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This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...
We investigate numerical simulations and visualizations of the problem of tying a knot in a piece of rope. The goal is to use the least possible rope of a fixed, prescribed radius to tie a particular knot, e.g. a trefoil, a figure eight, and so on. The rop ...
We consider the variational problem of finding the longest closed curves of given minimal thickness on the unit sphere. After establishing the existence of solutions for any given thickness between 0 and 1, we explicitly construct for each given thickness ...
For a mapping between Banach spaces, two weaker variants of the usual notion of asymptotic linearity are defined and explored. It is shown that, under inversion through the unit sphere, they correspond to Hadamard and weak Hadamard differentiability at the ...
We study co-rotational wave maps from (3 + 1)-Minkowski space to the three-sphere S-3. It is known that there exists a countable family {f(n)} of self-similar solutions. We investigate their stability under linear perturbations by operator theoretic method ...
We study linear perturbations of a self-similar wave map from Minkowski space to the three-sphere which is conjectured to be linearly stable. Considering analytic mode solutions of the evolution equation for the perturbations we prove that there are no rea ...
In this paper, we derive an explicit form of the convolution theorem for functions on an n-sphere. Our motivation comes from the design of a probability density estimator for n-dimensional random vectors. We propose a probability density function (pdf) est ...
Institute of Electrical and Electronics Engineers2010
We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give s ...
To retrieve scene informations using a single omnidirectional camera, we have based our work on a shape from texture method proposed by Lindeberg. To do so, we have adapted the method of Lindeberg, that was developed for planar images, in order to use it o ...
We review the coherent state or group-theoretical construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two-sheeted hyperboloid, emphasizing the similarities between the ...
