Let X be a normed linear space, and let S(X) = fx 2 X : kxk = 1g be the unit sphere of X. Brodskii and Milman 1] introduced the following geometric concept: Deenition 1. A bounded, convex subset K of a Banach space X is said to have normal structure if every convex subset H of K that contains more than one point contains a point x 0 2 H, such that supfkx 0 ? yk : y 2 Hg < d(H); where d(H) = sup...

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.

Significance Mutations that activate LRRK2 protein kinase cause Parkinson's disease. phosphorylates a subset of Rab GTPases, in particular Rab8 and Rab10. We show here details related to the mechanism by which Rab10 phosphorylation blocks initiation cilia formation, fundamental information how pathogenic interferes with normal cell physiology.

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...