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FINITE TWO-DISTANCE TIGHT FRAMES
Spherical two-distance sets finite tight frames strongly regular graphs spherical 2-designs spherical designs of harmonic index 2
2015/12/10
A finite collection of unit vectors S ⊂ Rn is called a spherical two-distance set if there are two numbers a and b such that the inner products of distinct vectors from S are either a or b. We p...
In this paper, we prove that a set of $N$ points in ${\bf R}^2$ has at least $c{N \over \log N}$ distinct distances, thus obtaining the sharp exponent in a problem of Erd\"os. We follow the set-up of...
Geodesics and distance on the Riemannian manifold of Riemannian metrics
the Riemannian manifold Riemannian metrics
2010/11/11
Given a fixed closed manifold M, we exhibit an explicit formula for the distance function of the canonical L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on M. Additionally, w...
Graphons, cut norm and distance, couplings and rearrangements
Graphons cut norm distance couplings rearrangements
2010/12/6
We give a survey of basic results on the cut norm and cut metric for graphons (and sometimes more general kernels), with emphasis on the equivalence problem. The main results are not new, but we add v...
The cardinality of a sphere relative to an edit distance
Alphabet Binomial coefficient Binomial theorem
2010/9/13
These cardinalities are showed to satisfy some curious recurrence relations. These recurrence relations incite us to introduce new types of binomial coefficients and binomial formula.
On the maximal distance between consecutive choices in the set of winning numbers in lottery
Lottery maximal gap
2010/9/17
We study the probability distribution of the biggest gap between two consecutive choices in an m-tuple of distinct integers, assuming the m-tuple is chosen uniformly from within the range 1, . . . , n...
On $\alpha-$distance in three dimensional space
metric taxicab distance CC-distance a-distance
2009/2/24
In this study we extend the concept ®¡distance, which is a
generalization of both of taxicab distance and chinese checker distance, to
three dimensional space.
On ®¡distance in three dimensional space
metric taxicab distance CC¡ distance ® ¡ distance
2009/1/7
In this study we extend the concept ®¡distance, which is a
generalization of both of taxicab distance and chinese checker distance, to
three dimensional space.
On alpha_i - distance in n-dimensional space
Taxicab distance CC- distance ® ¡ distance non-Euclidean geometry
2009/1/4
In this study, we introduce the concept of ®i¡distance, which
is a generalization of Taxicab, Chinese Checker, and ®¡distances from R2
to Rn.
Time neural network minimum distance classifier and its application to optical character recognition problem
neural network classifier minimum distance classification
2010/9/13
We propose a special neural network model, NNC, (Neural Network Classifier), which with a classification problem of l classes C1,C2, ...,Cl, classifies an unknown vector to one class using a minimum d...