Sökning: "digital mathematics"

Visar resultat 1 - 5 av 129 avhandlingar innehållade orden digital mathematics.

  1. 1. Digital lines, Sturmian words, and continued fractions

    Författare :Hanna Uscka-Wehlou; Christer Oscar Kiselman; Maciej Klimek; Gunilla Borgefors; Mikael Passare; Damien Jamet; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; digital geometry; digital line; hierarchy of runs; combinatorics on words; Sturmian word; upper mechanical word; characteristic word; irrational slope; continued fraction; Gauss map; fixed point; Discrete mathematics; Diskret matematik; matematik; Mathematics;

    Sammanfattning : In this thesis we present and solve selected problems arising from digital geometry and combinatorics on words. We consider digital straight lines and, equivalently, upper mechanical words with positive irrational slopes a... LÄS MER

  3. 2. Digital Geometry, Combinatorics, and Discrete Optimization

    Författare :Shiva Samieinia; Christer Kiselman; Rikard Bøgvad; Rémy Malgouyres; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Digital geometry; Khalimsky topology; Khalimsky plane; Khalimsky-continuous function; digital straight line segments; discrete optimization; discrete convexity; integral convexity; lateral convexity; marginal function; MATHEMATICS; MATEMATIK; Mathematics; matematik;

    Sammanfattning : This thesis consists of two parts: digital geometry and discrete optimization. In the first part we study the structure of digital straight line segments. We also study digital curves from a combinatorial point of view. LÄS MER

  4. 3. Digital Geometry and Khalimsky Spaces

    Författare :Erik Melin; Christer Kiselman; Gunilla Borgefors; Mikael Passare; Jean Serra; Uppsala universitet; []
    Nyckelord :Applied mathematics; Khalimsky topology; digital geometry; digital topology; Alexandrov space; digital surface; digital curve; digital manifold; continuous extension; smallest-neighborhood space; image processing; Tillämpad matematik;

    Sammanfattning : Digital geometry is the geometry of digital images. Compared to Euclid’s geometry, which has been studied for more than two thousand years, this field is very young.Efim Khalimsky’s topology on the integers, invented in the 1970s, is a digital counterpart of the Euclidean topology on the real line. LÄS MER

  5. 4. Split Trees, Cuttings and Explosions

    Författare :Cecilia Holmgren; Svante Janson; Luc Devroye; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Random Graphs; Random Trees; Split Trees; Renewal Theory; Binary Search Trees; Cuttings; Records; Tree Algorithms; Markov Chains; Galton-Watson Processes; MATHEMATICS; MATEMATIK; Mathematics; Matematik;

    Sammanfattning : This thesis is based on four papers investigating properties of split trees and also introducing new methods for studying such trees. Split trees comprise a large class of random trees of logarithmic height and include e.g., binary search trees, m-ary search trees, quadtrees, median of (2k+1)-trees, simplex trees, tries and digital search trees. LÄS MER

  7. 5. Fingerprinting digital documents

    Författare :Tina Lindkvist; Thomas Johansson; Linköpings universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

    Sammanfattning : In this thesis we look at the fingerprinting problem. Our belief is that it is very difficult to prevent illegal copying, so our solution is to mark each copy uniquely so that if it is spread illegally, the original owner of that copy can be found. The principle is the same as for a serial number on a product. LÄS MER