A note on the existence of Gibbs marked point processes with applications in stochastic geometry

summary:This paper generalizes a recent existence result for infinite-volume marked Gibbs point processes. We try to use the existence theorem for two models from stochastic geometry. First, we show the existence of Gibbs facet processes in $\mathbb{R}^d$ with repulsive interactions. We also prove that the finite-volume Gibbs facet processes with attractive interactions need not exist. Afterwards, we study Gibbs-Laguerre tessellations of $\mathbb{R}^2$. The mentioned existence result cannot be used, since one of its assumptions is not satisfied for tessellations, but we are able to show the existence of an infinite-volume Gibbs-Laguerre process with a particular energy function, under the assumption that we almost surely see a point

Gibbs particle processes

We consider a recent result for the existence of infinite-volume marked Gibbs point processes and try to apply it to geometric models. At first, we reformulate a problematic assumption of the considered existence result and check that the theorem still holds. We use this result for the family of Gibbs facet processes (a special case of particle processes) and prove the existence for repulsive interactions. We find counterexamples for the process with attractive interactions and prove that the finite-volume Gibbs facet process in R2 does not exist in this case. We also study the class of Gibbs-Laguerre tessellations of R2 . We cannot use the mentioned existence result in general, but we are able to prove the existence of an infinite-volume Gibbs-Laguerre process with particular energy function, under the assumption that we almost surely see a point. 1Cílem této práce byla aplikace nové existenční věty pro kótované Gibbsovy bodové procesy v nekonečném objemu na modely ze stochastické geometrie. Nejprve přeformulu- jeme problematický předpoklad existenční věty a poté ukážeme, že věta o existenci platí i s naší novou formulací. Poté uvažujeme rodinu Gibbsových procesů faset (speciální pří- pad procesů částic) a dokážeme, že existuje Gibbsův proces faset v nekonečném objemu s odpudivými interakcemi. Pro případ s přitažlivými interakcemi nalezneme protipříklad proti jednomu z předpokladů uvažované existenční věty a navíc ukážeme, že Gibbsovy pro- cesy faset v omezeném okně v R2 neexistují. Dále zkoumáme Gibbs-Laguerrovy mozaiky v R2 . Pro tuto třídu procesů nemůžeme použít zmíněnou existenční větu, ale podaří se nám dokázat, že existuje Gibbs-Laguerrova mozaika v nekonečném objemu pro speciální funkci energie, za předpokladu, že skoro jistě pozorujeme alespoň jeden bod. 1Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

An evaluation of characteristics of entrepreneurs by students of Czech and Slovakian universities and their tendency towards entrepreneurship

The aim of this article is to compare the assessment of significance of personality characteristics of entrepreneurs in the Czech and Slovak Republic as well as the tendency of students to start entrepreneurships after graduating from university. The research sample consisted of 409 students from 14 universities studying business in the last year in the Czech Republic and 568 students from 8 universities studying in the Slovak Republic. In order to meet the paper's aim, statistical hypotheses were formulated and validated using the Z-score method. One result is that students working in universities in the Slovak Republic are more interested that Czech students in doing business within three years after finishing their studies, unless unexpected circumstances happen in their families. More than 75% of the addressed students at the Slovak university considered endurance, expertise, responsibility and risk awareness as the most important qualities of an entrepreneur. More than 60% of Czech students have the same opinion. There are significant differences in opinions of the students from the Czech Republic and the Slovak Republic

Gibbs particle processes

We consider a recent result for the existence of infinite-volume marked Gibbs point processes and try to apply it to geometric models. At first, we reformulate a problematic assumption of the considered existence result and check that the theorem still holds. We use this result for the family of Gibbs facet processes (a special case of particle processes) and prove the existence for repulsive interactions. We find counterexamples for the process with attractive interactions and prove that the finite-volume Gibbs facet process in R2 does not exist in this case. We also study the class of Gibbs-Laguerre tessellations of R2 . We cannot use the mentioned existence result in general, but we are able to prove the existence of an infinite-volume Gibbs-Laguerre process with particular energy function, under the assumption that we almost surely see a point.

Communication in a selected organization

The aim of this thesis was to bring issues to the topic of communication in a selected organization , focusing on communication in business and seeking to improve the design issues. In the literary section is clarification and extension of the concept of communication. The practical part was focused on familiarization with the company , its divisions, where they are heading and how communication takes place

Separability of the intensity function of a Poisson point process

Our main interest in the thesis is Poisson point process and one of its charac- teristics - intensity function. Whenever Poisson process has intensity function, its distribution is uniquely determined by it. Our main goal is to determine how to deduce from observed data whether intensity function is separable. We present a formal test of this hypothesis assuming exponential model of the in- tensity function depending on finite number of parameters. Properties of this test are then examined in a simulation study. 1V práci se zabýváme Poissonovým bodovým procesem a jednou z jeho základ- ních charakteristik - funkcí intenzity. Pokud Poissonův proces má funkci inten- zity, pak je jejím tvarem jednoznačně určen. Zkoumáme, jak z napozorovaných dat poznat, že je funkce intenzity v součinovém tvaru. Pro speciální model s ex- ponenciální funkcí intenzity závislé na konečně mnoha parametrech sestavíme formální test této hypotézy. Jeho vlastnosti - dodržování zvolené hladiny a sílu proti různým alternativám - poté prozkoumáme v simulační studii. 1Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Separability of the intensity function of a Poisson point process

Our main interest in the thesis is Poisson point process and one of its charac- teristics - intensity function. Whenever Poisson process has intensity function, its distribution is uniquely determined by it. Our main goal is to determine how to deduce from observed data whether intensity function is separable. We present a formal test of this hypothesis assuming exponential model of the in- tensity function depending on finite number of parameters. Properties of this test are then examined in a simulation study.

Prices of flats n České Budějovice depending on the approach to the urban green

The main target of the thesis is to analyze the relationship of prices and access to urban green area for the selected location of the city, such as the substrate to determine values of urban greenery. This work is built on the application of the Hedonic pricing method.The thesis is divided into 4 parts. The study of literature was created the first chapter, which deals with the value of the green space, the environment in the Czech Republic and abroad, method of environmental valuation and the history of the Hedonic price method and his used. The second chapter contains target and methodology of work. The methodology describes the different steps of the methods of work. In the second part is the specification of the model, which is applied in the analysis. In this part is mentioned characteristic of the properties and collection of data. In the third chapter data analysis is divided in specific parts of the sections. The data are evaluated for the entire area, and then compare the area itself

Assessment of the cost of acquisition of residential buildings in terms of reducing the energy intensity of their operation

Constantly increasing energy and heat prices lead us to search for more effective use of technologies that reduce their consumption and hence operating costs during the life cycle of buildings and also reduce the negative effects on environment. In the past, we asked for a particular emphasis on the amount of purchase / investment costs by project assessment. Gradually, we recognize that it is important to monitor the future operating costs and realize that the thermal attributes of building materials, which affect the cost of acquisition of the object, also affect the amount of the operating costs of buildings in the phase of use. One way to reduce operating costs is the thermal insulation of buildings. How is it but with the effectiveness of funds spent? Heating do automatically reduce costs after insulation? What time will it take to get the investment returned and what are the factors that matter? These questions should be asked by the organizations providing / making the rental apartments

Degradation Performance of Open-Cell Biomaterials from Phosphated Carbonyl Iron Powder with PEG Coating

Advances in biomedicine and development of modern technologies in the last century have fostered the improvement in human longevity and well-being. This progress simultaneously initiated the need for novel biomaterials. Recently, degradable metallic biomaterials have attracted serious attention in scientific and clinical research owing to their utilization in some specific applications. This work investigates the effect of the polyethylene glycol (PEG) coating of open-cell iron and phosphorus/iron foams on their microstructure and corrosion properties. The addition of phosphorus causes a slight increase in pore size and the deposition of a polymer coating results in a smoothened surface and a moderate decrease in pore diameter. The PEG coating leads to an increase in corrosion rates in both foams and potentially a more desirable product