Institute of Mathematics AS CR, v. v. i.
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Guaranteed a-posteriori error estimation for finite element solutions of nonstationary heat conduction problems based on their elliptic reconstructions
No full textsummary:We deal with the a-posteriori estimation of the error for finite element solutions of nonstationary heat conduction problems with mixed boundary conditions on bounded polygonal domains. The a-posteriori error estimates are constucted by solving stationary ``reconstruction'' problems, obtained by replacing the time derivative of the exact solution by the time derivative of the finite element solution. The main result is that the reconstructed solutions, or reconstructions, are superconvergent approximations of the exact solution (they are more accurate than the finite element solution) when the error is measured in the gradient or the energy-norm. Because of this, the error in the gradient of the finite element solution can be estimated reliably, by computing its difference from the gradient of its reconstructions. Numerical examples show that ``reconstruction estimates'' are reliable for the most general classes of solutions which can occur in practical \hbox {computations}
The Clairaut's theorem on rotational surfaces in pseudo-Euclidean 4-space with index 2
No full textsummary:Clairaut’s theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the hyperbolic surfaces of rotation and the elliptic surface of rotation, respectively
Galerkin-type solution of non-stationary aeroelastic stochastic problems
No full textsummary:The assessment of vibration characteristics in slender engineering structures, influenced by both deterministic harmonic and stochastic excitation, poses a challenging problem. Due to its complexity, transverse vibration of the structure (relative to the wind direction) is typically modelled using the single-degree-of-freedom van der Pol-type equation. Determining the response probability density function comprises solving the Fokker-Planck equation, a task that generally necessitates the use of approximate numerical methods. Some of these methods rely on Galerkin-type approximation employing orthogonal polynomial or exponential-polynomial basis functions. This contribution reviews available techniques for stationary and non-stationary cases and proposes some modifications while highlighting unresolved questions in the field
On the possibilities of computational modelling of interaction of a structure with subsoil
No full textsummary:The following possibilities of reduction of dimension in the computational analysis of strain and stresses transferred to the subsoil massive are available: i) coming from the effective subsoil model by Kolář & Němec (1989), based on the assumptions of the Pasternak's model (1954), where the pair of material parameters of a surface model is evaluated from the energy equivalence, ii) reducing a large sparse matrix of soil massive stiffness to a smaller one, using Schur's complement technique. In both cases i), ii) the steady-state analysis is decisive: inclusion of more complicated combination of loads can be performed without repeated computations
Creation of LaTeX documents using a cloud-based pipeline
No full textsummary:Používání webových služeb pro kolaborativní přípravu dokumentů v (La)TeXu je dnes běžné, ale tyto nástroje se zaměřují na psaní dokumentů, nikoliv na tvorbu šablon nebo balíčků. Používání serverů pro průběžnou integraci a doručení je běžné ve vývoji softwaru, ale může být snadno přizpůsobeno pro TeX a přátele. Tento článek ukazuje, jak začít s používáním automatizace na webových službách jako GitHub, Forgejo nebo GitLab, a to jak pro autory dokumentů, tak pro vývojáře (La)TeX ových balíčků.summary:Using web-based platforms for collaborative editing of LaTeX documents is common these days. These tools focus on writing documents and not on creation of templates or packages. Using build servers with automated pipelines is common within software development but can easily be adapted for TeX & friends. This article will show how to get started using automated workflows on platforms like GitHub, Forgejo, or GitLab for document authors as well as TeX developers
A property which ensures that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent
No full textsummary:Let be the class of groups satisfying the minimal condition on normal subgroups and let be the class of groups of finite lower central depth, that is groups such that for some positive integer . The main result states that if is a finitely generated hyper-(Abelian-by-finite) group such that for every , there exists a normal subgroup of finite index in satisfying for every , then is finite-by-nilpotent. As a consequence of this result, we prove that a finitely generated hyper-(Abelian-by-finite) group such that for every , there exists a normal subgroup of finite index in satisfying for every , is periodic-by-nilpotent; where stands for the class of periodic groups
One-sided -suspended categories
No full textsummary:For an integer , we introduce a simultaneous generalization of -exact categories and -angulated categories, referred to as one-sided -suspended categories. Notably, one-sided -angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their -angulated counterparts. Additionally, we present a method for constructing -angulated quotient categories from Frobenius -prile categories. Our results unify and extend the previous work of Jasso on -exact categories, Lin on -angulated categories, and Li on one-sided suspended categories
