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&#...

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&...

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...

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&#...

The topic of this thesis are estimates of principal eigenvalue of boundary value problems. We deduced a formula for upper bound using Rayleigh quotient and for lower bound with Picone identity. We focused on building the test function using the cubic spline. We utilized an...

This bachelor thesis describes the basic theory of manifolds. The aim of this work is to introduce concepts from this area using interesting examples, counterexamples and using the pictures created in the software Mathematica. At the end of the thesis, we derive Stoke's theorem...

The aim of this thesis is to introduce the introduction to the theory of continued fractions. There is a finite and infinite continued fraction defined here. Furthermore, a convergents and its properties are defined. The criteria for convergence of continued fractions are also...

This Bachelor Thesis dedicates to the study of Fučík spectrum for the second order boundary value problem with a non-local boundary condition. At first there is found an analytic description of Fučík spectrum as zero level of two dimensional function at alpha, beta. Thanks&#x...

This bachelor thesis deals with statistical processing of data from entrance tests in mathematics, which are written by students of the first years of some fields of study of the University of West Bohemia in Pilsen. The thesis focuses on the relationship among students respon...

The focus of this thesis is on a group of selected indicators for evaluating the financial health of a business. The goal is to create a model for complex financial analysis including the areas of absolute, differential and ratio indicators, and the pyramidal decomposition&#x...

This thesis deals with a L(2,1)-labelling of graphs and studies upper and lower bounds on the number lambda(2,1). The thesis further summarizes known results on the number lambda(2,1) of basic graphs classes, planar graphs, Cartesian products of graphs, circular graphs, Kneser graphs, s...

This thesis describes the problematics of the economic and financial aspects of a small business. In order to compile the profit and loss account the cash flow overview, a full spectrum of possible revenues, costs, incomes and expenses is presented and their progressio...

The aim of this thesis is to try to predict NBA results using selected ranking models and to compare the predictive success of these models with each other and with a betting office. Three models were selected, namely Keener's method, Elo rating and PageRank. For each...

This bachelor thesis deals with Ramsey theory. There are summarized the basic results of Ramsey theory on graphs and online Ramsey theory. In the last chapter we are dealing with upper bound for online Ramsey numbers of even and odd cycles.