Depth profiling of latex blends of fluorinated and fluorine‐free acrylates with laser‐induced secondary mass spectrometry

We explored phase separation and self‐assembly of perfluoroalkyl segments at the surface of polymer films obtained from latices of semifluorinated acrylate copolymers and the corresponding latex blends of nonfluorinated and semifluorinated polyacrylates. With laser‐induced secondary mass spectrometry the fluorine distribution was measured after annealing above the minimum film‐forming temperature of the polymers up to a depth of several micrometers. Depth profiles of a semifluorinated acrylate homopolymer and latex blends thereof with fluorine‐free alkylacrylates with 25, 50, and 75 mol % semifluorinated acrylate as well as a copolymer comprised of alkyl acrylate and semifluorinated acrylate (50/50 mol %) were investigated. In the case of latex blends containing both semifluorinated polyacrylates and fluorine‐free or low‐fluorine polymers, self‐assembly accounted for enrichment of the perfluoroalkyl segments at the surface. Coatings exhibiting low surface energy and having a substantially reduced total fluorine content were obtained. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 360–367, 2003     

Completeness and unbiased estimation of mean vector in the multivariate group sequential case

We consider estimation after a group sequential test about a multivariate normal mean, such as a χ² test or a sequential version of the Bonferroni procedure. We derive the density function of the sufficient statistics and show that the sample mean remains to be the maximum likelihood estimator but is no longer unbiased. We propose an alternative Rao-Blackwell type unbiased estimator. We show that the family of distributions of the sufficient statistic is not complete, and there exist infinitely many unbiased estimators of the mean vector and none has uniformly minimum variance. However, when restricted to truncation-adaptable statistics, completeness holds and the Rao-Blackwell estimator has uniformly minimum variance.     

Random multiblock poly(ester amide)s containing poly(L‐lactide) and cycloaliphatic amide segments: Synthesis and biodegradation studies

Novel multiblock poly(ester amide)s containing poly(L ‐lactide) and cycloaliphatic amide segments were synthesized from telechelic oligomer of α,ω‐hydroxyl terminated poly(L ‐lactide), 1,3‐cyclohexylbis(methylamine), and sebacoylchloride by the “two‐step” interfacial polycondensation method. The blocky nature of PEAs was established by FTIR and ¹H NMR spectroscopies. The effect of relative content of ester and amide segments on the crystallization nature of PEAs was investigated by WAXD and DSC analyses. PEAs having lower content of PLLA, PEA 1 and PEA 2, showed a crystallization pattern analogous to polyamides, whereas PEA 3, having higher content of PLLA, showed two crystalline phases characterized by polyester and polyamide segments. Random nature of PEAs was observed from single T_g values. Biodegradation studies using the enzyme lipase from Candida Cylindracea showed higher degradation rate for PEA 3 than that for PEA 1 and PEA 2. FTIR, ¹H NMR, and DSC analyses of the degraded products indicated the involvement of ester linkages in the degradation process. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3250–3260, 2006     

Stability of transonic shocks in supersonic flow past a wedge

In this paper we study the stability of transonic shocks in steady supersonic flow past a wedge. We take the potential flow equation as the mathematical model to describe the compressible flow. It is known that in generic case such a problem admits two possible location of shock, connecting the flow ahead it and behind it. They can be distinguished as supersonic-supersonic shock and supersonic-subsonic shock (or transonic shock). Both these possible shocks satisfy the Rankine-Hugoniot conditions and entropy condition. In this paper we prove that the transonic shock is also stable under perturbation of the coming flow provided the pressure at infinity is well controlled.     

Theory and Application of Characteristic Finite Element Domain Decomposition Procedures for Coupled System of Dynamics of Fluids in Porous Media

For a coupled system of multiplayer dynamics of fluids in porous media,the characteristic finiteelement domain decomposition procedures applicable to parallel arithmetic are put forward.Techniques suchas calculus of variations,domain decomposition,characteristic method,negative norm estimate,energy methodand the theory of prior estimates are adopted.Optimal order estimates in L~2 norm are derived for the error inthe approximate solution.     

Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem

In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders.     

Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations

We study here instability problems of standing waves for the nonlinear Klein–Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave's frequency or the wave's speed of propagation and on the nonlinearity.     

A simple model for magnetic after-effects in magnetite at room temperature

Magnetic after-effects in vacancy-doped magnetite at room temperature are considered on the basis of a statistical thermodynamic treatment. In this paper we study the kinetics of a very small vacancy concentration distributed on the four non-equivalent octahedral sites of the inverse spinel structure. It is to be noted that satisfactory agreement is found between recent experimental results and the theoretical model.     

Corrigendum to the paper ``Adjoining an Order Unit to a Matrix Ordered Space'

An error has been detected (and also corrected) in Theorem 2.8 of the paper entitled “Adjoining an Order Unit to a Matrix Ordered Space” (Positivity, (2005)9: 207–223; DOI ). Accordingly, some of the results of the paper have been modified. Also, a notion of C*-matricially, Riesz normed spaces has been introduced.