Recent Submissions

Now showing 1 - 5 of 6
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    On differentiation of a Lebesgue Integral with respect to a Parameter
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2012) Šremr, Jiří
    The aim of this paper is to discuss the absolute continuity of certain composite functions and di erentiation of a Lebesgue integral with respect to a parameter. The results obtained are useful when analyzing strong solutions of partial di erential equations with Carath eodory right-hand sides.
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    A dynamic Effect Algebras with Dual Operation
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2012) Paseka, Jan; Janda, Jiří
    Tense operators for MV-algebras were introduced by Diaconescu and Georgescu. Based on their de nition Chajda and Kola r k presented the de nition of tense operators for lattice e ect algebras. Chajda and Paseka tackled the problem of axiomatizing tense operators on an e ect algebra by introducing the notion of a partial dynamic e ect algebra. They also gave representation theorems for dynamic e ect algebras. We continue to extend their work for partial S-dynamic e ect algebras i.e. in the case when tense operators satisfy required conditions also for the dual e ect algebraic operation . We show that whenever tense operators are total our stronger notion coincides with their de nition. We give also a representation theorem for partial S-dynamic e ect algebras and its version for strict dynamic e ect algebras.
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    On a Two-point Boundary Value Problem for Third-order Linear Functional Differential Equations. Part I.
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2012) Hakl, Robert
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    A Hybrid Drift Diffusion Model: Derivation, Weak Steady State Solutions and Simulations
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2012) Chiarelli, Simone; di Michele, Federica; Rubino, Bruno
    In this paper we derive a new hybrid model for drift di usion equations. This model provides a description of the quantum phenomena in the parts of the device where they are relevant, and degenerates to a semiclassical model where quantum e ects are negligible, so that the system can be considered classically. The study of quantum correction to the equation of state of an electron gas in a semiconductor with the assumption of localized quantum e ects leads to a further condition on the classical-quantum interface. Moreover, we prove the existence of weak solutions for our hybrid model. Finally, we present numerical results for di erent devices, by means of Colsys software.
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    Rule-restricted Automaton-grammar transducers: Power and Linguistic Applications
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2012) Čermák, Martin; Horáček, Petr; Meduna, Alexander
    This paper introduces the notion of a new transducer as a two-component system, which consists of a nite automaton and a context-free grammar. In essence, while the automaton reads its input string, the grammar produces its output string, and their cooperation is controlled by a set, which restricts the usage of their rules. From a theoretical viewpoint, the present paper discusses the power of this system working in an ordinary way as well as in a leftmost way. In addition, the paper introduces an appearance checking, which allows us to check whether some symbols are present in the rewritten string, and studies its e ect on the power. It achieves the following three main results. First, the system generates and accepts languages de ned by matrix grammars and partially blind multi-counter automata, respectively. Second, if we place a leftmost restriction on derivation in the context-free grammar, both accepting and generating power of the system is equal to generative power of context-free grammars. Third, the system with appearance checking can accept and generate all recursively enumerable languages. From more pragmatical viewpoint, this paper describes several linguistic applications. A special attention is paid to the Japanese-Czech translation.