We use numerical simulations to study reaction-diffusion problems with diffusion driven by fractional Laplacian. Fractional Laplacian appears, e.g., in mathematical models of population dynamics where the dispersion of individuals is due to the so called Levy flights rather than due to Brown...

In this thesis we investigate applications of the Lovász local lemma and its related methods. We are going to describe the gradual development of these methods and show the specific examples of its use in the field of research on independent transversals and hypergraphs.

This thesis is focused on option pricing in stochastic volatility models using neural networks. First, option prices in the Heston model are generated using the Heston-Lewis formula. A neural network is then trained using these prices to first estimate the parameters of the Heston&...

This paper deals with a BVP for a system which consists of two ordinary differential equations of the second order with concave and convex nonlinearities and Dirichlet boundary conditions. One of the equations contains a positive parameter $\lambda$. The aim of this work is&#x...

Nowadays, the majority of financial markets are order-driven. An order book is a record of all buy and sell orders for a particular financial instrument. A limit order is an instruction given by a trader to buy or sell a financial instrument at a specified price or&#...

This thesis focuses on planning and optimization of an industrial paint shop production process. It aims to provide a comprehensive view of the paint shop planning issues and to propose an optimized model that can be effectively used to improve the production process. The pape...

The thesis demonstrates a possible implementation of project-based teaching of mathematics at a secondary school. Two fully developed projects have undergone a pilot implementation at a grammar school, including student preparation, specific assignments and evaluations, supplemented with student outputs.&#...

This work deals with the teaching process of complex numbers and fractals in high schools. The complex numbers from a historical point of view were presented in the introduction. Subsequently, research was carried out on the teaching process of this subject at the level of...

The aim of this thesis is to contribute to the study of the constitutive laws of groundwater flow in porous media of the fractured rock type. In this work, the constitutive laws are obtained from a series of numerical simulations of water flow in a small section ...

In this thesis we investigate the boundary value problem consisting of a second order differencial equation, Sturm-Liouville condition and integral type condition. We are going to describe eigenvalues of corresponding linear problem. We introduce an implicit description of the Fučík spectrum ...

Rough fractional stochastic volatility models are a progressive and promising field of research in derivative pricing. In the first part of this thesis, we give an introduction to option pricing and we outline the motivation that led to the development of the rough fractional ...

This thesis deals with L(p,q)-labellings of graphs and L(p,q,r)-labellings of graphs. By appropriate labellings we mean an assignment of non-negative integers to vertices of graph G according to the following rules: adjacent vertices are labelled by values differing by at least p, verti...

This thesis investigates heterogeneous versions of semi-discrete Nagumo equation with non-constant capacity. This system is assumed on discrete spatial structures - graph and infinite lattice. While there always exist non-trivial stationary solutions for homogeneous systems, heterogeneous systems may ...

This diploma thesis deals with conic section topic which takes an interesting part in math tuition as well as constructive geometry at secondary schools within the Czech Republic. This document contains a research of Framework Education Programme (curriculum), School Education Programme, sum...

This thesis is concerned with the study of the analytic theory of continued fractions and its application to general birth and death processes. The main aim of this work was to introduce the method of continued fractions to solve these processes. To better understand the ...

The thesis focuses on roofs from the point of view of descriptive geometry. In the first part, parts of the planes are used to roof the buildings. In the second part, other geometric surfaces are used. The thesis also presents ideas on how to make ...

This magister thesis is focused on analysis of stability of covariance matrix estimation. The estimate of covariance matrix is then used in the optimal portfolio model in the Markowitz sense. The greatest emphasis was put on it, how long to take the time series for the&#x...

In this thesis, the Binomial and Trinomial model for option pricing are compared using the real option contracts. The number of the steps is an important factor influencing the computational demand and the precision of the results. Therefore, the convergence criterium was defined f...

The diploma thesis is dedicated to basic tasks occurring in transport logistics.The first is the traveling salesman problem and its extension to the multiple traveling salesman problem. Further we deal in more detail with vehicle routing problem with capacities and bin packing problem,&...

The thesis is devoted to the qualitative analysis of a semilinear system of heat equations \begin{align} \begin{cases} \frac{\partial u_1}{\partial t} -\Delta u_1 = \lambda f_1(u_2) \tab &\text {v } \Omega_T,\\[7pt] \frac{\partial u...