Glosarium Matematika

273 p.; 24 cm

Abstracts of Ph.D. theses in mathematics

summary:Stolín, Radek: Teaching of financial and insurance mathematics at secondary and higher professional schools -- coinsurance in bonus-malus systems in automobile insurance. Olejníèková, Jana: Scientific work of Bohumil Bydžovský. Flašková, Jana: Ultrafilters and small sets. Pražák, Pavel: Differential equations and their applications in economics. Bartl, David: Theorems of the alternative and linear programming in infinite-dimensional spaces. Smetana, Petr: Some problems of the private health insurance. Kosinka, Jiøí: Algorithms for Minkowski Pythagorean hodograph curves. Kopa, Miloš: Utility functions in portfolio optimization. Orsáková, Martina: M-estimation in nonlinear regression for longitudal data. Šiman, Miroslav: On portmanteau tests of randomness. Purmová, Lucie: Continuous population models for single species. Koubková, Alena: Sequential change-point analysis. Omelka, Marek: Second order properties of some M-estimators and R-estimators. Barto, Libor: Full embeddings and their modifications. Pecinová, Eliška: Ladislav Svante Rieger (1916--1963). Nguyen, Duc Huy: On existence and regularity of solutions to perturbed systems of Stokes type. Prachaø, Aleš: Analysis of the discontinuous Galerkin method for elliptic problems. Franek, Peter: Several Dirac operators in parabolic geometry. Hladík, Milan: Explicit description of supporting and separating hyperplanes of two convex polyhedral sets depending on parameters. Janeèek, Martin: Valuation techniques of life insurance liabilities. Ranocha, Pavel: Stationary distribution of time series. Bímová, Daniela: Kinematic geometry in $n$-dimensional Euclidean space

Digital Curvature Estimation: An Operator Theoretic Approach

This thesis is divided into two parts. The first part is devoted to the curvature estimation of piecewise smooth curves using variation diminishing splines. The variation diminishing property combined with the ability to reconstruct linear functions leads to a convexity preserving approximation that is crucial if additional sign changes in the curvature estimation have to be avoided. To this end, we will first establish the foundations of variation diminishing transforms and introduce the Bernstein and the Schoenberg operator on the space of continuous functions and its generalization to the Lp-spaces. In order to be able to detect C2-singularities in piecewise smooth curves, we establish lower estimates for the approximation error in terms of the second order modulus of smoothness for Schoenberg’s variation diminishing operator. Afterwards, we consider smooth curve approximations using only finitely many samples of the curve, where the approximation, its first, and its second derivative converge uniformly to its corresponding part of the curve to be approximated. In this case, we can show that the estimated curvature converges uniformly to the real curvature if the number of samples goes to infinity. Based on the lower estimates that relates the decay rate of the approximation error with smoothness we propose a multi-scale algorithm to estimate the curvature and to detect C2-singularities. We numerically evaluate our algorithm and compare it to others to show that our algorithm achieves competitive accuracy while our curvature estimations are significantly faster to compute. The second part deals with generalizations of the established lower estimates for the Schoenberg operator. We will show that such estimates can be obtained for linear operators on a general Banach function space with smooth range provided that the iterates of the operator converge uniformly and a semi-norm defined on the range of the operator annihilates the fixed points of the operator. To this end, we will prove by spectral properties that the iterates of every positive finite-rank operator converge uniformly. As highlight of this thesis, we show a constructive way using a Gramian matrix where the dual fixed points operate on the fixed points of an operator to derive the limit of the iterates for an arbitrary quasi-compact operator defined on a general Banach space

Smoothness assumptions in human and machine vision, and their implications for optimal surface interpolation

In this paper we shall examine what smoothness assumptions are made about object surfaces, object motion, and image intensities. We begin by looking into the physiological limits of vision and how these might influence our perception of smoothness. We then look at a sampling of the computer vision and psychology literature, inferring smoothness constraints from the mathematical assumptions tacitly presumed by researchers. This look at computer vision and psychology of vision is not meant to be an inclusive study, but rather representative of the assumptions made, and in part representative of the mathematical models used therein. We shall conclude that prevalent assumptions are that surfaces, motion, and intensity images are functions in C2, eland c2 respectively. In the latter portion of this paper we examine one use of explicit assumptions on smoothness in the definition of existing method for obtaining "optimal" surface interpolation. We briefly introduce the nomenclature of information-based complexity originated by Traub, Wozniakowski, and their colleagues, which is the mathematical machinery used in obtaining these "optimal" surfaces. This theory requires that we know the class of functions from which our desired surface comes, and part of the definition of a class is the degree of smoothness. We then survey many possible classes for the visual interpolation problem of two dimensional surfaces, and state formulas from which one can obtain the optimal surface interpolating given depth data

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Digital Image Processing

This book presents several recent advances that are related or fall under the umbrella of 'digital image processing', with the purpose of providing an insight into the possibilities offered by digital image processing algorithms in various fields. The presented mathematical algorithms are accompanied by graphical representations and illustrative examples for an enhanced readability. The chapters are written in a manner that allows even a reader with basic experience and knowledge in the digital image processing field to properly understand the presented algorithms. Concurrently, the structure of the information in this book is such that fellow scientists will be able to use it to push the development of the presented subjects even further