Existence and uniform decay for Euler–Bernoulli beam equation with memory term

In this article we prove the existence of the solution to the mixed problem for Euler–Bernoulli beam equation with memory term. The existence is proved by means of the Faedo–Galerkin method and the exponential decay is obtained by making use of the multiplier technique combined with integral inequalities due to Komornik. Copyright © 2004 John Wiley & Sons, Ltd.     

Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type

The approximation of solutions to boundary value problems on unbounded domains by those on bounded domains is one of the main applications for artificial boundary conditions. Based on asymptotic analysis, here a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly. Existence and uniqueness of approximating solutions are proved together with asymptotically precise error estimates. One class of important examples includes boundary value problems for anisotropic elasticity and piezoelectricity. Copyright © 2004 John Wiley & Sons, Ltd.     

Mean curvature flows and isotopy of maps between spheres

Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area‐decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map. © 2004 Wiley Periodicals, Inc.     

Nowhere zero 4‐flow in regular matroids

Jensen and Toft 8 conjectured that every 2‐edge‐connected graph without a K₅‐minor has a nowhere zero 4‐flow. Walton and Welsh 19 proved that if a coloopless regular matroid M does not have a minor in {M(K_3,3), M*(K₅)}, then M admits a nowhere zero 4‐flow. In this note, we prove that if a coloopless regular matroid M does not have a minor in {M(K₅), M*(K₅)}, then M admits a nowhere zero 4‐flow. Our result implies the Jensen and Toft conjecture. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Synthesis of 2,7‐Carbazolenevinylene‐Based Copolymers and Characterization of Their Photovoltaic Properties

New electroactive and photoactive conjugated copolymers consisting of alternating 2,7‐carbazole and oligothiophene moieties linked by vinylene groups have been developed. Different oligothiophene units have been introduced to study the relationship between the polymer structure and the electronic properties. The resulting copolymers are characterized by UV‐vis spectroscopy, size‐exclusion chromatography, and thermal and electrochemical analyses. Bulk heterojunction photovoltaic cells from different copolymers and a soluble fullerene derivative, [6,6]‐phenyl‐C₆₁ butyric acid methyl ester, have been fabricated, and promising preliminary results are obtained. For instance, non‐optimized devices using poly(N‐(4‐octyloxyphenyl)‐2,7‐carbazolenevinylene‐alt‐3″,4″‐dihexyl‐2,2′;5′,2″;5″,2″′;5″′,2″″‐quinquethiophenevinylene 1″,1″‐dioxide) as an absorbing and hole‐carrier semiconductor exhibit power conversion efficiency up to 0.8 % under air mass (AM) 1.5 illumination. These features make 2,7‐carbazolenevinylene‐based and related polymers attractive candidates for solar‐cell applications.     

Water‐Stable,Magnetic Silica–Cobalt/Cobalt Oxide–Silica Multishell Submicrometer Spheres

A method to produce monodisperse magnetic composite spheres with diameters from less than 100 nm to more than 1 μm in water solution is reported. The spheres consist of a dielectric silica core and a cobalt/cobalt oxide shell which can be protected from further oxidation with an outer shell of silica or, alternatively, they can be covered with the polymer polyvinylpyrrolidone as a stabilizer. The formation of a uniform magnetic shell proceeds with the adsorption of metallic cobalt seeds, produced by the reduction of cobalt chloride with sodium borohydride, on a self‐assembled layer of polyelectrolytes on the silica core. In the second step, an outer silica shell can be formed by the hydrolysis and condensation of (3‐aminopropyl)trimethoxysilane and tetraethoxysilane. The double‐shell composite spheres show excellent sphericity, monodispersity, and a magnetic hysteresis loop at room temperature.     

Analytic Feynman integrals of transforms of variation of cylinder type functions over Wiener paths in abstract Wiener space

In this paper, we evaluate various analytic Feynman integrals of first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of cylinder type functions defined over Wiener paths in abstract Wiener space. We also derive the analytic Feynman integral of the conditional Fourier-Feynman transform for the product of the cylinder type functions which define the functions in a Banach algebra introduced by Yoo, with n linear factors.     

Fast DCT algorithm with fewer multiplication stages

A novel fast DCT scheme with reduced multiplication stages and fewer additions and multiplications is proposed. The proposed algorithm is structured so that most multiplications tend to be performed at the final stage, which reduces the propagation error that could occur in the fixed-point computation. Minimisation of the multiplication stages can further decrease the error