Structure and properties of self-assembled fluorocarbon–silica nanocomposites

The formation of fluorocarbon–silica nanocomposites by the self-assembly of a fluorinated surfactant and aminoalkoxysilane coupling agents was studied by X-ray diffraction, electron microscopy, NMR spectroscopy and thermal analysis. The prepared materials posses a lamellar nanostructure consisting of non-crystalline fluorinated and condensed silica layers, the latter being very thin. The prepared materials show interesting properties for applications, such as hydrophobicity, thermal stability, high content of aminopropyl groups and low dielectric constant (≈2.8), which is almost independent on frequency. Moreover, the dielectric response can be interpreted in the framework of the Maxwell–Wagner model.     

Substituents effect on the properties of sulfonated polyimide copolymers

A series of sulfonated polyimide (SPI) copolymers containing methyl, methoxy, or fluorine groups were synthesized to elucidate the substituents effect on their proton conducting properties as well as thermal, hydrolytic, and oxidative stability for polymer electrolyte membrane fuel cell applications. SPIs of high molecular weight (M_w > 200 kDa, M_n > 80 kDa) along with the ion exchange capacity (IEC) varying between 1.34 and 1.91 mequiv/g were obtained, which gave tough, ductile, and flexible membranes by solution casting. The thermal properties of the SPIs were dominated by the electronic structure of the sulfonated aromatic rings. The electron‐donating methyl groups lowered the thermal decomposition temperature. The hydrolytic and oxidative stability was roughly in the order of IEC (the higher IEC membranes were less stable). Fluorine groups, either as ? F or ? CF₃, had negative effect on the hydrolytic and oxidative stability. In the water uptake and proton conductivity, hydrophobic components are rather more influential than the substituents. It was found out that the SPI(5, 8, 0.7) containing bis(phenoxy)biphenylene sulfone moieties as a rigid hydrophobic component showed the best balanced properties in terms of the stability and the proton conductivity for its rather low IEC. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4469–4478, 2008     

On a variational inequality associated with a stopping game combined with a control

We study a non-linear elliptic variational inequality which corresponds to a zero-sum stopping game (Dynkin game) combined with a control. Our result is a generalization of the existing works by Bensoussan [ Stochastic Control by Functional Analysis Methods (North-Holland, Amsterdam), 1982], Bensoussan and Lions [ Applications des Inéquations Variationnelles en Contrôle Stochastique (Dunod, Paris), 1978] and Friedman [ Stochastic Differential Equations and Applications (Academic Press, New York), 1976] in the sense that a non-linear term appears in the variational inequality, or equivalently, that the underlying process for the corresponding stopping game is subject to a control. By using the dynamic programming principle and the method of penalization, we show the existence and uniqueness of a viscosity solution of the variational inequality and describe it as the value function of the corresponding combined-stochastic game problem.     

On a local energy decay estimate of solutions to the hyperbolic type Stokes equations

In this paper, we discuss a local energy decay estimate of solutions to the initial-boundary value problem for the hyperbolic type Stokes equations of incompressible fluid flow in an exterior domain and a perturbed half-space. The equations are linearized version of the hyperbolic Navier–Stokes equations introduced by Racke and Saal [15], which are obtained as a delayed case for the deformation tensor in the incompressible Navier–Stokes equations. Our proof of the local energy decay estimate is based on Dan and Shibata [2]. In [2], they treated the dissipative wave equations in an exterior domain and discussed the local energy decay estimate. Our approach uses the fact that applying the Helmholtz projection to the hyperbolic type Stokes equations, we obtain equations similar to the dissipative wave ones.     

Asymptotic profile of solutions to nonlinear dissipative evolution system with ellipticity

We consider the Cauchy problem for the nonlinear dissipative evolution system with ellipticity on one dimensional space

Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schr?dinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in . Received: 13 July 2000 / Published online: 1 February 2002     

How to make a linear network code (strongly) secure

A linear network code is called k-secure if it is secure even if an adversary eavesdrops at most k edges. In this paper, we show an efficient deterministic construction algorithm of a linear transformation T that transforms an (insecure) linear network code to a k-secure one for any k, and extend this algorithm to strong k-security for any k . Our algorithms run in polynomial time if k is a constant, and these time complexities are explicitly presented. We also present a concrete size of \(|\mathsf{F}|\) for strong k-security, where \(\mathsf{F}\) is the underling finite field.