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Difference equations and their applications in economical models
Ivanková, Kristýna ; John, Oldřich (advisor) ; Bárta, Tomáš (referee)
Ndzev prdc.e: Diferencni rovnice a jejich vyuziti v ekononrickych modelech Autor: Kristyna. Ivankova Katedra (uxtav): Katedra matematicke analyzy Vedouei bakaldrske prdce: Doc.RNDr. Oldfich John, C/Sc. e-mail vedouciho: jorm@karlin.mff.cuni.cz Abstrakt: V praci studujeiue linearni diferencni rovnice prvniho fadu a je- jich vyuziti pfi fonnulaci a liledani feseni inikroekononiickych a niakroekono- mickycli inodclu. Modoly, ktere v praci uvadinio, jsou natolik zjednodusenc, aby byio inoznc ziskat jojich fesoni poinoci zkounianeho niateniatickeho aparatu. U dii'ereiicnich rovnic sc xaniefinie na feseni iechto rovnic pro spccialni prave strany. Ziskane vysledky nasledno pouzijcme v inikroeko- nomickycli modelcch rovnuvahy trim. Zakladnim inodelein je zdc pavuci- novy model, z nej jsou odvozeuy uiodoly s noririalni cenou a a adaptivninii ocekavanimi. V zavern prace so zabyvame zkoiiirianim stability a dynamiky multiplikatoru v inakroekononiickych modelcch uzavfenc ekonomiky (rnodely zdaneni, spofeiii a zvyky spotrebitelu) i otevfeue ekonomiky. Kltcovd slova: linearni dilerencni rovnice, ekonoinicke modely, pavucinovy model, mnltiplikatory, stabilHa feseni Title: DifTerence oquaLioiis and their upplic.ations in economical models Author: Kristyna Ivankova. Department: Department of mathematical analysis...
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Banach Function Spaces
Marko, Ján ; Pick, Luboš (advisor) ; John, Oldřich (referee)
N'a/ev prace: Banarhovy prostory fuiikci Autor: Jan Marko Katcdr;i: KaTedra inaleniaticke analy/y Yedouci bakalarske prace: doc1. UN Dr. Lubus Pick. CSc.. DSc. t'-inail vedoudho: Lubos.Pick'i'inff.cuni.c/ Abst.ra.kt.: V t.ejto ])riici su popisane xakladne vlastnosti Baimchovho priostoru funkcii. jeho podpriestor funkfii s absolutnc spujitou iiorniou a asociovany Banai-liov priestor I'luikcii. Zaobcra sa lie/ problcinal.ikou Lcbcsgucovycli pricslorov ['unkcii. branycli ako Banadiovo priest ory funkcif. \ Icxte su vyprarovaiu'1 priklady lykajuce sa.vlastnosti niicr ineratel'nych priosl.orov a k-h vplyv na ist udovanc'1 podpricstory. Taklio/ su vypracovaiK'1 priklady Baiia- chovyi'li iiorioni. iin ])n'sliisiio limiacliovc priest ory funkfii a. ich /;ikladne. N'la Klfcova slova: Banacliuva noriiia. Banacliov prieslor I'uukcif, asociovany prieslor. spojita noriua Title: Banach funct ion spaces Author: Jan Marko Department: Department of Mathematical Analysis Supervisor: doc. HNDr. Lubus Pick, CSc.. DSc. 'rvisor's e-mail address: Lubos.Pick'imir.cuni.cx Abstract: This thesis describes basic properties of Banach function spaces, its subspace of functions of absolutely continuous norm and its associa.lt; space.. II.also deals with problems of Lebesgue spaces considered to be Banach function spaces. Several problems...
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Habitat selection game
Slavík, Jakub ; Pražák, Dalibor (advisor) ; John, Oldřich (referee)
In the presented work we study an application of evolutionary game theory in behavioral ecology, specifically the habitat selection game, which describes the distribution of population into a finite number of patches. We also show the existence, uniqueness and evolutionary stability of the ideal free distribution (IFD) observed in natural environments. To describe the process of the distri- bution we specify the dynamics of the habitat selection game using dispersion dynamics, and we show the stability of the IFD for different types of dispersion dynamics using the classical theory of ordinary differential equations and the theory of ordinary differential equations with discontinuous righthand sides. 1
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Isoperimetric problem in economics
Volek, Mikoláš ; John, Oldřich (advisor) ; Bárta, Tomáš (referee)
The isoperimetric problem is one of the broad class of optimal control problems, which draw on the generalization of classical calculus developed in the mid-20th century. In the bachelor's thesis I lay down the mathematical framework that permits to rigorously prove both the necessary and sufficient conditions for the existence of a maximizer of the objective function. I analyze a simple problem from the field of project planning, which is a branch of applied economics. On the basis of a 1973 article by Cullingford and Prideaux I present an augmented cost function that involves the concept of the time value of money, which is key to proper economic reasoning. I give an explicit solution along with graphical depictions of the impact of a non-zero discount factor on project planing under the model in question. Finally, I introduce additional constraints and discuss the subproblem of multiple equality and non-equality constraints.
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