Viability property for a backward stochastic differential equation and applications to partial differential equations

In the present paper, we study conditions under which the solutions of a backward stochastic differential equation remains in a given set of constraints. This property is the so-called “viability property”. In a separate section, this condition is translated to a class of partial differential equations. Received: 23 April 1998 / Published online: 14 February 2000     

Nucleation and Crystallization of PLDA-b-PE and PLLA-b-PE Diblock Copolymers

The nucleation and crystallization of two types of strongly segregated poly(lactide)-block-polyethylene diblock copolymers with an approximate 50/50 composition has been investigated. One material contains an amorphous PLDA block (PLDA-b-PE) and the other contains a semicrystalline PLLA block (PLLA-b-PE). The overall isothermal crystallization rate of the PLLA block was slowed down as compared to homo-PLLA by the covalently bonded PE chains that were molten at the PLLA crystallization temperatures. This crystallization rate depression of the PLLA block produces a coincident crystallization process when PLLA-b-PE is cooled down from the melt at rates larger than 2 °C/min. The overall crystallization rate of the PE block is faster when it is covalently bonded to previously crystallized PLLA than when it is attached to a rubbery PDLA block, this results from a nucleation effect of PLLA on the PE block. Polarized Light Optical Microscopy (PLOM) confirmed the confined nature of the crystallization process within lamellar microdomains for both diblock copolymers, since neither PLLA nor PE are capable of breaking out and spherulites can not be formed.     

Was wissen Calamari über Sarin? Enzymatische Dekontamination von Nervenkampfstoffen

Together with detection and use of protective clothing, decontamination is the third important part in NBC defence and NBC protection. Enzymes play an important role in the research field of new and environmentally friendly decontaminants. In 1946, organophosphate cleaving enzymes were first mentioned, and in the next decades further enzymes (i.e., DFPase) against G‐type nerve agents were discovered. After the cloning of the DFPase gene sequence in the 90s, the potential of DFPase as an environmentally friendly decontaminant was shown. In technical decontamination experiments, it was shown that the conditions for an enzyme‐based decontamination concept could be met for one class of chemical agents. However, the success of a general enzyme decontamination concept depends on the discovery of new enzymes against other classes of chemical agents, i.e., mustard and VX.     

RAFT Polymerization of Pentafluorophenyl Methacrylate: Preparation of Reactive Linear Diblock Copolymers

Summary: Reversible addition fragmentation chain transfer (RAFT) polymerization of pentafluorophenyl methacrylate (PFMA) was carried out in the presence of cumyldithiobenzoate and 4‐cyano‐4‐((thiobenzoyl)sulfanyl)pentanoic acid, respectively. These chain transfer agents with 2,2′‐azoisobutyronitrile (AIBN) as initiator yielded the active ester polymer poly(PFMA) with up to 17 000 g · mol⁻¹ and low polydispersity index ( < 1.2). Kinetic analysis using ¹⁹F NMR spectroscopy and gel permeation chromatography (GPC) measurements showed controlled polymerization behavior for both chain transfer agents. Successful preparation of linear diblock copolymers consisting of an active ester block and methyl methacrylate, N‐acryloylmorpholine, or N,N‐diethylacrylamide, respectively, could be demonstrated. These polymers could easily react with amines in a polymer analogous reaction to form multifunctional polymers.

     

Di­methyl (1R,8R)-1,11,11-tri­methyl-2,3-di­aza­tri­cyclo­[6.2.1.02,6]­undeca-3,5-diene-4,5-di­carboxyl­ate,a chiral mol­ecule with an approximate centrosymmetric crystal structure

The crystal structure of the title compound, C₁₆H₂₂N₂O₄, has two independent chiral mol­ecules related by a pseudo-inversion centre. 14 of the 22 non-H atoms have a centrosymmetric counterpart within a tolerance of 0.17 Å. A search of the Cambridge Structural Database [Spring 2000; Allen & Kennard (1993). Chem. Des. Autom. News, 8 , 1, 31–37] shows at least 10% of the crystal structures reported in the literature with space group P2₁ and Z = 4 to be chiral compounds with a pseudo-P2₁/c packing.     

An Ordered Nanoporous Monolith from an Elastomeric Crosslinked Block Copolymer Precursor

Summary: An ordered nanoporous monolith was prepared from a poly(isoprene‐b‐dimethylsiloxane) (PI‐PDMS) hexagonally packed cylinder precursor. The PDMS cylinders were macroscopically aligned, the PI was crosslinked with dicumyl peroxide, and the PDMS was removed using tetrabutylammonium fluoride. The stability of the pores depended on the modulus of the matrix. At high crosslink density the pores were stable, but they collapsed at a low crosslink density. The nanoporous materials could be swollen in toluene.

A scanning electron micrograph of the end‐on view of crosslinked degraded poly(isoprene‐b‐dimethylsiloxane).     

Effect of pH on interface composition and on quality of oil-in-water emulsions made with hen egg yolk

Constituents of egg yolk are key ingredients of many food emulsions. They contribute to create an interfacial film between oil and water, which determines largely the characteristics of the emulsions. Food emulsions prepared with yolk are made at various pHs. However, the effect of pH on the adsorption of yolk constituents and on the composition of the interfacial film is not known. The present study deals with the influence of pH (3, 6 and 9), on protein interface concentration and composition, change in interfacial tension, and oil droplet diameter, of emulsions made with yolk. Emulsions were prepared as follows: 0.5% w/v of yolk; oil volume fraction: 0.375, homogenisation rate: 20 000 rpm/2 min. pH 6 provided the best conditions to prepare emulsion with yolk. The average diameter of oil droplets was lower at pH 6 (8.5 μm) than at pH 3 (11.8 μm) and pH 9 (13.5 μm). The interfacial protein concentration was higher at pH 6 (1.7 mg m⁻²) than at pH 3 and pH 9 (0.5 mg m⁻²). At pH 6, all the proteins of yolk, except phosvitin, were adsorbed at the interface and the interfacial tension at steady-state was lower (10 mN m⁻¹) than at pH 3 (15 mN m⁻¹) and pH 9 (30 mN m⁻¹). At pH 3, proteins at the interface are mainly phosvitin, and, at pH 9, some apoproteins of LDL and HDL. The pH modulates the composition of yolk proteins at the interface, mainly by modifying the net charge of the proteins causing their repulsion or dimerisation.     

On coupled gradient-dependent plasticity and damage theories with a view to localization analysis

Combinations of gradient plasticity with scalar damage and of gradient damage with isotropic plasticity are proposed and implemented within a consistently linearized format. Both constitutive models incorporate a Laplacian of a strain measure and an internal length parameter associated with it, which makes them suitable for localization analysis.The theories are used for finite element simulations of localization in a one-dimensional model problem. The physical relevance of coupling hardening/softening plasticity with damage governed by different damage evolution functions is discussed. The sensitivity of the results with respect to the discretization and to some model parameters is analyzed. The model which combines gradient-damage with hardening plasticity is used to predict fracture mechanisms in a Compact Tension test.     

The Kelvin–Nevanlinna–Royden criterion for p-parabolicity

We generalize the so called Kelvin–Nevanlinna–Royden criterion for the parabolicity of manifolds to the case of p-parabolicity for all . Received July 29, 1998; in final form September 25, 1998