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Morfogeneze orálního skeletu mihule ve vztahu k evoluci čelistí
Romášek, Marek ; Černý, Robert (advisor) ; Jandzík, Dávid (referee)
4 Neural crest-derived cellular cartilage is one of the defining characteristics of vertebrates. Elaboration of this tissue and its patterning allowed the evolution of jaws in the gnathostome lineage. Together these hallmarks helped jawed vertebrates become one of the dominant taxons in the animal kingdom. Lampreys, as basal jawless vertebrates, lie at a unique phylogenetic position that makes them ideal organisms for the study of evolution of vertebrate/gnathostome novelties. Larval lampreys possess a special oral skeleton composed of a tissue related to cartilage, termed mucocartilage. Despite considerable attention that has been paid to the evolutionary significance of mucocartilage, it is not yet clear, how this unique feature arises in development and to what extent it is homologous to gnathostome jaws. In this study, the development of oro-pharyngeal region was analyzed in the sea lamprey Petromyzon marinus. SEM imaging revealed shaping and topographic relationships of embryonic tissues, detailed plastic histology coupled with expression analyses of several molecular markers were used to describe origin, histogenesis and morphogenesis of mucocartilage. Furthermore, genetic regulation of the tissue was investigated in order to identify its unique or shared features. Mucocartilage is seen to...
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Mountain Pass Theorem and its applications
Příhoda, Vojtěch ; Černý, Robert (advisor) ; Vlasák, Václav (referee)
Cílem této práce je formulovat a dokázat Větu o horském sedle a ukázat příklady její aplikace tak, aby student třetího ročníku matematiky nebo fy- ziky, jenž absolvoval alespoň úvodní kurs funkcionální analýzy, byl schopen práci porozumět. D·kaz Věty o horském sedle provedeme s pomocí Ekelan- dova variačního principu, který si rovněž formulujeme a dokážeme. Následně si ukážeme dva příklady její aplikace na d·kaz existence netriviálního sla- bého řešení eliptické parciální diferenciální rovnice obsahující nelinearitu se subkritickým r·stem. 1
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Infinite products
Kudrnáč, Vojtěch ; Rokyta, Mirko (advisor) ; Černý, Robert (referee)
This paper offers a brief insight into the basic theory of convergence of the infinite products of real or complex sequences. Then it focuses mainly on the possibilities of developing some selected functions into the form of infinite product and on the corollaries and utilizations of being familiar with these. Purpose of the paper is not to prove the existence of infinite products for functions with certain characteristics in general, but rather to derive specific formulas and prove their validity. The attention is paid to those elementary functions which are derived from the exponential function, especially the sinus function, the nonelementary functions mentioned are the gamma and the zeta function. The text should be understandable even for a person, who has never came upon infinite products before.
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Neural crest biology with respect to diversity of vertebrates
Štundl, Jan ; Černý, Robert (advisor) ; Němec, Pavel (referee)
Neural crest is an extensively migrating population of cells that arise during early development of vertebrate embryos. It provides a huge variety of different cell types that generate new tissues which occur only in vertebrates. Neural crest cells together with the mesoderm participate on the formation of the head of vertebrates, which is viewed as one of the most important innovations in the evolution of vertebrates. Thanks to their skeletogenic potencial neural crest cells are percieved as a key factor causing massive craniofacial diversity. The aim of this thesis was to get acquainted with the population of neural crest cells and try to understand its importance for the evolution of vertebrates and especially for generating craniofacial diversity.
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Elementary methods for solution to difference equations
Sadil, Antonín ; Stará, Jana (referee) ; Černý, Robert (advisor)
Nazev prace: Eleinentanii melody fcseni diferencnieh rovnic Autor: Antonin Sadil Katedra (ustav): Katedra matematieke analyzy Vcdonci bakalafske prace: RNDr. Robert Corny,Ph.D. e-mail vedouciho: rc.erny^karlm.mff.eimi.e/ Abstrakl: Tato prace pojednava o metodaeh feseni linearnich diferencnieli rovnic. Zamefuje se na. vlastnosti feseni homogomn'ch rovnic a nalezeni fundamentalniho systemu pro jodnodnoho, nasobne i komplexni kofeny charakteristickeho polynomu. U nchomogcnnich rovnic sc pak zamefuje pfedevsim na inctody pro nalezeni partiku- larniho feseni. Dale so kratco zal">yva fosenim linoarni diferencni rovnice prvniho fadu s nekonstaiiUiimi kooficienty a v zaveru popisuje uietody feseni sonstav liiioarnich diforencnich rovnic prvniho radii. Cola toorie jo poistavona na dnkazoch a pro lopsi pochopeni je proloiona nekolika ilustrativnimi pfiklady. Klicova slova: homogenni rovnice, nohoniogonni rovnice, fundainentalni system Title: Elementary methods for solution to difference equations Author: Antonin Sadil Department: Department of Mathematical Analysis Supervisor: RNDr. Robert Ceriiy,Ph.D. Supervisor's e-mail address: rrerny^karlin.mfT.cuni.cz Abstract: This work presents aboul methods for solution to difference equations, ft focus on characteristics of solutions of the homogeneous equations and finding...
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Functional equations
Konopecký, František ; Černý, Robert (referee) ; Hencl, Stanislav (advisor)
Nazev pracc: Funkcionalni rovnice Autor: Frantisck Konopccky Katedra (ustav): Katcdra matcmaticke analyzy Vedouci bakalafske pracc: RNDr. Stanislav Hcncl, Ph.D. e-mail vedouciho: hencK(.i)karlni.mrT.cmri.cz Abstrakt: V pfcdlozcnc praci ye zabyvame mctodami fcscni funkcionalnich rovnic, triky, kterc fescni usnadnuji, vlastnostmi funkci, kterc pfi fescni pomahaji a myslenkovymi po- stupy pfi samotnem fescni. Nejprve za/Jvame pojem a praci s funkcionalni rovnici. Pote vysvetlnjeme dvc hlavni inetody - Substitucni-A Cauchyova. Naslcduji diilczite vlastnosti fnnkci a po nich ka]>itola o castych chybach pfi foscni. Ko konci se venujcme Cauchyove rovnici z vice stran a naslednje nckolik fesenych i nofcsenych pfikladu. Klicova slova: Fnnkcc, funkcionalni rovnice. Title: Functional Equations Author: Frantisek Konopccky Department; Department of Mathematical Analysis Supervisor: RNDr. Stanislav Hcncl, Ph.D. Supervisor's e-mail address: hencK(fikarlin.mfi.cnui.cz Abstract: In this thesis we study methods of solving strategies of functional equations, tricks, which make solving easier, special function properties, that help in solution and also ideas in solution itself. Firstly we get closer to term functional equation and show how to work with it. Then we explain two main methods Substitution method and Cauchy's...
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