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Large Harnack inequalities, Kobayashi distances and holomorphic motions
Large Harnack inequalities Kobayashi distances holomorphic motions Complex Variables
2012/4/18
We prove some generalizations and analogies of Harnack inequalities for pluriharmonic, holomorphic and "almost holomorphic" functions. The results are applied to the proving of smoothness properties o...
Sets avoiding integral distances
excluded distances Euclidean Ramsey theory integral distances Erdos-type problems
2012/4/18
We study open point sets in Euclidean spaces $\mathbb{R}^d$ without a pair of points an integral distance apart. By a result of Furstenberg, Katznelson, and Weiss such sets must be of Lebesgue upper d...
Quaternary Constant-Composition Codes with Weight Four and Distances Five or Six
Quaternary Constant-Composition Codes Weight Four Distances Five or Six
2012/3/1
The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their construction...
Distances and Riemannian metrics for multivariate spectral densities
Riemannian metrics multivariate spectral densities Optimization and Control
2011/8/26
Abstract: We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal predic...
Abstract: We show that the number of unit distances determined by n points in R^3 is O(n^{3/2}), slightly improving the bound of Clarkson et al. established in 1990. The new proof uses the recently in...
On maximal distances in a commuting graph
Algebraically closed field Matrix algebra Centralizer
2010/12/14
We study maximal distances in the commuting graphs of matrix algebras defined over algebraically closed fields. In particular,we show that the maximal distance can be attained only between two nondero...
Hopf fibration: geodesics and distances
Sub-Riemannian geometry Hopf fibration, geodesic Carnot-Carath´ eodory dis-tance
2010/12/13
Here we study geodesics connecting two given points on odd-dimensional spheres respecting the Hopf fibration. This geodesic boundary value problem is completely solved in the case of 3-dimensional sph...
We introduce a new multi-player geometric game, which we will refer；to as the isolation game, and study its Nash equilibria and best or better response
dynamics. The isolation game is inspired by the...