Ústav matematiky a deskriptivní geometrie
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- ItemRigidity of Holomorphically Projective Mappings of Kähler Spaces with Finite Complete Geodesics(MDPI, 2024-04-19) Vítková, Lenka; Hinterleitner, Irena; Mikeš, JosefIn this work, we consider holomorphically projective mappings of (pseudo-) K & auml;hler spaces. We determine the conditions for finite complete geodesics that must be satisfied for the mappings to be trivial; i.e., these spaces are rigid.
- ItemLarge time behavior of nonautonomous linear differential equations with Kirchhoff coefficients(Elsevier, 2024-03-31) Diblík, Josef; Pituk, Mihaly; Szederkényi, GáborNonautonomous linear ordinary differential equations with Kirchhoff coefficients are considered. Under appropriate assumptions on the topology of the directed graphs of the coefficients, it is shown that if the Perron vectors of the coefficients are slowly varying at infinity, then every solution is asymptotic to a constant multiple of the Perron vectors at infinity. Our results improve and generalize some recent convergence theorems.
- ItemUse of cohesive approaches for modelling critical states in fibre-reinforced structural materials(MDPI, 2024-07-01) Kozák, Vladislav; Vala, JiříDuring the operation of structures, stress and deformation fields occur inside the materials used, which often ends in fatal damage of the entire structure. Therefore, the modelling of this damage, including the possible formation and growth of cracks, is at the forefront of numerical and applied mathematics. The finite element method (FEM) and its modification will allow us to predict the behaviour of these structural materials. Furthermore, some practical applications based on cohesive approach are tested. The main effort is devoted to composites with fibres and searching for procedures for their accurate modelling, mainly in the area where damage can be expected to occur. The use of the cohesive approach of elements that represent the physical nature of energy release in front of the crack front has proven to be promising not only in the direct use of cohesive elements, but also in combination with modified methods of standard finite elements.
- ItemBounded solutions of delay dynamic equations on time scales(Springer Nature, 2012-10-24) Diblík, Josef; Vítovec, JiříIn this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where $f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$ is a delay function and $\mathbb{T}$ is a time scale. We formulate a principle which gives the guarantee that the graph of at least one solution of above mentioned equation stays in the prescribed domain. This principle uses the idea of the retraction method and is a suitable tool for investigating the asymptotic behavior of solutions of dynamic equations. This is illustrated by an example.
- ItemAsymptotic convergence of the solutions of a dynamic equation on discrete time scales(Hindawi, 2012-01-03) Diblík, Josef; Růžičková, Miroslava; Šmarda, Zdeněk; Šutá, ZuzanaIt is proved that, for the asymptotic convergence of all solutions, the existence of an increasing and asymptotically convergent solution is sufficient. Therefore, the main attention is paid to the criteria for the existence of an increasing solution asymptotically convergent for n goes to infinity. The results are presented as inequalities for the function beta. Examples demonstrate that the criteria obtained are sharp in a sense.