemistries. The immobilization of molecular entities on the functionalized silica surfaces was monitored using various microscopic techniques (scanning electron, fluorescence, and atomic force microscopies). Further, gold nanoparticle-based signal enhancement analyses were performed with protein conjugation on different functionalized surfaces using a waveguide-mode sensor. Based on these analyses, the sensor surfaces modified with glutaraldehyde (Glu) and carbonyldiimidazole were found to be good for molecules of different sizes. In addition, it can be inferred that the Glu-modified surface may be suitable for small molecules with diameters around 5 nm owing to its surface roughness. The modified surface with carbonyldiimidazole is suitable for the direct immobilization of larger molecules especially for biomolecular assemblies without intermediate chemical modifications.