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Repository of the Czech Academy of Sciences
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  • Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions

    We consider a reaction–diffusion system of activator–inhibitor or substrate-depletion type which is subject to diffusion-driven instability if supplemented by pure Neumann boundary conditions. We show by a degree-theoretic approach that an obstacle (e.g. a unilateral membrane) modeled in terms of inequalities, introduces new bifurcation of spatial patterns in a parameter domain where the trivial solution of the problem without the obstacle is stable. Moreover, this parameter domain is rather ...

    Separable reductions and rich families in theory of Fréchet subdifferentials

    Fabian, M. (2015)
    We consider important properties of Fréchet subdifferentials, in particular: the non-emptiness of subdifferentials, the non-zeroness of normal cones, the fuzzy calculus, and the extremal principle; all statements being considered in Fréchet sense. Given a nonseparable Banach space X, we show how the validity of these statements is implied by the validity of them in every separable subspace of X. Such a reasoning is called “separable reduction”. We show that, behind this approach, there is a m...

    Electrodiffusion Method of Near-Wall Flow Diagnostics in Microfluidic Systems

    A novel technique for fabrication of plastic microfluidic systems with integrated metal microelectrodes (called technique of sacrificed substrate) enables us to produce microfluidic devices with precisely shaped sensors for wall shear stress measurements. Several micrometer thick gold sensors built-in a plastic substrate exhibit good mechanical resistance and smoothness. Proper functioning of prepared chips with microsensors has been first tested in various calibration experiments (polarizati...

    On the existence of a sigma-closed dense subset

    It is consistent with the axioms of set theory that there are two condense partial orders, one of them sigma-closed and the other one without a sigma-closed dense subset.

    Mathias forcing and combinatorial covering properties of filters

    We give topological characterizations of filters ... on omega such that the Mathias forcing ... adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzmán, Hrušák, Martínez, Minami, and Tsaban.
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