The thesis is concerned with a detailed examination of the most familiar short-rate models.Furthermore,it contains some author's own derivations of formulas for prices of interest rate derivatives and some relationships between certain discretizations of these short-rate models. These formulas are then used for calibration of ceratain chosen models to the actual market data.All the calculations are performed in R using author's own functions,which are along with the other more involved derivations placed in the appendix.

Probabilistic Spacetime is a simple generalization of the classical model of spa- cetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a generalization is a possible application in the context of some quantum gravity approaches, na- mely those using the path integral. It is argued that this model might be used to restrict the precision of the geometry on small scales without postulating discrete structure; or it may be used as an effective description of a probabilistic geometry resulting from a full-fledged quantum gravity computation.

This Master’s Thesis focuses on development and realization of analog system software simulator for simulation of various kinds and orders systems and for function verification of microcontrollers’ control systems. The development and realization of PSD controller is part of this thesis as well. The simulator is written in C++/CLI programming language which combines fast execution of native code and provides an advantage of managed code which has its execution managed by the .NET Framework. The data acquisition is performed via National Instrument’s USB multifunctional DAQ. The PSD regulator is realized by using modern ARM processor architecture.

The aim of this thesis is design and programming of a numerical model of shrinkage of cement composites using physical discretization and solved by parallel processing. Introduction is about the shrinkage of cement composites and explanation of terms, which are included in this thesis. The main part deals with programming of the output model, the procedure of its creation and the results of simulations.

Inequalities for discrete and continuous supremum operators Rastislav O , lhava In this thesis we study continuous and discrete supremum operators. In the first part we investigate general properties of Hardy-type operators involving suprema. The boundedness of supremum operators is used for characterization of interpo- lation spaces between two Marcinkiewicz spaces. In the second part we provide equivalent conditions for boundedness of supremum operators in the situation when the domain space in one of the classical Lorentz spaces Λp w1 or Γp w1 and the target space Λq w2 or Γq w2 . In the case p ≤ q we use inserting technique obtaining continuous conditions. In the setting of coefficients p > q we provide only partial results obtaining discrete conditions using discretization method. In the third part we deal with a three-weight inequality for an iterated discrete Hardy-type operator. We find its characterization which enables us to reduce the problematic case when the domain space is a weighted ℓp with p ∈ (0, 1) into the one with p = 1. This leads to a continuous analogue of investigated discrete inequality. The work consists of author's published and unpublished results along with material appearing in the literature.

The presented work highlights the remarkable potential of physical discretization – lattice model FyDiK in three-dimensional modelling of non-linear problems in structural mechanics. To achieve the objectives a software application, that implements the model FyDiK along with the 3D graphical user interface has been developed and thus is able to assemble a spring network model. Such a model was used for modelling the formation of cracks and fracture in the concrete specimens and also to model a plastic behaviour of steel I-beam. The calculations were performed by a massive parallelization on CUDA platform. In the first part the basic principles on which the work is based are introduced. Subsequently, a detailed description of individual parts of the model and the issue of parallelization by graphics cards are presented. In the next part the creation of the required software and improving of the model properties of mentioned materials are described. That is followed by evaluation of the achieved results with the comparison of other modelling software. The conclusion summarizes the achievements and suggestions for the further development possibilities of the presented method of modelling.

The aim of this study is to evaluate feasibility of using Bayes classifiers for predicting corporate bankruptcies. The results obtain show that Bayes classifiers do reach comparable results to then more commonly used methods such the logistic regression and the decision trees. The comparison has been carried out based on Czech and Polish data sets. The overall accuracy rate of these so called naive Bayes classifiers, using entropic discretization along with the hybrid pre-selection of the explanatory attributes, reaches 77.19 % for the Czech dataset and 79.76 % for the Polish set respectively. The AUC values for these data sets are 0.81 and 0.87. The results obtained for the Polish data set have been compared to the already published articles by Tsai (2009) and Wang et al. (2014) who applied different classification algorithms. The method proposed in my study, when compared to the above earlier works, comes out as quite successful. The thesis also includes comparing various approaches as regards the discretisation of numerical attributes and selecting the relevant explanatory attributes. These are the key issues for increasing performance of the naive Bayes classifiers

The thesis deals with dynamic simulation of real bell behavior over time. The model is created according to principles of physical discretization as a spring in the FyDiK3D software. In order for the model to be declared as relevant, it is necessary to prove the behavior of the structures used in the elementary tasks of the mechanics. It shows the correlation between the stiffness of normal and diagonal springs. Describes how to use software import tools to create a model. The resulting model approaches its real bell behavior.

The paper describes basic principles of the finite element method. Further, basic properties of triangulation are discussed. The thesis is primarily focused on the Delaunay and Greedy triangulation. Greedy triangulation is simple to implement, but may not produce the optimal shape of triangles. Delaunay method is used due to its robustness in a wide range of fields especially in computer graphics. This method is relatively easy to implement and provides triangles with high quality.

Title: Estimation of the algebraic error and stopping criteria in numerical solution of partial differential equations Author: Jan Papež Department: Department of Numerical Mathematics Supervisor of the master thesis: Zdeněk Strakoš Abstract: After introduction of the model problem and its properties we describe the Conjugate Gradient Method (CG). We present the estimates of the energy norm of the error and a heuristic for the adaptive refinement of the estimate. The difference in the local behaviour of the discretization and the algebraic error is illustrated by numerical experiments using the given model problem. A posteriori estimates for the discretization and the total error that take into account the inexact solution of the algebraic system are then discussed. In order to get a useful perspective, we briefly recall the multigrid method. Then the Cascadic Conjugate Gradient Method of Deuflhard (CCG) is presented. Using the estimates for the error presented in the preceding parts of the thesis, the new stopping criteria for CCG are proposed. The CCG method with the new stopping criteria is then tested. Keywords: numerical PDE, discretization error, algebraic error, error es- timates, locality of the error, adaptivity