Well-posedness of general nonlocal nonhomogeneous boundary value problems for pseudodifferential equations with partial derivatives

In the article we study the questions of well-posedness of general nonlocal boundary value problems for pseudodifferential equations in the Besov-type limit spaces.     

The matrix equation AXB+CYD=Eover a simple artinian ring

This paper discussed the matrix equation AXB+CYD=Eover a simple Artinian ring, obtains several necessary and sufficient conditions for existence of a solution, gives the representation of solution by g-inverses, and extends a theorem of W.E. Roth's simple Artinian rings.     

Estimates of Oscillations of the Hardy Transform

For the Hardy transform of a nonincreasing function we obtain a sharp two-sided estimate of the BLO-norm and sharp inequalities between the BMO- and the BLO-norms of a nonincreasing function. A well-known lower bound for the BMO-norm of the Hardy transform is improved on the basis of these inequalities.     

On Convergence Approach Spaces

The extension of two axioms due to Cook and Fischer to the category CAP of convergence approach spaces leads to the study of non-Archimedean approach spaces as well as two versions of regularity appropriate to CAP and related categories.     

Partial decay on simple manifolds

Existence, uniqueness and weighted regularity of solutions of linear and nonlinear second-order uniformly elliptic differential equations on complete punctured compact N-manifolds, N > 2. Application to prescribed curvature problems: scalar curvature in a quasi-isometry class (including a contribution to the Lichnérowicz-York equation of General Relativity); Ricci curvature in a weighted Kähler class (with a related result in equiaffine geometry). A new asymptonic behaviour is allowed throughout, called partial decay, which requires its own maximum principle.Current support: CNRS; partial support; CEE contract GADGET # SC1-0105-C.     

Specific heat and thermal conductivity of low-stress amorphous Si-N membranes

We present values of the specific heat and thermal conductivity from 3-300 K of low-stress amorphous silicon-nitride thin-films determined from measurements using a membrane-based microcalorimeter. The thermal conductivity has a temperature dependence often seen in amorphous solids, but the magnitude is large, with the expected plateau occurring at significantly higher temperatures than seen in other amorphous systems. Specific heat measurements show that the expected ‘peak’ in the vibrational spectrum also occurs at relatively high temperatures. The estimated phonon mean-free-path at 300 K is ≈5 Å, comparable to the inter-atomic spacing, as seen in other amorphous solids. Below ≈ 20 K the mean free path is comparable to or exceeds the thickness of the membrane, indicating that surface scattering dominates the thermal transport. This surface scattering is found to be either specular or diffuse, depending on details of the membrane processing, which affects both the thermal conductivity and specific heat below 10 K.     

Surfactants: Perfect heteroepitaxy of Ge on Si(111)

The hetero growth of Ge on Si results in formation of 3D clusters with an uncontrolled defect structure. Introduction of a monolayer of a surfactant completely changes the growth mode to a 2D-layer growth (Frankvan der Merwe) with a continuous and smooth Ge film on Si(111). The surfactant is not incorporated but segregates and floates on the growing Ge film. The saturation of the dangling bonds of the semiconductor reduces the surface free energy and drives the strong segregation. The effect on the growth process is the selective change of activation energies which are important for diffusion and the mobility of the Ge. Up to a thickness of 8 MLs (MonoLayers) the misfit-related strain of the pseudomorphic Ge film is relaxed by formation of a micro rough surface. This allows a partial relaxation of the Ge towards its bulk lattice constant which would not be possible for a flat and continuous film. For thicker Ge films the misfit of 4.2% is relieved by a periodic dislocation network, which is confined to the Si-Ge interface. Ge-films thicker than 20 MLs are free of defects and completely relaxed to the Ge bulk lattice constant: a model system for perfect heteroepitaxial growth.     

Mössbauer Study of Thin Iron Film Beryllization

Beryllium coating of the iron foil is made by means of magnetron sputtering. Mössbauer studies are performed by means of two registration techniques: conversion electron Mössbauer spectroscopy (CEMS) and the γ-ray technique in absorption geometry. Performed investigations confirm the original thermodynamic approach to creation of thermally stable multi-layer materials.

     

Forcing matchings on square grids

Let G be a graph that admits a perfect matching. The forcing number of a perfect matching M of G is defined as the smallest number of edges in a subset S M, such that S is in no other perfect matching. We show that for the 2n × 2n square grid, the forcing number of any perfect matching is bounded below by n and above by n². Both bounds are sharp. We also establish a connection between the forcing problem and the minimum feedback set problem. Finally, we present some conjectures about forcing numbers in other graphs.     

Uncertain input data problems and the worst scenario method

An introduction to the worst scenario method is given. We start with an example and a general abstract scheme. An analysis of the method both on the continuous and approximate levels is discussed. We show a possible incorporation of the method into the fuzzy set theory. Finally, we present a survey of applications published during the last decade. This work was supported by grant 201/04/1503 from the Czech Science Foundation and by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503