This thesis targets the topic of non-autonomous growth models. Firstly, with consideration of several examples of non-autonomous phenomena, it is explained why and under what circumstances it could be beneficial to consider a growth model with time-dependent parameters. Additionally, Verhulst's&#x...

This thesis addresses the spectral properties of graphs, a key aspect of graph theory that finds broad applications across various fields of science and technology. The work provides an overview of both fundamental and advanced concepts of spectral matrix and graph theory, with an&...

This bachelor's thesis is dedicated to both theoretical and practical parts of timetabling problems. Concepts needed for the construction of timetables are defined in the introductory part of the thesis. These are mainly concepts related to graph theory and linear programming. One p...

In the present thesis we familiarize the reader with the Union-closed sets conjecture. The conjecture states that any nite union-closed family of sets has an element that belongs to at least half of the member sets. We examine in detail the conjecture's assumptions, known ...

In this work, we will introduce the concept of vertex colouring of graphs. Subsequently, we will present Reed's conjecture (B. Reed. omega, Delta, and chi), which provides an upper bound on the chromatic number of a graph G, expressed as chi(G) <= ceil((omega(G) + Delta...

Let $G$ be a graph and $k\geq 0$. The $k$-iterated line graph of a graph $G$ is $L^k(G)= L(L^{k-1}(G))$, where $L^0(G) = G$ and $L^1(G) = L(G)$. The minimum number $k$ such that iterated line graph $L^k(G)$ has hamiltonian cycle, path is called hamiltonian index, ham...

This bachelor thesis is focused on the problem of flows in networks. The tasks of finding the maximum flow and finding the minimum cost flow are presented here. The main output of the work is familiarization with flows with convex prices, implementation of algorithms solving&#...

This bachelor's thesis focuses on the purchase of real estate and its short-term rental through the Airbnb platform. The aim of the thesis is the evaluation of said investment. The thesis introduces basic concepts of financial mathematics related to this topic. Three possible f...

This thesis deals with dynamical properties of models of chemical reaction systems. We introduce different types of chemical reactions from the point of view of reaction kinetics, and the basic notation used in this thesis and then the derivation of differential equations describing...

This bachelor thesis focuses on the eigenvalue problem with weights. For simplicity, we consider a particular second order ordinary differential operator with Dirichlet boundary conditions. We first determine the eigenvalues and eigenfunctions in the case of a piecewise constant weight function&#...

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.