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Equidistribution on the Sphere
SIAM Journal on Scientific Computing, 1997Summary: A concept of generalized discrepancy, which involves pseudodifferential operators to give a criterion of equidistributed point sets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy.
Freeden, Willi, Cui, J.
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Future Generation Computer Systems, 1994
Abstract We present a parallel simulated annealing algorithm for crystallization of N -body systems. The implementation uses systolic simulated annealing with additional parallel cost function evaluation. We have a hybrid topology which consists of a systolic ring and attached to each ring processor a tree of processors.
Voogd, J.M., Sloot, P.M.A., Dantzig, R.
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Abstract We present a parallel simulated annealing algorithm for crystallization of N -body systems. The implementation uses systolic simulated annealing with additional parallel cost function evaluation. We have a hybrid topology which consists of a systolic ring and attached to each ring processor a tree of processors.
Voogd, J.M., Sloot, P.M.A., Dantzig, R.
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Approximating spheres and sphere patches
Computer Aided Geometric Design, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Covering a sphere with spheres
Mathematika, 1963We work throughout in n-dimensional Euclidean space. It has been clear, since the publication of [1], that it should be possible to obtain quite good upper bounds for the number of spherical caps of chord 2 required to cover the surface of a sphere of radius R > 1, and for the number of spheres of radius 1 required to cover a sphere of radius R > 1 ...
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Canadian Journal of Mathematics, 1987
In 1924 at the Toronto meeting of the International Congress of Mathematicians, B. N. Delone introduced his empty sphere method for lattices. We have titled our paper after this method as a tribute to his memory.We have studied the sets of integer solutions of equations of the form1where f satisfies the following condition in which Z denotes the ...
Erdahl, R. M., Ryshkov, S. S.
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In 1924 at the Toronto meeting of the International Congress of Mathematicians, B. N. Delone introduced his empty sphere method for lattices. We have titled our paper after this method as a tribute to his memory.We have studied the sets of integer solutions of equations of the form1where f satisfies the following condition in which Z denotes the ...
Erdahl, R. M., Ryshkov, S. S.
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The Annals of Mathematics, 1950
(1) K: f(x,y,z) _ 1, which is symmetrical about 0, defines a convex body K say, in a three-dimensional Euclidean space. Let A denote any lattice of points admissible for K, so that all points of A, other than 0, lie outside or on the boundary of K.
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(1) K: f(x,y,z) _ 1, which is symmetrical about 0, defines a convex body K say, in a three-dimensional Euclidean space. Let A denote any lattice of points admissible for K, so that all points of A, other than 0, lie outside or on the boundary of K.
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The Annals of Mathematics, 1957
1. R. H. Bing [1] has given an example of an involution of a 3-sphere whose fixed points constitute a wild (horned) 2-sphere. This shows that an involution in a euclidean n-sphere, SO, is not necessarily conjugate, in the group of homeomorphisms SO' -* S~', to an orthogonal transformation (cf. Problem 39 in [2]).
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1. R. H. Bing [1] has given an example of an involution of a 3-sphere whose fixed points constitute a wild (horned) 2-sphere. This shows that an involution in a euclidean n-sphere, SO, is not necessarily conjugate, in the group of homeomorphisms SO' -* S~', to an orthogonal transformation (cf. Problem 39 in [2]).
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American Sociological Review, 1972
This is a study of network representation: The data represent a set of interlocked directorates—specifically, the network in which the boards of major banks are interlocked with the boards of major industrials. The problem is to represent this network so as to organize it and describe its major outlines.
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This is a study of network representation: The data represent a set of interlocked directorates—specifically, the network in which the boards of major banks are interlocked with the boards of major industrials. The problem is to represent this network so as to organize it and describe its major outlines.
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Proceedings. 1998 IEEE Conference on Information Visualization. An International Conference on Computer Visualization and Graphics (Cat. No.98TB100246), 2002
There are many problems that involve data fitting of sets on the surface of a sphere, many of them for example in the geosciences. They are usually treated using some kind of mapping onto the plane, in order to later apply some method for the plane which is well-known and proven. This means precision loss in some zones and problems at the poles.
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There are many problems that involve data fitting of sets on the surface of a sphere, many of them for example in the geosciences. They are usually treated using some kind of mapping onto the plane, in order to later apply some method for the plane which is well-known and proven. This means precision loss in some zones and problems at the poles.
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Heegaard reducing spheres for the 3-sphere
2011In a previous paper with W. Thurston the author defined an invariant in \({\mathbb Q}/2\) of a knot with unknotting tunnel \(\gamma\). To construct this invariant they characterized reducing spheres for genus two Heegaard splittings of \(S^3\). In the paper under review the author generalizes this characterisation to arbitrary genus Heegaard splittings
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