A Superlinear Lower Bound on the Number of 5-Holes

Let P be a finite set of points in the plane in general position, that is, no three points of P are on a common line. We say that a set H of five points from P is a 5-hole in P if H is the vertex set of a convex 5-gon containing no other points of P. For a positive integer n, let h_5(n) be the minimum number of 5-holes among all sets of n points in the plane in general position. Despite many efforts in the last 30 years, the best known asymptotic lower and upper bounds for h_5(n) have been of order Omega(n) and O(n^2), respectively. We show that h_5(n) = Omega(n(log n)^(4/5)), obtaining the first superlinear lower bound on h_5(n). The following structural result, which might be of independent interest, is a crucial step in the proof of this lower bound. If a finite set P of points in the plane in general position is partitioned by a line l into two subsets, each of size at least 5 and not in convex position, then l intersects the convex hull of some 5-hole in P. The proof of this result is computer-assisted

Legal and economic analysis of adjustments of the system of building savings in the Czech Republic with an emphasis on treatment of 2011

This bachelor thesis describes the product of building savings. Further, the thesis deals with the legislative adjustments of the building savings since its origin in 1993 to the present and focuses on analyzing the impacts of these adjustments to all participants of the system of building savings. The focus of this thesis is to analyze the implications of proposed legislation in 2011 on expenditure and government revenue, product provider and for the end consumer and serves as a comprehensive macro-economic perspective on the current state of housing savings schemes in the Czech Republic. The thesis discusses the possible impacts of the approved revised in 2012 and outlines a new possibilities for building societies resulting from this treatment. The thesis also includes comparison of building savings with alternative products

Numerical solution of 3D ow

Nazev prace-: Numericke fesem tfirozrnorneho proucleni Autor: Martin Kyncl Katcdra: Katedra numericke iiiatcinatiky Vedouci diplomove prace: Doc. RNDr. Jifi Felcman, CSc. e-mail vedouciho: felcman(G>karlm.inff.cuni.c/ Abstrakt: Prace se zabyva numorickym modelovanim nevazkeho a vazkeho stlacitelneho proudeni plynu ve 3D. Pou/iLa mutoda fes(Mif jn zalo2cna na ro/lo/rni systemu, kterym jc proudoni popsano, na nevazkou a ciste vaxkou cast. V praci json uvedeny numericke vyskulky, ktcre uka/uji pou/Jtelnost navrzene metody. Klicova slova: stlacitelne proudeni, Eulerovy rovnice, Navier-SLokesovy rov- nice, mctoda konecnycli objeinu, motoda konecnych prvku, Dolauriayova tri- angulace Title: Numerical solution of 3D flow Author: Martin Kyncl Department: Department, of Numerics Supervisor: Doc. RNDr. Jin Felcman, CSc. Supervisor's e-mail address: folemanQkarlin.mff.cuni.c/ Abstract: The paper is concerned with numerical modelling of inviscid as well as viscous gas flow in 3D. The method is based on upwind flux vector splitting finite volume scheme combined with finite elements. The geomet- rical data and the computational results for the three-dimensional flow arc presented. Keywords: compressible flow, Euler equations, Navicr-Stokes equations, fi- nite volume method, finite element method, Delaunay..

Connections and similarities of the development of households and general government debt in the Czech Republic

Diplomová práce analyzuje souvislosti a podobnosti vývoje zadluženosti sektoru domácností a sektoru vládních institucí v České republice. V návaznosti na vymezení vlivu měnové a fiskální politiky na zadluženost obou sektorů je analyzován vývoj zadluženosti sektoru domácností a sektoru vládních institucí v České republice a vybraných členských zemích Evropské unie v letech 2000 -- 2012, a to z hlediska její výše a struktury.This thesis analyses connections and similarities of indebtedness between household sector and the general government sector in the Czech Republic. Following the definition of the influence of monetary and fiscal policy on indebtedness of both sectors this thesis analyses indebtedness of the household sector and the government sector in the Czech Republic and selected EU countries in the period 2000 -- 2012 in terms of its amount and structure

Optimization of the Production Process of Vibrocasted Refractory Products

This paper deals with the optimization of the production process of vibrocasted refractory products. The main goal is to make efficient and automate the production of moulds for refractory blocks. A theoretical research was followed by an expert analysis of the current state of the manufacturing process at an industrial partner. The next step was to analyze complete portfolio of refractory vibrocasted products, which results in choosing a representative sample whose dimensions most correspond to majority of the moulds produced. Subsequently, a design was done, to make the production process more effective with respect to time, technology and construction aspects, focusing on increasing productivity, reducing human labour and increasing production modernization. In the end, the design options were evaluated in terms of time and cost, and the ideal process of the manufacturing production was recommended with respect to the latest technology. It includes a solution for material composition and optimized design of moulds for vibrocasted refractory materials to increase production efficiency moulds and cost reduction while maintaining mould accuracy and quality. These products are subject to high demands in terms of material quality and precision, and at the same time costly to produce due to manual manufacturing

Term of the euro adoption in the Czech republic in the context of the global financial crisis

Bachelor thesis analyzes the influence of effects of the global financial crisis on the term of the euro adoption in the Czech republic. Effects of the global financial crisis are analyzed in connection with OCA theory, on which this thesis is theoretically based, as an economic shock whose impacts on the members of EMU are asymetric. Thesis also analyzes potential benefits and costs of the euro adoption in the Czech republic and tries to estimate its range. In conclusion thesis summarizes how advantageous the option of the fast euro adoption in the Czech republic is.Bakalářská práce analyzuje vliv dopadů globální finanční krize na termín přijetí eura v České republice. Dopady globální finanční krize jsou v návaznosti na teorii OCA, z níž práce teoreticky vychází, analyzovány jako hospodářský šok dopadající na členy EMU asymetricky. Dále práce zkoumá potenciální přínosy a náklady zavedení eura v České republice a pokouší se odhadnout jejich výši. V závěru se na základě provedené analýzy snaží vyhodnotit nakolik je varianta rychlého přijetí eura v České republice v současné době výhodná

Analysis of credit risks accepted by a bank during assignment of loans to middle-sized companies in the Czech Republic

Hlavním cílem diplomové práce je stanovení úvěrových limitů pro krátkodobý provozní a dlouhodobý investiční úvěr vybrané společnosti. První část práce je teoretická a zaměřuje se na vymezení, kvantifikaci a řízení úvěrového rizika. Druhá část práce je prakticky zaměřená a věnuje se finanční a strategické analýze, na jejichž závěrech je sestaven finanční plán, který slouží k odhadu budoucích volných peněžních toků, který je základním podkladem pro stanovení úvěrových limitů pro krátkodobý provozní a dlouhodobý investiční úvěr.The main aim of this diploma thesis is to assign a credit limit for an short-term operating and long-term investment loan for a selected company. First part of thesis is theoretical and it focuses on definition, quantification and managing of credit risk. Second part is practically oriented and it deals with financial and strategic analysis which concludes to development of business plan which is used for prediction of future free cash flow which is basic tool for assigning credit limits for short-term operating and long-term investment loan

Numerical solution of 3D ow

Nazev prace-: Numericke fesem tfirozrnorneho proucleni Autor: Martin Kyncl Katcdra: Katedra numericke iiiatcinatiky Vedouci diplomove prace: Doc. RNDr. Jifi Felcman, CSc. e-mail vedouciho: felcman(G>karlm.inff.cuni.c/ Abstrakt: Prace se zabyva numorickym modelovanim nevazkeho a vazkeho stlacitelneho proudeni plynu ve 3D. Pou/iLa mutoda fes(Mif jn zalo2cna na ro/lo/rni systemu, kterym jc proudoni popsano, na nevazkou a ciste vaxkou cast. V praci json uvedeny numericke vyskulky, ktcre uka/uji pou/Jtelnost navrzene metody. Klicova slova: stlacitelne proudeni, Eulerovy rovnice, Navier-SLokesovy rov- nice, mctoda konecnycli objeinu, motoda konecnych prvku, Dolauriayova tri- angulace Title: Numerical solution of 3D flow Author: Martin Kyncl Department: Department, of Numerics Supervisor: Doc. RNDr. Jin Felcman, CSc. Supervisor's e-mail address: folemanQkarlin.mff.cuni.c/ Abstract: The paper is concerned with numerical modelling of inviscid as well as viscous gas flow in 3D. The method is based on upwind flux vector splitting finite volume scheme combined with finite elements. The geomet- rical data and the computational results for the three-dimensional flow arc presented. Keywords: compressible flow, Euler equations, Navicr-Stokes equations, fi- nite volume method, finite element method, Delaunay..

Term of the euro adoption in the Czech republic in the context of the global financial crisis

Bachelor thesis analyzes the influence of effects of the global financial crisis on the term of the euro adoption in the Czech republic. Effects of the global financial crisis are analyzed in connection with OCA theory, on which this thesis is theoretically based, as an economic shock whose impacts on the members of EMU are asymetric. Thesis also analyzes potential benefits and costs of the euro adoption in the Czech republic and tries to estimate its range. In conclusion thesis summarizes how advantageous the option of the fast euro adoption in the Czech republic is