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**11 - 13**of**13**### Examples of Moments Problems Related With Some Combinatorial Numbers

, 2003

"... We interpret as determined probability moments some sequences of combinatorial integers and most of the time we can explicit the underlying probability measure . Key words: Moments problems, Generalized and ordinary Bell numbers, Bessel numbers, Subordinators, Exponential functionals, Carleman crite ..."

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We interpret as determined probability moments some sequences of combinatorial integers and most of the time we can explicit the underlying probability measure . Key words: Moments problems, Generalized and ordinary Bell numbers, Bessel numbers, Subordinators, Exponential functionals, Carleman criterion. 1

### INEQUALITIES FOR THE GAMMA FUNCTION AND ESTIMATES FOR THE VOLUME OF SECTIONS OF B n p

, 2000

"... Abstract. Let Bn p = {(xi) ∈ Rn; ∑n 1 |xi | p ≤ 1} and let E be a k-dimensional subspace of Rn. We prove that |E ∩ Bn p | 1/k k ≥ |Bn p | 1/n n, for 1 ≤ k ≤ (n − 1)/2 and k = n − 1 whenever 1 < p < 2. We also consider 0 < p < 1 and other related cases. We obtain sharp inequalities involving Gamma f ..."

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Abstract. Let Bn p = {(xi) ∈ Rn; ∑n 1 |xi | p ≤ 1} and let E be a k-dimensional subspace of Rn. We prove that |E ∩ Bn p | 1/k k ≥ |Bn p | 1/n n, for 1 ≤ k ≤ (n − 1)/2 and k = n − 1 whenever 1 < p < 2. We also consider 0 < p < 1 and other related cases. We obtain sharp inequalities involving Gamma function in order to get these results.

### TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION

, 902

"... Abstract. In the present paper, we give two new proofs for the necessary and sufficient condition α ≤ 1 such that the function x α [lnx − ψ(x)] is completely monotonic on (0, ∞). 1. ..."

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Abstract. In the present paper, we give two new proofs for the necessary and sufficient condition α ≤ 1 such that the function x α [lnx − ψ(x)] is completely monotonic on (0, ∞). 1.