the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.

a computational study of the electronic structure and stability of complexes formed between zeolite y and boric acid was carried out at the hf and b3lyp levels using 6-31g* basis set. five structures located as local minimum in pes of complex (structures d, e, f, g, and h). the most stable structure is formed due to hydrogen bonding between two hydroxyl of boric acid and both oxygen of ...

a recursive-circulant $g(n; d)$ is defined to be acirculant graph with $n$ vertices and jumps of powers of $d$.$g(n; d)$ is vertex-transitive, and has some strong hamiltonianproperties. $g(n; d)$ has a recursive structure when $n = cd^m$,$1 leq c < d $ [10]. in this paper, we will find the automorphismgroup of some classes of recursive-circulant graphs. in particular, wewill find that the autom...

the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka&apos;s $d$-poset and prove the basic properties ofconditional expectation on this  structure.