Institute of Mathematics AS CR, v. v. i.
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Visualisations of a conditional probability problem
No full textsummary:Uvedené postupy vizualizace při řešení úloh z podmíněné pravděpodobnosti
Some nonlinear nonlocal elliptic problems under weak conditions on the diffusion coefficients
No full textsummary:Under weak conditions on the diffusion coefficients, we prove existence theorems of weak solutions for some nonlinear nonlocal elliptic problems. Our approach is based on the Schauder fixed point theorem combined with an approximation technique. We also give uniqueness results and an example to support them
On proper colorings of functions
No full textsummary:We investigate the infinite version of the -switch problem of D. Greenwell and L. Lovász. A function is a proper coloring if whenever and are totally different elements of , i.e. for each . We call (i) weakly uniform if and only if there are pairwise totally different with ; (ii) tight if no proper coloring differs from at exactly one point. We prove that a proper coloring is weakly uniform if and only if there is a -complete ultrafilter on and there is a permutation such that for each , We also show that there are tight proper colorings which cannot be obtained in this way
Ludwig Otto Blumenthal (1876-1944)
No full textsummary:Před osmdesáti lety zemřel v Terezíně německý matematik Ludwig Otto Blumenthal, žák Davida Hilberta. Trochu kuriózní je fakt, že se do Terezína dostal na vlastní žádost. Mezi německými matematiky přelomu 19. a 20. století je jeho osud jedním z nejtragičtějších. V textu připomínáme jeho život a oblasti matematiky, kterým se věnoval
News and Announcements
No full textsummary:Profesor Miloslav Havlíček (1938--2024). Evropský matematický kongres v Seville. 41. mezinárodní konference Historie matematiky
Non-fragile observers design for nonlinear systems with unknown Lipschitz constant
Get PDFsummary:In this paper, the problem of globally asymptotically stable non-fragile observer design is investigated for nonlinear systems with unknown Lipschitz constant. Firstly, a definition of globally asymptotically stable non-fragile observer is given for nonlinear systems. Then, an observer function of output is derived by an output filter, and a dynamic high-gain is constructed to deal with unknown Lipschitz constant. Even the observer gains contain diverse large disturbances, the observer errors are proven to converge to the origin based on Lyapunov stability theorem and a matrix inequality. Finally, an experimental simulation is provided to confirm the validity of the proposed method
Responsive Design and Automatic Typesetting with LuaLaTeX
No full textsummary:Tento článek představuje využití metod responzivního designu a pokročilých vlastností LuaLaTeXu pro automatickou sazbu dokumentů určených pro různé cílové výstupy, jak tištěné, tak elektronické, například mobilní telefony, tablety nebo čtečky e-knih. Konkrétně se zaměřuje na využití LuaLaTeXu pro automatizovanou sazbu s pomocí balíčků Responsive pro nastavení velikosti písma a řádkování podle velikosti stránky, Luavlna pro zamezení výskytu jednopísmenných předložek na koncích řádků, Lua-widow-control pro omezení osamocených řádků na koncích a začátcích stránek a Linebreaker, který brání přetečení řádků.summary:This article focuses on the use of responsive design techniques to display web pages on devices with different display sizes, such as mobile phones, tablets, large monitors and printers. These methods allow optimizing the readability of a document on all devices by using different font sizes, individual page elements, and margins. We present how similar functionality can be achieved using LaTeX. Specifically, it focuses on the use of LuaLaTeX for automated typesetting, using packages Responsive for setting font size and line spacing according to page size, Luavlna to prevent the occurrence of single-letter prepositions at line breaks, Lua-widow-control to reduce orphan lines at page breaks and page starts, and Linebreaker to prevent line overflow. With these methods, a single source document can be used for different outputs, such as print versions, e-book readers, and web pages, and achieve optimal document display on all devices
Quantised -differential algebras
No full textsummary:We propose a definition of a quantised -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of are natural examples of such algebras
Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition
No full textsummary:We present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis. Anisotropic meshes can be used for this purpose. The main contributions of this study include providing a new proof of the term consistency. This enables us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart-Thomas and Morley finite-element spaces. Our results indicate optimal convergence rates and imply that the modified Morley FEM may be effective for errors