Interpolation and approximation in

Assume a standard Brownian motion W=(W_t)_t[0,1], a Borel function such that f(W₁)L₂, and the standard Gaussian measure γ on the real line. We characterize that f belongs to the Besov space , obtained via the real interpolation method, by the behavior of , where is a deterministic time net and the orthogonal projection onto a subspace of ‘discrete’ stochastic integrals with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the problem is reduced to a deterministic one. The approximation numbers a_X(f(X₁);τ) can be used to describe the L₂-error in discrete time simulations of the martingale generated by f(W₁) and (in stochastic finance) to describe the minimal quadratic hedging error of certain discretely adjusted portfolios.     

Metachromins R--T, new sesquiterpenoids from marine sponge Spongia sp

Three new sesquiterpenoids, metachromins R--T (1--3), have been isolated from an Okinawan marine sponge Spongia sp. The structures and stereochemistry of 1--3 were elucidated on the basis of the spectroscopic data. Metachromins S (2) and T (3) showed modest cytotoxicity.     

Molecular aggregates of partially fluorinated quaternary ammonium salt gemini surfactants

The size and shape of novel partially fluorinated gemini surfactant 1,2-bis[dimethyl-(3-perfluoroalkyl-2-hydroxypropyl)ammonium]ethane bromide (CnFC3-2-C3CnF, where n=4, 6, and 8) were investigated in aqueous solution by means of light scattering and transmission electron microscopy (TEM). The sizes of these molecular aggregates changed with increasing carbon number of the alkyl chain and concentration. For example, the apparent hydrodynamic radius by dynamic light scattering was 18 nm at a concentration of cmcx5 for n=4, 115 nm at the cmcx15 for n=6, and 62 nm at the cmcx30 for n=8, at 298.2 K. The shapes of CnFC3-2-C3CnF aggregates drastically changed with the alkyl chain length; the aggregates were mainly in the form of large or irregular small aggregates (n=4), string-like aggregates (n=6), and vesicles (n=8). The bromide-ion activity was measured using a bromide-ion-selective electrode to determine the degree of counterion binding to the aggregates. The degree of counterion binding to aggregate was very small compared with that in the typical hydrogenated gemini surfactants. These results indicated that the small curvature of large aggregates was not influenced by an electrostatic repulsion between the cationic head groups in the case of the bulky molecular volume of fluorinated gemini surfactants.     

Surface modification with well-defined biocompatible triblock copolymers Improvement of biointerfacial phenomena on a poly(dimethylsiloxane) surface

To improve interfacial phenomena of poly(dimethylsiloxane) (PDMS) as biomaterials, well-defined triblock copolymers were prepared as coating materials by reversible addition-fragmentation chain transfer (RAFT) controlled polymerization. Hydroxy-terminated poly(vinylmethylsiloxane-co-dimethylsiloxane) (HO–PV_lD_mMS–OH) was synthesized by ring-opening polymerization. The copolymerization ratio of vinylmethylsiloxane to dimethylsiloxane was 1/9. The molecular weight of HO–PV_lD_mMS–OH ranged from (1.43 to 4.44) × 10⁴, and their molecular weight distribution (M_w/M_n) as determined by size-exclusion chromatography equipped with multiangle laser light scattering (SEC-MALS) was 1.16. 4-Cyanopentanoic acid dithiobenzoate was reacted with HO–PV_lD_mMS–OH to obtain macromolecular chain transfer agents (macro-CTA). 2-Methacryloyloxyethyl phosphorylcholine (MPC) was polymerized with macro-CTAs. The gel-permeation chromatography (GPC) chart of synthesized polymers was a single peak and M_w/M_n was relatively narrow (1.3–1.6). Then the poly(MPC) (PMPC)–PV_lD_mMS–PMPC triblock copolymers were synthesized. The molecular weight of PMPC in a triblock copolymer was easily controllable by changing the polymerization time or the composition of the macro-CTA to a monomer in the feed. The synthesized block copolymers were slightly soluble in water and extremely soluble in ethanol and 2-propanol.

Surface modification was performed via hydrosilylation. The block copolymer was coated on the PDMS film whose surface was pretreated with poly(hydromethylsiloxane). The surface wettability and lubrication of the PDMS film were effectively improved by immobilization with the block copolymers. In addition, the number of adherent platelets from human platelet-rich plasma (PRP) was dramatically reduced by surface modification. Particularly, the triblock copolymer having a high composition ratio of MPC units to silicone units was effective in improving the surface properties of PDMS.

By selective decomposition of the Si–H bond at the surface of the PDMS substrate by irradiation with UV light, the coating region of the triblock copolymer was easily controlled, resulting in the fabrication of micropatterns. On the surface, albumin adsorption was well manipulated.     

Novel use of mesoporous aluminas as supports for Cp2ZrCl2 and Cp*ZrMe3: Ethylene polymerization and formation of polyethylene nanofibers

Mesoporous aluminas with average pore sizes of 4.3–7.8 nm were prepared by anodization of an aluminum film (AAO), and by a sol–gel templating method (TPL). In addition to a commercial alumina and sulfated TPL, the aluminas were used as supports for cyclopentadienyl zirconocene dichloride (Cp₂ZrCl₂) and trimethyl(η5‐pentamethylcyclopentadienyl)zirconium (Cp*ZrMe₃) and tested in the polymerization of ethylene. The metallocenes supported on the alumina prepared with the templating method and its sulfated modification exhibited polymerization activities of 440 and 350 kg_PE/(mol_Zr × h × bar), respectively, comparable to that obtained with silica‐supported metallocenes (390 kg_PE/(mol_Zr × h × bar)). The acid site distribution of the aluminas was studied with FTIR and temperature programmed desorption (TPD) of pyridine, and also the amount of medium and strong acid sites was determined gravimetrically from the adsorption of pyridine. Relative to the surface area, AAO with the highest amount of acid sites (2.10 μmol_py/m) adsorbed Cp₂ZrCl₂ and Cp*ZrMe₃ the most. Study of the polymers' morphology with a scanning electron microscope revealed polyethylene nanofibers in all the polymer samples, also in those obtained from the reference polymerizations with homogeneous Cp₂ZrCl₂ and Cp*ZrMe₃. This finding suggests that a catalyst support with a tubular pore structure is not a prerequisite for the formation of polymer nanofibers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4002–4012, 2007     

Cooperativity in a spin transition ferrous polymer: Interacting domain model, thermodynamic, optical and EPR study

A new thermodynamic model is proposed in order to account for the high spin low spin conversion in metal-organic polymers. The model, based on the idea that the spin conversion occurs in interacting domains of like-spin metal ions, allows to explain most of the important features of various types of spin conversion. The sine qua non condition of the existence of spin transitions with hysteresis is obtained. In the case of very large cooperativity, the model predicts unusual behaviour of the spin conversion system due to a low-temperature metastable high spin state. Existence of such a state is interesting in the context of the light induced excited spin state trapping recently observed in some ferrous compounds. The model is applied to interpret the spin transition in polycrystalline ferrous polymer [Fe _1-y Cu _y (Htrz)₂ trz] (BF ₄) with y = 0.00, 0.01 and 0.10, detected by differential scanning calorimetry, optical reflectivity and electron paramagnetic resonance. The domain size and the interaction energy between the domains are estimated as, respectively, n = 11 and for the y = 0 compound. As the copper content is growing, n and tend to decrease, resulting in transformations of the shape of hysteresis loop which becomes less steep, narrows and shifts to lower temperatures. The electron paramagnetic resonance gives further evidence of the presence of like-spin domains. Received 27 November 1998 and Received in final form 19 April 1999     

Real structures of Teichmüller spaces, Dehn twists, and moduli spaces of real curves

An orientation reversing involution of a topological compact genus surface induces an antiholomorphic involution of the Teichmüller space of genus g Riemann surfaces. Two such involutions and are conjugate in the mapping class group if and only if the corresponding orientation reversing involutions and of are conjugate in the automorphism group of . This is equivalent to saying that the quotient surfaces and are homeomorphic. Hence the Teichmüller space has distinct antiholomorphic involutions, which are also called real structures of ([7]). This result is a simple fact that follows from Royden's theorem ([4]) stating that the the mapping class group is the full group of holomorphic automorphisms of the Teichmüller space (). Let and be two real structures that are not conjugate in the mapping class group. In this paper we construct a real analytic diffeomorphism such that This mapping d is a product of full and half Dehn–twists around certain simple closed curves on the surface . This has applications to the moduli spaces of real algebraic curves. A compact Riemann surface admitting an antiholomorphic involution is a real algebraic curve of the topological type . All fixed–points of the real structure of the Teichmüller space , are real curves of the above topological type and every real curve of that topological type is represented by an element of the fixed–point set of . The fixed–point set is the Teichmüller space of real algebraic curves of the corresponding topological type. Given two different real structures and , let d the the real analytic mapping satisfying (1). It follows that d maps onto and is an explicit real analytic diffeomorphism between these Teichmüller spaces. Received 8 December 1997; accepted 12 August 1998     

On all-optical laser cleaning and inspection of contaminated concave metal surfaces

A technique for all-optical laser cleaning and surface quality monitoring of concave metal surfaces is suggested. Contaminated pharmaceutical punches from a tablet compression machine were cleaned using high-energy laser pulses. Image information obtained from a diffractive-optical-element-based sensor was used in inspection of the surface quality change of the concave punches due to laser cleaning. Alternative method for mechanical cleaning of punches is introduced, which is based on simultaneous laser cleaning and surface quality inspection of the punches.     

Review: Different types of ordering

Homogeneous structures A_xB_y with identical A–A or B–B self‐coordination numbers T₁, T₂, T₃, of nearest, next‐nearest and third neighbors are selected. The maximum T_i values are 2 2 2 (1D row), 6 6 6 (2D hexagonal net) and 12 6 24 (3D cubic close‐packing). Reduced T₁ or T₂ values for A_xB_y can be related with attractive or repulsive A–A (or B–B) interactions. A single set of T₁ T₂ T₃; y/x values was obtained for y/x = 1–4 and 6. The y/x = 2 structures of three equivalent positions A, B and C are unfavourable for A = ⊕ and B = ⊖ charge or direction of magnetic moments. The spatial distribution of positive and negative potential near A⁺ and B⁻ positions gives rise to neutral C positions. Frustrated magnetic moments at C positions are disordered. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

ASAXS study of styrene‐grafted sulfonated poly(vinylidene fluoride) membranes

Small‐angle and wide‐angle X‐ray scattering and anomalous small‐angle X‐ray scattering were used to investigate proton‐conducting membranes prepared by radiation‐induced styrene grafting and sulfonation of commercial poly(vinylidene fluoride) (PVDF‐g‐PS) films. The membranes retain the lamellar and highly oriented structure of the original PVDF films even through excessive grafting and sulfonation. The sulfonate groups aggregate in the central part of the amorphous layers, where they form a weakly ordered structure that does not show any preferred orientation. This structure is suggested to be lamellar with alternate metal‐sulfonated hydrate and PVDF‐g‐PS layers. The lamellar period is 15.1 Å. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1734–1748, 2000