1,720,986 research outputs found
Measures with specified support and arbitrary Assouad dimensions
No full textWe show that if the upper Assouad dimension of the compact set E ⊆ R is positive, then given any D > dimA E there is a measure with support E and upper Assouad (or regularity) dimension D. Similarly, given any 0 ≤ d < dimL E, there is a measure on E with lower Assouad dimension d.Fil: Hare, Kathryn E.. University of Waterloo; CanadáFil: Mendivil, Franklin. Acadia University; CanadáFil: Zuberman, Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; Argentin
PacKing and hausdorff measures of Cantor sets associated with series
Full text linkWe study a generalization of Mor´an´s sum sets, obtaining information about the h-Hausdorff and h-packing measures of these sets and certain of their subsets.Fil: Hare, Kathryn. University Of Waterloo; CanadáFil: Mendivil, Franklin. Acadia University; CanadáFil: Zuberman, Leandro. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Assouad dimensions of complementary sets
Full text linkGiven a positive, decreasing sequence a, whose sum is L, we consider all the closed subsets of [0, L] such that the lengths of their complementary open intervals are in one-to-one correspondence with the sequence a. The aim of this paper is to investigate the possible values that Assouad-type dimensions can attain for this class of sets. In many cases, the set of attainable values is a closed interval whose endpoints we determine.Fil: Garcia, Ignacio Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Hare, Kathryn. University of Waterloo; CanadáFil: Mendivil, Franklin. Acadia University; Canad
Minkowski dimension and content of fractals
No full textThis thesis focuses upon fractal geometry and how we can characterise various fractals by two properties known as the Minkowski dimension and the Minkowski content. A fractal is treated as a geometric construct of a generic set of points considered in an m-dimensional Euclidean space. We rst explain how Minkowski dimension and content are important in measur- ing the \size" of a set. Measuring the size by length if the set is 1-dimensional, area if the set is in a plane, or volume if the set is in 3-dimensional space will only work for certain simplistic sets, for example a polygon or polyhedron. Hence we need another method of measure. Chapter 1 explains how this can be done with Minkowski dimen- sion and content and how subsets of 1-dimensional Euclidean space or a straight line can be measured with Minkowski dimension and content. We then go into a section that goes through various properties that make Minkowski dimension and content useful in certain respects. The third chapter looks at sets in higher dimensions where we try to nd sets of points that have any given positive Minkowski dimension. We create a two-dimensional cut-out set where we remove various rectangles out of a larger rectangle, leaving only straight lines. Given any Minkowski dimension between 1 and 2, we can create a set using this construction. The Minkowski content is easily calculable. Then we look at a set consisting the perimeters of concentric squares and then a subset of this set consisting of only countably many points. What is special about this construction is that not only can we generate a set with any Minkowski dimension between 0 and 2, but we can do so where the set only has one limit point. We then consider an analo- gous set in m-dimensions where we construct a set consisting of the m-1-dimensional surface area of concentric m-dimensional hypercubes and then again a subset of this set consisting of only countably many points. Again, the construction of the count- ably many points only as one limit point and such a set can be constructed that has any Minkowski dimension between 0 and m. The Minkowski content is not calculated for these sets, but a di erent kind of Minkowski content was calculated
An investigation of local zeta functions of self-similar fractal strings
No full textWe give an overview of fractal strings and examine the relationship between theirMinkowski dimension/content to their complex dimensions and their geometric zeta functions with the aim of demonstrating the geometric information made available by studying these entities. Building on this knowledge, we propose a way of searching for locally defined geometric zeta functions by looking at simple examples of self-similar fractal strings
A characterization of the set of invariant distributions of a random walk on a graph
No full textIn this paper, a characterization of the set of attainable limiting distributions of a random walk on a strongly connected directed graph is described. This result is shown in terms of the invariant distributions of Markov chains. The exisitence of invariant distributions of Markov chains is proven by way of the Perron-Frobenius theorem. Then it is shown that the set of possible limiting distributions of a graph Gis the convex hull of the uniform cycle distributions of the cycles of G
Total variation denoising of diffusion MRI images using a modified monge-kantorovich norm
No full textEfficient methods for denoising various forms of data are contantly evolving and are crucial in fields like medical imaging where even small amounts of noise can affect a doctor's diagnosis. It has been proposed in a 2016 paper (D. La Torre et al) that using the Monge-Kantorovich metric, along with total variation and regularization, one could create an effective and hopefully efficient method for denoising diffusion MRI images. In this thesis this aforementioned method for denoising will be discussed as well as the advantages of a Monge-Kantorovich style norm versus a Euclidean or other type of norm. Finally the effectiveness of a python-based implementation that was created summer 2019 will be discussed as a measure of the efficiency of the algorithm.</p
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