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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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Symbiosis as a model for a new biology
Lhotský, Josef ; Markoš, Anton (advisor) ; Černý, Robert (referee)
Contemporary biology belongs among the most diversified sciences; yet one of its most fundamental and controversial questions is surprisingly: "What is life?". The aim of this study is to point out that biology is special among other natural sciences because its need of the notion of meaning. Meaning takes the central position in the biological rea-soning. Compared to other sciences, biology has to reflect the dimension of information and its interpretation: language-like properties, communication and interpretation belong to the basic characteristics of life. In spite of the fact, most contemporary theories of evo-lution deny active participation of living beings on the very process - living being come out of its description as puppets or zombies controlled by external forces. As a remedy from such a situation, biology should start with a new model for living entities. A bene-ficial methapor seems to be that of natural languages, i.e. an analogy between a net of historical interactions and conventional ways of interpretation of meaning in (i) living entities and (ii) in system of natural languages. I consider as the most appropriate biolo-gical systems for modeling of such a network of symbiotic interactions, i. e. the pheno-menon of symbiosis and especially symbiogenesis. Keywords: life,...
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Early craniofacial and dental morphogenesis in bichir, P. senegalus
Kráľovič, Martin ; Buchtová, Marcela (referee) ; Černý, Robert (advisor)
Polypterid fishes are considered the basal-most group of extant actinopterygians and thus may serve as a direct link for understanding the evolution of the first bony fishes. Their embryonic and larval material, however, is extremely scarce what makes it difficult to study their developmental patterns and processes. This work of mine is based on several successful breedings of the bichir Polypterus senegalus that allowed me to analyse development of some 70 specimens at key developmental stages. I have focused my attention to the early morphogenesis of teeth and dentition on several locations within a developmental context of oropharyngeal cavity. Oropharyngeal cavity develops quite differently when compared to other vertebrate species: it arises by means of a schizocoeliclike split of epithelial layers and, moreover, the earliest mouth cavity seems to be strongly constrained by the presence of cement (attachment) glands. Mouth opening proceeds by development of new, enigmatic structures that I have entitled the epithelial bridges (Kralovic et al., 2009) and that might represent the ectoderm-endoderm border often judged to be essential for tooth initiation and patterning. I have described a pronounced delay in initiation of pharyngeal teeth when compared to the oral teeth, probably as a direct consequence...
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