In this manuscript we study the action of one-dimensional integral operators on rearrangement-invariant Banach function spaces. Our principal goal is to characterize optimal target and optimal domain spaces corresponding to given spaces within the category of rearrangement-invariant Banach function spaces as well as to establish pointwise estimates of the non-increasing rearrangement of a given operator applied on a given function. We apply these general results to proving optimality relations between special rearrangement-invariant spaces. We pay special attention to the Laplace transform, which is a pivotal example of the operators in question. Powered by TCPDF (www.tcpdf.org)

Using interpolation methods, new results on the boundedness of quasilinear joint weak type operators on Lorentz-Karamata (LK) spaces are established. LK spaces generalize many function spaces introduced before in literature, for example, the generalized Lorentz- Zygmund spaces, the Zygmund spaces, the Lorentz spaces and, of course, the Lebesgue spaces. The focus is mainly on the limiting cases of interpolation, where the spaces involved are, in certain sense, very close to the endpoint spaces. The results contain both necessary and sufficient conditions for the boundedness of the given operator on LK spaces. The complete characterization of embeddings of LK spaces is also included and the optimality of achieved results is then discussed. Finally, we apply our results to the conjugate function operator, which is known to be bounded on $L_p$ only if $1<p<\infty.$ Powered by TCPDF (www.tcpdf.org)

Finding a topologically accurate approximation of a real planar algebraic curve is a classic problem in Computer Aided Geometric Design. Algorithms describing the topology search primarily the singular points and are usually based on algebraic techniques applied directly to the curve equation. In this thesis we propose a more geometric approach, taking into account the subsequent high-precision approximation. Our algorithm is primarily based on the identification and approximation of smooth monotonous curve segments, which can in certain cases cross the singularities of the curve. To find the characteristic points we use not only the primary algebraic equation of the curve but also, and more importantly, its implicit support function representation. Using the rational Puiseux series, we describe local properties of curve branches at the points of interest and exploit them to find their connectivity. The support function representation is also used for an approximation of the segments. In this way, we obtain an approximate graph of the entire curve with several nice properties. It approximates the curve within a given Hausdorff distance. The actual error can be measured efficiently. The ap- proximate curve and its offsets are piecewise rational. And the question of topological equivalence of the...

The aim of the master thesis is to sum up theoretical information about beamforming methods of microphone arrays and to verify their functionality. At the beginning of this work there are simulated different varietes of linear uniform and nonuniform microphone arrays and circular arrays. The results are verificated by a practical measurement in ideal conditions. Then I will focuse on implementation of the DAS(Delay And Sum), SAB(Sub Array Beamforming), CDB(Constant Directivity Beamforming), CDB-CA(CDB-Circular Arrays) beamformer including theoretical and practical verification of the functionality in ideal conditions. At the end of this thesis are all beamforming methods compared with each other at SNR(signal to Noise Ratio) and directivity parameters.

This master’s thesis deals with the issue of digital to analog conversion and possibility of its realization in digital circuits. Goal of this project is to design sigma-delta digital to analog converter with resolution of 14 bits and frequency band (0 ÷ 20) kHz. Main functional blocks: interpolator and modulator sigma-delta will be realized like digital structures. Reconstruction filter will be realized like an analog structure. For design a check of parameters of designed converter programs MATLAB and Simulink are used. Designed digital structures will be described by VHDL language.

The diploma thesis deals with registration and analysis of images from the experimental low-cost fundus camera that reaches a low SNR (around 10 dB) and low temporal and spatial resolution. The aim of the diploma tesis is to explore the possibilities of digital processing leading to the creation of a videosequence that has real benefits for medical diagnostics. The well-known program elastix is used for registration. Preprocessing filters and interpolation are implemented in Matlab. The program provides a wide range of setting options, out of which many combinations were tested and evaluated. To assess the accuracy achieved, spatial variations in the detected motion of blood-vessels are evaluated. Best results with a precision below 0.3 px were achieved by using a band-pass filter, a~suitably sized mask, rigid registration and a metric of the mutual information. Test sequences were registered precisely enough both for visual assessment and basic computational analysis. Registered sequences and the developed application that both can be used in the further development of the experimental camera are the main contributions of the diploma thesis.

This diploma thesis is devoted to the multivariate cryptosystems. It includes an overview of commutative algebra with emphasis on Gröbner bases. Of all algorithms, especially the ones using Gröbner bases are studied, i.e. Buchberger's algorithm, which is already implemented in Wolfram Mathematica, and F4 algorithm, for which a program package has been created in the Wolfram Mathematica environment. Also Zhuang-Zi algorithm is described. To simplify its steps a program to compute the Lagrange interpolation polynomial has been created in Python.

The main goal of this project was to familiarize readers with the techniques used in real-time animation of 3D characters. This work is focused on two types of animation: keyframe animation and skeletal animation. There are described algorithms for software and hardware accelerated model deformations, keyframe interpolations, animation blending, inverse kinematics and ragdoll. The result of this project is a framework, which consists of an animation library, examples demonstrating library functions and tools for export animations from 3D Studio Max and MilkShape 3D.

The aim of the work is to describe procedural texturing and usage of a noise for creating textures of real materials. The reader will learn the fundamentals of the noise, its properties and a way of using it. Random numbers and interpolation methods are important parts of the noise evaluations, therefore there are chapters about random numbers generating and interpolation methods. Obviously, there is not missing the chapter, which is depicting properties and principles of several methods of creating noise. The main part of this work is effective implementation of library with a chosen noise methods, so next chapters are about choosing methods and design of the interface, implementation and many kinds of tests and optimalizations. Achieved results and final conclusions are at the end of this work.

In this master’s thesis we focus on the basic properties of computer curves and their practical applicability. We explain how the curve can be understood in general, what are polynomial curves and their composing possibilities. Then we focus on the description of Bezier curves, especially the Bezier cubic. We discuss in more detail some of fundamental algorithms that are used for modelling these curves on computers and then we will show their practical interpretation. Then we explain non uniform rational B-spline curves and De Boor algorithm. In the end we discuss topic rasterization of segment, thick line, circle and ellipse. The aim of master’s thesis is the creation of the set of interactive applets, simulating some of the methods and algorithm we discussed in theoretical part. This applets will help facilitate understanding and will make the teaching more effective.