K. Borsuk in 1979, at the Topological Conference in Moscow, introduced concept of the capacity of a compactum and asked some questions concerning properties of the capacity ofcompacta. In this paper, we give partial positive answers to three of these questions in some cases. In fact, by describing spaces homotopy dominated by Moore and Eilenberg-MacLane spaces, the capacities of a Moore space $...

Abstract: In this paper, with the help of the Hardy and Dedekind sums we will give many properties of the sum B1(h, k), which was defined by Cetin et al. Then we will give the connections of this sum with the other well-known finite sums such as the Dedekind sums, the Hardy sums, the Simsek sums Y(h, k) and the sum C1(h, k). By using the Fibonacci numbers and two-term polynomial relation, we wi...

Given a tree containing n vertices, consider the sum of the distance between all vertices and a k-leaf-subtree (subtree which contains exactly k leaves). A k-tree-core is a k-leaf-subtree which minimizes the sum of the distances. In this paper, we propose a linear time algorithm for nding a k-tree-core for a given k.

Abstract In this work, we study the resonance contributions to decay $$B^-\rightarrow K^+K^-\pi ^-$$ B - → K + π , which is dominated by scalar $$f_0(980), K_0^*(1430)$$ <mml:msub...

For a graph G and k a real number, we consider the sum of the k-th powers of the degrees of the vertices of G. We present some general bounds on this sum for various values of k.

More than twenty years ago, Manickam, Miklós, and Singhi conjectured that for any integers n, k satisfying n ≥ 4k, every set of n real numbers with nonnegative sum has at least ( n−1 k−1 ) kelement subsets whose sum is also nonnegative. In this paper we discuss the connection of this problem with matchings and fractional covers of hypergraphs, and with the question of estimating the probability...

In this paper we study recurrences concerning the combinatorial sum k≡r (mod m) n k and the alternate sum k≡r (mod m) (−1) (k−r)/m n k , where m > 0, n 0 and r are integers. For example, we show that if n m − 1 then