DC FieldValueLanguage
dc.contributor.authorVršek, Jan
dc.date.accepted2012-05-18
dc.date.accessioned2013-06-19T06:28:43Z
dc.date.available2011-06-06cs
dc.date.available2013-06-19T06:28:43Z
dc.date.issued2012
dc.date.submitted2012-05-18
dc.identifier51230
dc.identifier.urihttp://hdl.handle.net/11025/5388
dc.format.mimetypeapplication/pdf
dc.language.isoenen
dc.rightsPlný text práce je přístupný bez omezení.cs
dc.subjectkonvolucecs
dc.subjectincidenční varietacs
dc.subjectvarieta parametrůcs
dc.subjectopěrná funkcecs
dc.subjectkonvoluční stupeňcs
dc.subjectkoherentní formacs
dc.title.alternativeAlgebraic analysis of convolutions of algebraic hypersurfacesen
dc.typerigorózní prácecs
dc.thesis.degree-nameRNDr.cs
dc.thesis.degree-levelRigoróznícs
dc.thesis.degree-grantorZápadočeská univerzita v Plzni. Fakulta aplikovaných vědcs
dc.description.departmentKatedra matematikycs
dc.thesis.degree-programMatematika - rigorozní řízenícs
dc.description.resultObhájenocs
dc.rights.accessopenAccess
dc.description.abstract-translatedIn recent years, studying convolutions of hypersurfaces (especially of curves and surfaces) has become an active research area. For instance, one of the fundamental operations in Computer Aided Design, i.e., offsetting, can be expressed as the convolution with a circle/sphere. The main goal of the thesis is to provide the theoretical analysis of convolutions of hypersurfaces from the algebraic point of view. This goal will be accomplished in the first part of the thesis. Although we will prove that the convolution of irreducible algebraic hypersurfaces is generically irreducible, it can still decomposes into more irreducible components. The upper bound for the number of components, in the terms of the so-called convolution degrees of the hypersurfaces, will be given. Further, a formula expressing the~convolution degree of a plane curve using the algebraic degree and the genus of the curve will be derived. In addition, a detailed analysis of the so-called special and degenerated components is provided. The special attention will be devoted to rational hypersurfaces and rational components The second part of the thesis will focuse on the two simplest classes of algebraic hypersurfaces with respect to the operation of convolution, namely on the hypersurfaces with the convolution degree one and two. The former case turns out to coincide with the well-known LN hypersurfaces, i.e., hypersurfaces with Linear Normals, and the most prominent example of later hypersurfaces are hyperspheres. The problem of rationality of convolutions with these hypersurfaces will be studied in more detail. In the curve case, the genus formula is derived. Moreover the decomposition of curves with low convolution degree into the convolution of finite number of simple fundamental ones will be provided.en
dc.subject.translatedconvolutionen
dc.subject.translatedincidence varietyen
dc.subject.translatedparameter varietyen
dc.subject.translatedsupport functionen
dc.subject.translatedconvolution degreeen
dc.subject.translatedLN hypersurfaceen
dc.subject.translatedQN hypersurfaceen
dc.subject.translatedcoherent formen
Appears in Collections:Rigorózní práce / Rigorous theses (KMA)

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