Abstract For every $k \geq 2$ and $n , we construct n pairwise homotopically inequivalent simply connected, closed $4k$ -dimensional manifolds, all of which are stably diffeomorphic to one another. Each these manifolds has hyperbolic intersection form is parallelisable. In dimension four, exhibit an analogous phenomenon for spin $^{c}$ structures on $S^2 \times S^2$ . $m\geq 1$ also provide sim...

We present a survey of results on the edge disjoint paths problem and re late this problem to the edge disjoint homotopic path and the edge disjoint homotopic cycle problem The latter problem is given a graph G V E embedded on a surface S and closed curves C Ck on S nd necessary and su cient conditions for the existence of pairwise edge disjoint cycles e C e Ck in G so that e Ci is homotopic to...

We prove that the first-order theory of the Medvedev degrees, the first-order theory of the Muchnik degrees, and the third-order theory of true arithmetic are pairwise recursively isomorphic (obtained independently by Lewis, Nies, and Sorbi [7]). We then restrict our attention to the degrees of closed sets and prove that the following theories are pairwise recursively isomorphic: the first-orde...

in this paper, we generalize some results of chandra and goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). furthermore, we give baum and katz’s [1] type results on estimate for the rate of convergence in these laws.

In this paper, we introduce the concepts of fuzzy pairwise (r, s)-irresolute, fuzzy pairwise (r, s)-presemiopen and fuzzy pairwise (r, s)-presemiclosed mappings in smooth bitopological spaces and then we investigate some of their characteristic properties.