In Pareto bi-objective integer optimization the optimal result corresponds to a set of nondominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available integer solutions, and cutting plane generation taking advantage of integer objective values. The developed algorithm is applied to the bi-objective team ori...

The name comes from elementary geometry: if a right triangle has leg lengths x and y and hypotenuse length z, then x + y = z. Of course here x, y, z are positive real numbers. For most integer values of x and y, the integer x + y will not be a perfect square, so the positive real number √ x2 + y2 will be irrational: e.g. x = y = 1 =⇒ z = √ 2. However, a few integer solutions to x + y = z are fa...

Time-frequency domain compression of an ECG is the new and still underestimated issue. This paper is devoted to the statistical analysis of the ECG' dynamic ranges on various aspects of time-frequency plane. The traditional approach to the signal values distribution, originally introduced by Huffman, is now studied for integer time-frequency coefficients obtained with use of reversible integer-...

Let P (x) ∈ Z[x] be an integer-valued polynomial taking only positive values and let d be any fixed positive integer. The aim of this short note is to show, by elementary means, that for any sufficiently large integer N ≥ N0(P, d) there exists n such that P (n) contains exactly N occurrences of the block (q − 1, q − 1, . . . , q − 1) in its digital expansion in base q. The method of proof is co...

We show that the density μ of the Smith normal form (SNF) of a random integer matrix exists and equals a product of densities μps of SNF over Z/p sZ with p a prime and s some positive integer. Our approach is to connect the SNF of a matrix with the greatest common divisors (gcds) of certain polynomials of matrix entries, and develop the theory of multi-gcd distribution of polynomial values at a...

The ζ function is defined by ζ(s) = ∑ n 1/n . This talk is a study of the irrationality of the zeta function on odd integer values > 2.

‎for any integer $kge 1$‎, ‎a minus $k$-dominating function is a‎ ‎function $f‎ : ‎v (g)rightarrow {-1,0‎, ‎1}$ satisfying $sum_{win‎‎n[v]} f(w)ge k$ for every $vin v(g)$‎, ‎where $n(v) ={u in‎‎v(g)mid uvin e(g)}$ and $n[v] =n(v)cup {v}$‎. ‎the minimum of‎‎the values of $sum_{vin v(g)}f(v)$‎, ‎taken over all minus‎‎$k$-dominating functions $f$‎, ‎is called the minus $k$-domination‎‎number and i...