Thesis--University of Florida, 1975. / Description based on print version record. Typescript. Vita. Includes bibliographical references.

Thesis (M.S.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains xi, 180 p. : ill. (some col.), maps (some col.). Includes abstract. Includes bibliographical references (p. 77-81).

Thesis (M.S.)--University of Wisconsin--Madison. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 298-301).

4 pp. / Originally published 2/2011. / Arizona's rural areas are dotted with small acreage properties that are too big to mow and too small to farm. This fact sheet describes the legal processes that create these kinds of properties and inform the reader on the difference between lot-split properties and those that undergo a legal subdivision process with a local county government. Revised 9/2016; Originally published 2/2011.

The topological entropy of the subdivision map of a finite subdivision rule restricted to the 1-skeleton of its model subdivision complex, which we call textbf{core entropy}, is examined. We consider core entropy for finite subdivision rules realizing quadratic Misiurewicz polynomials and matings of such polynomials. It is shown that for a non-restrictive class of finite subdivision rules realizing quadratic Misiurewicz polynomials, core entropy equals Thurston's core entropy. We also show that the core entropy of formal and degenerate matings of Misiurewicz polynomials is determined by Thurston's core entropy of the mated polynomials. / Doctor of Philosophy / Imagine taking a programmable calculator, inputting a number, and repeatedly pushing one of the buttons which corresponds to one of the calculator's built-in functions. For example, starting by inputting 0.5 and hitting the "x2" button over and over, or starting with 1.47 and repeatedly pressing the "sin(x)" button. The calculator may eventually return numbers that get closer and closer to a specific value, it may repeatedly cycle through some collection of specific numbers, it may not exhibit a clear pattern at all. It is of interest to understand, in some average sense, when, how often, and in what manner these patterns are exhibited and, in a quantitative fashion, compare how complicated the patterns are for different buttons on the calculator corresponding to different functions. For example, is the "x2" button, in some average sense, more or less "complex", in terms of the patterns exhibited by the above procedure, than the "sin(x)" button? Modeling or simulating physical phenomena such as particle motion or the orbits of collections of celestial bodies often entails the use of computer programs. These computer programs carry out calculations which often involves repeated application of various pre-programmed functions. Repeatedly pushing a button on a calculator can be viewed as a simplified version of what goes on with the calculations that a computer carries out in simulating physical phenomena. Understanding how to compare the patterns exhibited by simple, fundamental collections of functions makes for a good starting point for understanding the models that represent various physical phenomena. This work contributes to this endeavor by investigating a quantity which measures the complexity of some fundamental functions.

Thesis (M.L.A.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 36-37).

Thesis (M.L.A.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 36-37) Also available in print.

Dans ce travail, nous considérons le problème suivant : étant donné un graphe orienté D, contient-il une subdivision d’un digraphe fixé F ? Nous pensons qu’il existe une dichotomie entre les instances polynomiales et NP-complètes. Nous donnons plusieurs exemples pour les deux cas. En particulier, sauf pour cinq instances, nous sommes capable de classer tous les digraphes d’ordre 4. Alors que toutes les preuves NP-complétude sont faites par réduction de une version du problème 2-linkage en digraphes, nous utilisons différents outils algorithmiques pour prouver la solvabilité en temps polynomial de certains cas, certains d’entre eux impliquant des algorithmes relativement complexes. Les techniques varient des simples algorithmes de force brute, aux algorithmes basés sur des calculs maximale de flot, et aux décompositions en anses des digraphes fortement connexes, entre autres. Pour terminer, nous traitons le cas particulier où F étant une union disjointe de cycles dirigés. En particulier, nous montrons que les cycles dirigés de longueur au moins 3 possède la Propriété d’Erdos-Pósa : pour tout n, il existe un entier tn tel que pour tout digraphe D, soit D a n cycles dirigés disjoints de longueur au moins 3, soit il y a un ensemble T d’au plus tn sommets qui intersecte tous les cycles dirigés de longueur au moins 3. De ce résultat, nous déduisons que si F est l’union disjointe de cycles dirigés de longueur au plus 3, alors on peut décider en temps polynomial si un digraphe contient une subdivision de F. / In this work, we consider the following problem: Given a directed graph D, does it contain a subdivision of a prescribed digraph F? We believe that there is a dichotomy between NP-complete and polynomial-time solvable instances of this problem. We present many examples of both cases. In particular, except for five instances, we are able to classify all the digraphs F of order 4.While all NP-hardness proofs are made by reduction from some version of the 2-linkage problem in digraphs, we use different algorithmic tools for proving polynomial-time solvability of certain instances, some of them involving relatively complicated algorithms. The techniques vary from easy brute force algorithms, algorithms based on maximum-flow calculations, handle decompositions of strongly connected digraphs, among others. Finally, we treat the very special case of F being the disjoint union of directed cycles. In particular, we show that the directed cycles of length at least 3 have the Erdos-Pósa Property: for every n, there exists an integer tn such that for every digraph D, either D contains n disjoint directed cycles of length at least 3, or there is a set T of tn vertices that meets every directed cycle of length at least 3. From this result, we deduce that if F is the disjoint union of directed cycles of length at most 3, then one can decide in polynomial time if a digraph contains a subdivision of F.

Les schémas de subdivision sont largement utilisés pour la génération rapide de courbes ou de surfaces. Des développements récents ont produit des schémas variés, en particulier non-linéaires, non-interpolants ou non-homogènes.Pour pouvoir être utilisés en compression, analyse ou contrôle de données, ces schémas de subdivision doivent être incorporés dans une analyse multiresolution qui, imitant les analyses en ondelettes, fournit une décomposition multi-échelle d'un signal, d'une courbe ou d'une surface. Les ingrédients nécessaires à la définition d'une analyse multiresolution associée à un schéma de subdivision sont des schémas de décimation et de détails. Leur construction est facile quand le schéma de multiresolution est interpolant.Cette thèse est consacrée à la construction de schémas de décimation et de détails compatibles avec un schéma de subdivision le plus général possible. Nous commençons par une construction générique dans le cas d'opérateurs homogènes (mais pas interpolants) puis nous généralisons à des situations non-homogènes et non-linéaires. Nous construisons ainsi des analyses multiresolutions compatibles avec de nombreux schémas récemment développés. L'analyse des performances des analyses ainsi construitesest effectuée. Nous présentons des applications numériques en compression d'images. / Subdivision schemes are widely used for rapid curve or surface generation. Recent developments have produced various schemes, in particular non-linear, non-interpolatory or non-uniform.To be used in compression, analysis or control of data, subdivision schemes should be incorporated in a multiresolution analysis that, mimicking wavelet analyses, provides a multi-scale decomposition of a signal, a curve, or a surface. The ingredients needed to define a multiresolution analysis associated with a subdivision scheme are decimation scheme and detail operators. Their construction is straightforward when the multiresolution scheme is interpolatory.This thesis is devoted to the construction of decimation schemes and detail operators compatible with general subdivision schemes. We start with a generic construction in the uniform (but not interpolatory) case and then generalize to non-uniform and non-linear situations. Applying these results, we build multiresolution analyses that are compatible with many recently developed schemes. Analysis of the performances of the constructed analyses is carried out. We present numerical applications in image compression.

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