$K$-to-$1$ functions on arcs for $K$ even

Polarization constant $mathcal{K}(n,X)=1$ for entire functions of exponential type

In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized  inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have t...

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

Making k-means Even Faster

The k-means algorithm is widely used for clustering, compressing, and summarizing vector data. In this paper, we propose a new acceleration for exact k-means that gives the same answer, but is much faster in practice. Like Elkan’s accelerated algorithm [8], our algorithm avoids distance computations using distance bounds and the triangle inequality. Our algorithm uses one novel lower bound for ...

On the family of Diophantine triples { k − 1 , k + 1 , 16 k 3 − 4 k }

It is proven that if k ≥ 2 is an integer and d is a positive integer such that the product of any two distinct elements of the set {k − 1, k + 1, 16k − 4k, d} increased by 1 is a perfect square, then d = 4k or d = 64k−48k+8k. Together with a recent result of Fujita, this shows that all Diophantine quadruples of the form {k − 1, k + 1, c, d} are regular.

On the Trinomial Arcs J ( p , k , r , n )

We study the trinomial arcs J(p, k, r, n) and we prove the monotonicity of this category of arcs. Mathematics Subject Classification: 26C10, 30C15, 14H45, 26A48