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Differential Calculus of Functions of Several Variables
Ráž, Adam ; Mlček, Josef (advisor) ; Balcar, Bohuslav (referee)
The thesis follows on Petr Vopìnka's alternative theory of sets and semisets by extending notions of in nite closeness and monad for real spaces of several variables. It speci es and explains on examples the basic terminology of this theory, namely notions of sets, semisets and domains. It brings up two worlds | an ancient and a classical one | by which it shows a dual way of looking at real functions of several variables. That is used for examining local properties like continuity, limit or derivative of a function at a point. The peak of the thesis is an alternative formulation of the implicit function theorem and the inverse function theorem. The thesis also contains translation rules, which allow us to reformulate all these results from an alternative into a traditional formulation used in mathematical analysis.
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Differential Calculus of Functions of Several Variables
Ráž, Adam ; Mlček, Josef (advisor) ; Balcar, Bohuslav (referee)
The thesis follows on Petr Vopìnka's alternative theory of sets and semisets by extending notions of in nite closeness and monad for real spaces of several variables. It speci es and explains on examples the basic terminology of this theory, namely notions of sets, semisets and domains. It brings up two worlds | an ancient and a classical one | by which it shows a dual way of looking at real functions of several variables. That is used for examining local properties like continuity, limit or derivative of a function at a point. The peak of the thesis is an alternative formulation of the implicit function theorem and the inverse function theorem. The thesis also contains translation rules, which allow us to reformulate all these results from an alternative into a traditional formulation used in mathematical analysis.
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2D-analýza geotextilních trubic
Malík, Josef
The analysis describing both stress and geometry of geosynthetic tubes is presented. The parametric study shows that the most critical point responsible for stability is pumping pressure. A small pressure increase can result in a big increase or tension force in geosynthetic. On the other hand it has small infuence on volume capacity.
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Smooth Continuation for a Model of Unilaterally Supported Beam
Eisner, Jan ; Kučera, Milan ; Recke, L.
This note concerns a class of parameter dependent variational inequalities including a model of an elastic beam with a unilateral obstacle. A result about smooth continuation of solutions with respect to the parameter is described. Inparticular, the ends of the intervals, where the solutions touch the obstacle,depend smoothly on the parameter. Eventhough the problem is nonsmooth, .......
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