Institute of Mathematics AS CR, v. v. i.

    On subdifferentials of convex functions

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    Metapost a Houghova transformace

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    summary:The Hough transform is a powerful tool for searching shapes within images. The aim of this article is to explain the principles of the Hough transform and to provide a real example. MetaPost is a powerful language for producing figures for documents to be printed on PostScript printers. In the example, we show possibilities of MetaPost to programme the Hough transform

    Mlžná komora

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    Chapter 3: Goniometry of a general triangle

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    Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component

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    summary:We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of $u_3$ and $\omega _3$, which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004)

    Model of pulverized coal combustion in a furnace

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    summary:We describe behavior of the air-coal mixture using the Navier–Stokes equations for gas and particle phases, accompanied by a turbulence model. The undergoing chemical reactions are described by the Arrhenian kinetics (reaction rate proportional to $\mathrm{exp}\left(-\frac{E}{RT}\right),$ where $T$ is temperature). We also consider the heat transfer via conduction and radiation. Moreover we use improved turbulence-chemistry interactions for reaction terms. The system of PDEs is discretized using the finite volume method (FVM) and an advection upstream splitting method as the Riemann solver. The resulting ODEs are solved using the 4th-order Runge–Kutta method. Sample simulation results for typical power production levels are presented

    Book reviews

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    Existence of pole-zero structures in a rational matrix equation arising in a decentralized stabilization of expanding systems

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    summary:A necessary and sufficient condition for the existence of pole and zero structures in a proper rational matrix equation $T_{2} X = T_{1}$ is developed. This condition provides a new interpretation of sufficient conditions which ensure decentralized stabilizability of an expanded system. A numerical example illustrate the theoretical results

    On magic labellings of type $(1,1,1)$ for three classes of plane graphs

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    Decoupling normalizing transformations and local stabilization of nonlinear systems

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    summary:The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given
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