Existence and multiplicity of solutions for second order periodic systems with the <Emphasis Type="Italic">p</Emphasis>-Laplacian and a nonsmooth potential

In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The second is for systems and it is based on the nonsmooth local linking theorem.     

Microelectrode array fabricated in low temperature cofired ceramic (LTCC) technology

This work presents the development of a novel construction of an integrated microelectrode array. The device was fabricated on a ceramic support, with the use of low temperature cofired ceramics technology. Model potassium-selective membranes were applied on the surface of PdAg/AgCl electrodes formed on the ceramic substrate. The obtained microsensors exhibited very good repeatability, reproducibility, and sensitivity. The array of microelectrodes covered with polymeric layers of various selectivities was applied as an electronic tongue to differentiate between various diet supplements.     

A Bistable Molecular Switch Driven by Photoinduced Hydrogen‐Atom Transfer

The occurrence of photoinduced hydrogen atom transfer between two remote spots of a molecule is experimentally demonstrated. This photoprocess involves the intermediacy of an intramolecular “crane”. In an experimental case study, 7‐hydroxy‐4‐methylquinoline‐8‐carbaldehyde monomers isolated in low‐temperature Ar matrices are investigated. On UV (λ>295 nm) irradiation, a hydrogen atom is transferred from the O⁷H group to the N¹ atom of the quinoline ring. Subsequent irradiation with UV (λ>360 nm) light reveals that the phototransformation is partially photoreversible. In the studied hydrogen‐atom‐transfer process, the exocyclic carbaldehyde group plays the role of an intramolecular crane. The possible application of systems analogous to 7‐hydroxy‐4‐methylquinoline‐8‐carbaldehyde as optically driven molecular switches is discussed.     

Influence of electron beam irradiation on growth of Phytophthora cinnamomi and its control in substrates

Very extensive production procedure, especially in plants growing under covering, require methods, which would allow quick elimination or substantial reduction of populations of specific pathogens without affecting the growth and development of the cultivated plants. Among soil-borne pathogens, the Phytophthora species are especially dangerous for horticultural plants. In this study, irradiation with electron beam was applied to control Phytophthora cinnamomi. The influence of irradiation dose on the reduction of in vitro growth and the population density of the pathogen in treated peat and its mixture with composted pine bark (1:1), as well as the health of Chamaecyparis lawsoniana and Lavandula angustifolia plants were evaluated. Application of irradiation at a dose of 1.5 kGy completely inhibited the in vitro development of P. cinnamomi. This irradiation effect was connected with the disintegration of the hyphae and spores of the species. Irradiation of peat and its mixture with composted pine bark with 10 kGy resulted in the inhibition of stem base rot development in Ch. lawsoniana. Symptoms of the disease were not observed when the substrates were treated with 15 kGy. In the case of L. angustifolia, stem root rot was not observed on cuttings transplanted to infected peat irradiated at a dose of 10 kGy. Irradiation of the horticultural substrates did not affect plant growth.     

Porous alumina membranes with branched nanopores as templates for fabrication of Y-shaped nanowire arrays

Porous anodic alumina membranes with Y-branched and double-branched nanopores were fabricated by the stepwise reduction of anodizing potential during the second step of anodization carried out in 0.3 M oxalic acid. The process of nanoporous layer formation and influence of anodizing parameters on structural features of as-obtained anodic aluminum oxide (AAO) membranes were discussed in detail. The pore rearrangement process occurring after the potential decrease was investigated on the basis of the current density vs. time curves, and results were correlated with the field-emission scanning electron microscope images of the pore bottoms taken after different anodizing durations. It was found that the reorganization of nanopores begins after 600 and 500 s from the time of the potential reduction to 42 and 30 V and the process seems to be completed after about 900 and 800 s, respectively. The through-hole AAO membranes were used as templates for the fabrication of gold and polystyrene nanowires via electrochemical deposition and simple immersing in the polymer solution, respectively. The arrays of hierarchically branched nanowires were synthesized, and the dimensions of nanowires were consistent with the shape and structure of used AAO templates.

     

A pair of positive solutions for the Dirichlet p(z)-Laplacian with concave and convex nonlinearities

We consider a nonlinear parametric Dirichlet problem driven by the anisotropic p-Laplacian with the combined effects of “concave” and “convex” terms. The “superlinear” nonlinearity need not satisfy the Ambrosetti-Rabinowitz condition. Using variational methods based on the critical point theory and the Ekeland variational principle, we show that for small values of the parameter, the problem has at least two nontrivial smooth positive solutions.     

Integral representation of random set-valued measures

Abstract

We consider random set-valued measures with values in a separable Banach space. We prove two integral representation theorems using measurable multifunctions and set-valued integrals. The first theorem is valid for all separable Banach spaces, while the second holds for reflexive separable Banach spaces.     

A geometric criterion for compactness of invariant subspaces

Let M be a non-compact homogeneous Riemannian manifold, and let Ω be a compact subgroup of isometries of M. We show, under general conditions, that the Ω-invariant subspace A _Ω of a normed vector space ${A\hookrightarrow L^q(M)}$ A ? L q ( M ) is compactly embedded into L ^q (M) if and only if the group Ω has no orbits with a uniformly bounded diameter in a neighborhood of infinity.     

Existence and uniqueness of positive solutions for the Neumann p-Laplacian

We consider a nonlinear Neumann problem driven by the p-Laplacian and with a Carathéodory reaction which satisfies only a unilateral growth restriction. Using the principal eigenvalue of an eigenvalue problem involving the Neumann p-Laplacian plus an indefinite potential, we produce necessary and sufficient conditions for the existence and uniqueness of positive smooth solutions.