There is a concept in linear algebra called tridiagonal pair. The was motivated by the theory of $Q$-polynomial distance-regular graphs. We give tutorial introduction to pairs, working with special case as concrete example. totally bipartite, or bipartite (TB). Starting from first principles, we an elementary but comprehensive account TB pairs. following topics are discussed: (i) notion system;...

We examine the notion of "unrelatedness" in a probabilistic framework. Three formulations are presented. In the first formulation, two variables a and b are totally independent with respect to a set of variables U if they are independent given any value of the variables in U. In the second formu­ lation, two variables are totally uncoupled if U can be partitioned into two marginally independent...

We consider a variation of Construction A of lattices from linear codes based on two classes of number fields, totally real and CM Galois number fields. We propose a generic construction with explicit generator and Gram matrices, then focus on modular and unimodular lattices, obtained in the particular cases of totally real, respectively, imaginary, quadratic fields. Our motivation comes from c...

Our aim in this paper is to focus on some applications in differential geometry of the metallic means family (a generalization of the golden mean) and generalized Fibonacci sequences, using a class of polynomial structures defined on Riemannian manifolds. We search for properties of the induced structure on a submanifold by metallic Riemannian structures and we find a necessary and sufficient c...

We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant submanifolds in the form N N⊥×fNT by reversing two factor manifolds NT and N⊥. W...

conclusion our data suggest that catheter malfunctions of ticvps are more common in females than males. the incidence of ticvp malfunctions does not differ between the two devices (celsite® vs. humanport®). background malfunctions of totally implantable central venous ports (ticvps) have become a problem, as the usage of ticvps has increased enormously. objectives this study evaluated factors r...