The independent domatic queen number of a graph Qn is the maximum pairwise disjoint minimum dominating sets Pn and it denoted by id(Qn) while Id(Qn). We discuss about in this paper (maximum independent) on n × chess board.

Our ability to trust that a random number is truly essential for fields as diverse cryptography and fundamental tests of quantum mechanics. Existing solutions both come with drawbacks -- device-independent generators (QRNGs) are highly impractical standard semi-device-independent QRNGs limited specific physical implementation level trust. Here we propose new framework randomness certification, ...

The stability and error estimates for the mortar finite element method are well established. This work examines the dependence of constants in these estimates on shape and number of subdomains. By means of a Poincaré inequality and some scaling arguments, these estimates are found not to deteriorate with increase in number of subdomains.