Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.

In the transformation semigroup (X, S) we introduce the height of a closed nonempty invariant subset of X, define the transformed dimension of nonempty subset S of X and obtain some results and relations.

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

Intrusion detection systems are designed to provide security in computer networks, so that if the attacker crosses other security devices, they can detect and prevent the attack process. One of the most essential challenges in designing these systems is the so called curse of dimensionality. Therefore, in order to obtain satisfactory performance in these systems we have to take advantage of app...

To evaluate the fully automated FACSCanto software, we compared lymphocyte subpopulation counts obtained using three-color FACSCalibur-CELLQuest and six-color FACSCanto-FACSCanto software techniques. High correlations were observed between data obtained with these techniques. Our study indicated that FACSCanto clinical software is accurate and sensitive in single-platform lymphocyte immunopheno...

Let m + n particles be thrown randomly, independently of each other into N cells, using the following two-stage procedure. 1. The first m particles are allocated equiprobably, that is, the probability of a particle falling into any particular cell is 1/N . Let the ith cell contain mi particles on completion. Then associate with this cell the probability ai = mi/m and withdraw the particles. 2. ...

Let Fq be the finite field of q elements. Let H ⊆ Fq be a multiplicative subgroup. For a positive integer k and element b ∈ Fq, we give a sharp estimate for the number of k-element subsets of H which sum to b.