97 research outputs found

    Testing of random matrices

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    Let nn be a positive integer and X=[xij]1≤i,j≤nX = [x_{ij}]_{1 \leq i, j \leq n} be an n×nn \times n\linebreak \noindent sized matrix of independent random variables having joint uniform distribution \hbox{Pr} {x_{ij} = k \hbox{for} 1 \leq k \leq n} = \frac{1}{n} \quad (1 \leq i, j \leq n) \koz. A realization M=[mij]\mathcal{M} = [m_{ij}] of XX is called \textit{good}, if its each row and each column contains a permutation of the numbers 1,2,...,n1, 2,..., n. We present and analyse four typical algorithms which decide whether a given realization is good

    On additive functions satisfying a congruence

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    On the sum : ÎŁdd(f(n))

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    Change of the sum of digits by multiplication

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    On arithmetic functions with regularity properties

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    Additive functions with regularity properties

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