Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems

Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation is possible and can be done in different ways. Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002 RID="*" ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and NSF DMS-9802367 RID="**" ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated     

The Inverse Problem of the Calculus of Variations for Sixth- and Eighth-order Scalar Ordinary Differential Equations

On the equation manifold of the 2nth-order scalar ordinary differential equation, n3,

η%-Superconvergence of Finite Element Solutions and Error Estimators

This paper is a summary of our study on the superconvergence of the finite element solutions and error estimators. We will persent the analysis of %-superconvergence for finite element solutions of the Poisson equation in the interior of meshes of triangles with straight edges, as well as the analysis at the boundary. The %-superconvergence via local averaging will also be presented, and the error estimators are compared in the sense of %-superconvergence.     

Common invariant subspaces for collections of operators

Let be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that is finitely quasinilpotent at a vectorx ₀X whenever for any finite subset of the joint spectral radius of atx ₀ is equal 0. If such collection contains a non-zero compact operator, then and its commutant have a common non-trivial invariant, subspace. If in addition, is a collection of positive operators on a Banach lattice, then has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia.     

Tight Distance-Regular Graphs

We consider a distance-regular graph with diameter d 3 and eigenvalues k = ₀ > ₁ > ... > _d . We show the intersection numbers a ₁, b ₁ satisfy

A Generalization of Herrlich's Question on Almost Reflective and Coreflective Subclasses of Top and Unif

H. Herrlich asked in Topology Appl. 49 (1993), 251–264, whether there are nontrivial classes of topological spaces that are almost reflective and almost coreflective at the same time. This question was dealt with (in Huek and Tozzi, Appl. Categ. Structures 4 (1996), 57–68) in a more general setting than almost reflective and almost coreflective classes. The present paper investigates a modified question: when a nontrivial generalized reflective class of topological or uniform spaces is equivalent to a generalized coreflective class of spaces.     

Optical properties of semiconducting iron disilicide thin films

The iron silicides samples were prepared by annealing of iron films evaporated onto silicon wafers and capped with amorphous silicon thin overlayers. Semiconducting FeSi₂ phase is formed by annealing at the temperatures from 550°C to 850°C. The optical properties of the FeSi₂ layers have been deduced from reflectance and transmittance measurements carried out in the temperature range of (77–380) K. The spectral dependence of the absorption coefficient favours direct allowed transitions with forbidden energy gap of 0.87eV at the room temperature. The application of a simple three-parameter semiempirical formula to the temperature dependence of the direct energy gaps leads to the following best fit parameters: the band gap at zero temperature E _g (0) = (0.895 ± 0.004)eV, the dimensionless coupling parameter S = 2.0 ± 0.3, and the average phonon energy <hw> = (46 ± 8)meV. By examining all the reported triplets of parameters for -FeSi₂ fabricated by different techniques and thermal processes, an obvious discrepancy can be found for the lattice coupling parameter and average phonon energy, although the bandgaps at 0 K are very similar. Unlike the theoretical prediction and the earlier reported result, our results do not show any evidence of a particularly strong electron-phonon interaction, which would give the lower carrier mobilities. -FeSi₂ seems to be an intriguing material where states with energies near the band edges permit ambiguous interpretation of the character of transitions. From optical model for the thin film-substrate system we found the index of refraction to be (5–5.9) in the photon energy interval from 0.65 to 1.15eV. There is also indication of an additional higher-energy absorption edge at l.05eV.     

Monte Carlo simulations of electron dynamics in N2/CO2 mixtures

Motivated by experimental investigations of electrical discharges in N₂/CO₂/H₂O, Monte Carlo (MC) electron dynamics simulations in atmospheric N₂/CO₂ mixtures were performed. The goal was to obtain electron energy distribution functions (EEDFs), mean free path, drift velocity, collision frequency and mean energy of electrons, rate coefficients of electron-impact reactions, ionisation and attachment coefficients, as functions of the reduced electric field strength (E/N) and of the concentration of individual gas components. The results obtained by MC simulations were fitted with polynomials of up to the 3rd order with reasonable accuracy for E/N above 80 Td. The studied parameters below 80 Td were strongly non-linear as functions of E/N. This is mostly due to the influence of elastic collisions of electrons with CO₂ molecules prevailing in CO₂-dominant mixtures for E/N < 40 Td, and vibrational excitation collisions of N₂ species prevailing in N₂-dominant mixtures for E/N from 40 to 80 Td. The effect of these electron-impact processes was specific for each of the studied parameters.     

Shaping of picosecond pulses for pumping optical parametric amplification

The use of temporally shaped pump pulses for optical parametric chirped-pulse amplification can increase the efficiency and suppress possible spectral distortions in this process. With this goal in mind a novel method for shaping narrowband picosecond pulses has been developed. The method is based on the pulse stacking principle, where replicas of the incoming pulse are created in a specially designed four-beam interferometer. The replicas are recombined with appropriate relative delays. The interferometer design allows for a unique flexibility in varying the pulse shape, since all relevant degrees of freedom, such as relative intensities and delays between the pulse replicas are independently adjustable. Here we describe the design of our device in detail and report on the experimental demonstration of its pulse-shaping capabilities. PACS 42.65.Yj; 42.65.Re; 42.81.Gs