Among all collections of a given number of k-element subsets of an n-element groundset find a collection which maximizes the number of pairs of subsets which intersect in k − 1 elements. This problem was solved for k = 2 by Ahlswede and Katona, and is open for k > 2. We survey some linear algebra approaches which yield to estimations for the maximum number of pairs, and we present a new and sho...

background: the appendix is considered as part of the gut-associated lymphoid tissue; however, lymphocyte subsets in this tissue are not fully defined. objective: to investigate and compare the function and phenotype of lymphocyte subsets in peripheral blood and appendix of patients with normal and inflamed appendix tissues. methods: peripheral blood samples and appendiceal mononuclear cells we...

In this work we have solved an open problem related to the continuity of R-implications. We have fully characterized the class of continuous R-implications obtained from any arbitrary t-norm. Using this result, we also determine the exact intersection between the continuous subsets of R-implications and (S,N)implications. Keywords— R-implication, (S,N)-implication, Łukasiewicz implication, t-norm.

Background: The balance of TNFα receptors expression on cells which are actively involved in immunopathological processes affects both the density distribution and co-expression subsets. Previously it was shown that basic effective RA therapy with methotrexate glucocorticoids leads to equalization profile either percentage or number receptors, approaching those healthy donors, but not simultane...

For every natural number, let the sequence enumerate number of subsets S set {1,2, . ,n } including no three consecutive odd integers. We give generating function and closed form formula obtaining sixth order linear homogeneous recurrence relation with constant coefficients integer sequence. The is associated Tribonacci combinatorial representation obtained limit ratios terms found.

Let X be a metric continuum and n positive integer. Fn (X) the hyperspace of nonempty subsets with at most points. If 0 < m n, we consider quotient space Fnm = (X)/Fm (X). Given mapping f from into X, induced mappings fn fnm In this paper study relations among dynamics f, fn, answer some questions, by F. Barragán, A. Santiago-Santos J. Tenorio, related to properties: minimality, irreducibili...