* Correspondence: meraj79@gmail. com Department of Mathematics, University of Tabuk, Tabuk, Kingdom of Saudi Arabia Full list of author information is available at the end of the article Abstract In this article, we have obtained necessary and sufficient conditions in terms of canonical structure F on a semi-invariant submanifold of an almost contact manifold under which the submanifold reduced...

In this paper, by considering the notion of congruences on hyperlattices we define almost principal ideals on hyperlattices. We investigate some properties and prove some results about them. Also, we define compatible functions on hyperlattices and investigate connection between these functions and almost principal ideals. Then, we define tensor product of two hyperlattices and present several ...

On a Riemannian almost product manifold, the notion of a componentwise conformal vector field is introduced and several examples are exhibited. We show that this class of vector fields is a conformal invariant. For a compact manifold, a Bochner type integral formula for the Ricci tensor on such vector fields is obtained. Then, integral inequalities which link a curvature condition with the exis...

We consider weakly-verifiable puzzles which are challenge-response puzzles such that the responder may not be able to verify for itself whether it answered the challenge correctly. We consider k-wise direct product of such puzzles, where now the responder has to solve k puzzles chosen independently in parallel. Canetti et al have earlier shown that such direct product puzzles have a hardness wh...

The aim of this paper is to define the lower and upper limits on the family of IF-events with product. We compare two concepts of almost everywhere convergence and we show that they are equivalent, too.

In a recent paper we have presented a method to evaluate certain Hankel determinants as almost products; i.e. as a sum of a small number of products. The technique to find the explicit form of the almost product relies on differential-convolution equations and trace calculations. In the trace calculations a number of intermediate nonlinear terms involving determinants occur, but only to cancel ...

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...

Delaunay tessellations and Voronoi diagrams capture proximity relationships among sets of points. When applied to points representing protein atoms or residue positions, they are used to compute molecular surfaces and protein volumes, to define cavities and pockets, to analyze and score packing interactions, and to find structural motifs. Since atom and residue coordinates are known imprecisely...