On the nodal set of eigenfunctions
On the number of stationary patterns in reaction-diffusion systems
We study systems of two nonlinear reaction-diffusion partial differential equations undergoing diffusion driven instability. Such systems may have spatially inhomogeneous stationary solutions called Turing patterns. These solutions are typically non-unique and it is not clear how many of them exists. Since there are no analytical results available, we look for the number of distinct stationary solutions numerically. As a typical example, we investigate the reaction-diffusion system designed to model...
On the numerical solution of nonlinear partial differential equations on divergence form
On the open mapping theorem
On the properties of linear differential equations of the second order in the complex domain
On the -deformed Heisenberg uncertainty relations and discrete time
The opportunity for verifying the basic principles of quantum theory and possible -deformation appears in quantum cryptography (QC) – a new discipline of physics and information theory.The author, member of the group of cryptology of Praha, presents in this paper the possibility to verify the -deformation of Heisenberg uncertainty relation -deformed QM and possible discretization on the base of a model presented in the fourth section.In the seven sections, the author discusses these problems....
On the quality of local flux reconstructions for guaranteed error bounds
In this contribution we consider elliptic problems of a reaction-diffusion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, we concentrate on complementary error bounds whose values are determined by suitable flux reconstructions. We present numerical experiments comparing the performance of the local flux reconstruction of Ainsworth and Vejchodsky [2] and the reconstruction of Braess and Schöberl [5]. We evaluate the efficiency...
On the regularity and non-regularity of elliptic and parabolic systems
On the regularity for 2nd order nonlinear elliptic systems
On the regularity of weak solutions to variational equations and inequalities for nonlinear second order elliptic systems
On the saturation of a topological partial algebra with respect to a congruence relation
On the second order absolute differentiation
In this paper the authors compare two different approaches to the second order absolute differentiation of a fibered manifold (one of them was studied by the authors [Arch. Math., Brno 33, 23-35 (1997; Zbl 0910.53014)]. The main goal is the extension of one approach to connections on functional bundles of all smooth maps between the fibers of two fibered manifolds over the same base (we refer to the book “Natural Operations in Differential Geometry” [Springer, Berlin (1993; Zbl 0782.53013)] I. Kolar,...
On the sequential envelope
On the shape classification of manifold-like continua
On the shape of solutions to some variational problems
On the simplicial structure of some Weil bundles
The author considers the problem to give explicit descriptions for several types of bundles on smooth manifolds, naturally related with the bundle of -dimensional velocities, or -jets. In fact, this kind of bundles are very natural objects in differential geometry, mechanics and Lagrangian dynamics. For this the author considers Weil bundles that arose from Weil algebras. If a suitable combinatorial data is provided by a simplicial coloured structure, then the author describes the corresponding...
On the solution of elliptic partial differential equations with an unbounded Dirichlet integral
On the solution of indentation and crack problems in linear elasticity by use of higher special functions
On the solvability of the non-homogeneous potential problem at a corner singularity
On the structure constants of certain Hecke algebras
[For the entire collection see Zbl 0742.00067.]In the first part some general results on Hecke algebras are recalled; the structure constants corresponding to the standard basis are defined; in the following the example of the commuting algebra of the Gelfand- Graev representation of the general linear group is examined; here is a finite field of elements; the structure constants are explicitly determined first for the standard basis and then for a new basis obtained via a Mellin-transformation....