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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...
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...
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...
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.
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...
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.
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.
In this study, we introduce the concept of ®i¡distance, which is a generalization of Taxicab, Chinese Checker, and ®¡distances from R2 to Rn.
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...

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