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.

This thesis deals with Eigenvalues of Laplace operator and with their properties. We have gradually introduced a Laplace eigenvalue problem in one, and then in two dimensions. We have also shown the significant properties of these eigenvalues and the way to determine their ap...

The subject of this thesis are delay differential equations. Delay, system of delay differential equations, initial condition and initial value problem are defined here. The qualitative theory and solution methods for constant delay differential equations are also mentioned. Furthermore, examples ...

A vertex colouring f: V(G) -> N, of a graph G is called a 2-distance vertex colouring if every pair of vertices at distance at most two have different colours. That means f(u) is not equal f(v) for all u,v from V(G) with dist_G(u,v) <= 2. The value f(...

This bachelor thesis "Statistical Analysis of the System Imbalance in the Electric Power System" examines system imbalance that occures in the electrical grid. The examined data, describing system imbalance in a particular business hour, are tested for white noise using...

This bachelor thesis focuses on modeling and prediction of ice hockey match results, specificaly on the regular seasons of the highest-level Czech league, the Extraliga, between 2011 and 2017. The first section of the thesis comprises a list of basic models used in...

This bachelor thesis is focused on studying of multipoint boundary value problems. At first, we show how the multipoint boundary value problem looks like in general. We focuse on a particular four point boundary value problem for which we find eigenvalues and corresponding eigenfun...

This thesis deals with osculating curves and their families. First, definitions of basic terms are given. Further, the thesis deals with the definition of the contact of q-th order of two curves and its relation to the osculating curves. Then, a list of different kinds of...

The subject of this bachelor thesis is the graph invariant known as the interlace polynomial. We will first take a look at the circumstances that led to its creation, before describing its basic properties using previously-published articles. We will then try to find the itera...

This bachelor thesis deals with Estimates of Principal Eigenvalue of the Boundary Value Problems for second order Ordinary Differential Equations. In detail, the Estimates of Principal Eigenvalue of the Boundary Value Problems for second order Linear Ordinary Differential Equations a...

The Bachelor thesis deals with trading on stock markets. The main object is to compare several investment strategies according to trading simulation. The methods Buy and Hold, random closing of positions and the trading according to indicators with recommended values of parameters,...