We introduce U DS p-property (resp. U DT q-property) in Banach lattices as the property that every normalized disjoint sequence has a subse-quence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lat...

A family of sets is (p,q)-intersecting if every nonempty subfamily p or fewer has at least q elements in its total intersection. the (p,q)-Helly property intersection cardinality q. The (2,1)-Helly usual Helly property. hypergraph edge and hereditary each subhypergraphs graph (p,q)-clique-Helly maximal cliques induced subgraphs (p,q)-clique-Helly. classes (p,q)-biclique-Helly graphs are defined...

We answer the following question: Let P and Q be graded posets having some property and let ◦ be some poset operation. Is it true that P ◦Q has also this property? The considered properties are: being Sperner, a symmetric chain order, Peck, LYM, and rank compressed. The studied operations are: direct product, direct sum, ordinal sum, ordinal product, rankwise direct product, and exponentiation.

We demonstrate that the q-exponential family particularly admits natural geometrical structures among deformed exponential families. The property is the invariance of structures with respect to a general linear group, which transitively acts on the space of positive definite matrices. We prove this property via the correspondence between information geometry induced by a deformed potential on t...

In this paper, the complete monotonicity property of functions involving the q -gamma function is proven and used to establish sharp inequalities for the q -gamma and the q -polygamma functions for all q > 0 . These bounds for the q -gamma and the q -polygamma functions refine those given by Salem [17]. Mathematics subject classification (2010): 33D05, 26D07, 26A48.