In this paper, basing our consideration on the sets with the apartness relation, we analyze characteristics of some special relations to these sets such as co-order and co-quasiorder and coequality relations. In addition, we analyze two special classes of subsets, co-filters and co-ideals, of ordered set under a co-quasiorder relation. This investigation is into the Bishop’s Constructive mathem...

For a (co)monad Tl on a category M, an object X in M, and a functor Π : M → C, there is a (co)simplex Z := ΠTl ∗+1 X in C. The aim of this paper is to find criteria for para(co)cyclicity of Z. Our construction is built on a distributive law of Tl with a second (co)monad Tr on M, a natural transformation i : ΠTl → ΠTr , and a morphism w : TrX → TlX in M. The (symmetrical) relations i and w need ...

We define a pedagogic collective challenge as a CSCL learning situation where: (1) the problem is designed to make learners practice some target domain-related and/or metacognitive competencies; (2) a group of learners is involved, as a team, in the solving of the problem; (3) the solving requires the learners to join their forces; (4) the problem and the setting are designed to create a positi...

We define and studyco-Noetherian dimension of rings for which the injective envelopeof simple modules have finite Krull-dimension. This  is a Moritainvariant dimension that measures how far the ring is from beingco-Noetherian. The co-Noetherian dimension of certain rings,including commutative rings, are determined. It is shown that the class ${mathcal W}_n$ of rings with co-Noetherian dimension...

Nanowire is a cylindrical nano-structure with nanometer dimensions. In this research, the studied nanowire was made from the magnetic triple Ni-Fe-Co alloy.&#10 We utilized ordered porous anodic aluminum oxide as a template for the nanowire deposition. The nanowire arrays were electrodeposited in the cylindrical pores of the oxide layer by AC potential in a simple sulfate bath. Then the relatio...