In this article, we introduce a new family of polar codes from evaluation codes, called decreasing monomial-Cartesian and prove that families with multiple kernels over certain symmetric channels can be viewed as codes. This offers unified treatment for such any finite field. We define obtained set monomials closed under divisibility Cartesian product determine their parameters (length, dimensi...

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...

in this paper, the hyper - zagreb index of the cartesian product, composition and corona product of graphs are computed. these corrects some errors in g. h. shirdel et al.[11].

in this paper, some categorical properties of the category ${bf cpo}_{{bf act}text{-}s}$ of all {cpo $s$-acts}, cpo's equipped with actions of a monoid $s$ on them, and strict continuous action-preserving maps between them is considered. in particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. also, we show that the forgetful functor from...

We are learning strange things about cartesian products. Shapiro has shown that the cartesian product of a line and a certain example described by Whitehead [ló] is topologically E4. The example is a bounded open subset of E3 that is simply connected but which contains a simple closed curve which does not lie in any topological cube in it [3]. Glimm has given a proof of this result in [9] and a...