The bachelor's thesis deals with the occurrence of arbitral opportunities when betting on sports results in data from football, basketball and tennis and possible strategies of betting on arbitral opportunities with a guarantee of return on investment. Data from particular competitions a...

In this bachalor thesis we describe fundamental definitions and properties of a copula. We will focus primarly on Archimedean copulas, which are one of the most important class of copulas. We will introduce their definition, fundamental properties and severel families of Ar...

We investigate population models of mathematical biology and more specifically, the effect of harvesting. We consider one population whose internal dynamics is decribed by exponential, logistic, or bistable law. For these populations we study the change of dynamics by harvesting which models...

In this thesis a distribution problem is discussed. At first some basic problems are introduced together with corresponding solution methods. Next, more and more complex models are being presented involving product delivery problems from multiple producers to multiple consumers during some p...

In this thesis, we investigate the Fučík spectrum for the second order boundary value problem with one Robin and one non-local boundary conditions. We prove that the corresponding linear boundary value problem has infinitely many eigenvalues and we provide the description of these ...

This thesis investigates population models on two discretely separeted patches. The local population dynamics follows one of the basic models (exponential growth, logistical growth, bistable dynamics) on each of these patches. In addition, diffusion occurs between these areas. We examine the ...

This bachelor thesis is focused on comparing the benefits of buying and renting ski equipment based on the number of periods spent each year in the ski area. Ski equipment for beginners and advanced skiers will be evaluated separately. Furthermore, three variants of financing ...

This Bachelor thesis deals with the Fučík spectrum of $p$-Laplace operator. We examine a nonlocal boundary value problem, with one Dirichlet boundary condition and one integral boundary condition. We implicitly describe the Fučík spectrum, we also appoximate it numerically and based on ...

This document describes the differences between matching in undirected graphs and matching in undirected hypergraphs. The introductory chapter serves as an introduction to the basic terms of graph theory, to the mathematical optimization problem and computational complexity. Chapter ...

This bachelor thesis explores a probability model for two different counting methods of incoming customers into a shopping centre. The investigated counting devices are a sensor and a camera. The estimators of the model are proposed and evaluated using simulations.

The bachelor's thesis investigates the stability of stationary solutions of a two population system relying on the Lotka-Volterra model. General interaction properties of two populations characterised by symbiosis, competition and predator-prey type shall be investigated in detail. Furthermore, the...

This thesis is focused on an S-packing colorings of graphs. Let S = (a_1, a_2, . . .) be a non-decreasing sequence of positive integers. A mapping which assigns colors represented by positive integers to vertices of a graph G such that vertices with color i have ...

This work deals with cyclic properties of circulant graphs. It is mainly focused on pancyclicity of circulant graphs. Let 0 < a_1 < a_2 < ... <a_k <= n/2 be positive integers and n be natural number. The circulant graph C_n(a_1, a_2,.., a_k) is a graph...

Matrix structured population models are an example of systems of first-order difference equations, which are among the important model tools used when forest growth dynamics is studied. The dynamics of forest stand state is governed by the properties of~the Usher projection matrix, whic...

The thesis deals with S-packing edge colorings of graphs. For a non-decreasing sequence of positive integers S = (s_1, s_2, s_3, ...), an S-packing edge coloring of a graph is a function f that assigns colors from {1, 2, 3, . . . } to the edges of the...

This thesis is focused on Hamilton properties of directed graphs. The first chapter is a familiarization with some of the problems of graph theory. In the second chapter we define fundamental terms of graph theory for both undirected and directed graphs. In the third chapter&#...

The bachelor thesis titled "Identification of outliers" is focused on a detection of outliers in sets of univariate data. The aim of the work is to describe the chosen methods and demonstrate their advantages and disadvantages. The selected methods are then performed in a...

This bachelor thesis deals with evolutionary games on graphs. Standard models of evolutionary games (e.g., replicator dynamics) do not consider any population structure. Using graphs, we introduce a structure into the evolutionary game which can affect the dynamics of the game. The aim&...

In the thesis, we study expected cover time of a random walk on a graph. We consider expected cover time as an average number of steps which takes to visit all vertices of the graph. We will show the derivation of an expected cover time formula for the comp...

This bachelor thesis deals with \vyraz{L(i,j,k)}-labelling of graphs with special focus on \vyraz{L(3,2,1)}-labelling, and searches for minimal spread or upper and lower bounds on this spread by which the graph can be evaluated. For integers \vyraz{i, j, k}, \vyraz{L(i,j,k)}-labelling&#...