A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...

Let R be a Noetherian commutative ring containing a eld. The test ideal, introduced by Hochster and Huneke in HH1], has emerged as an important object associated to R. The test ideal can be deened as the largest ideal J of R such that JI I for all ideals I of R where I denotes the tight closure of I. Although it is not obvious that a ring R admits a non-zero test ideal, Hochster and Huneke show...

Abstract We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here are abstract partial-differential algebraic considered in Hilbert spaces. The catch is to consider time-dependent partial differential an exponentially weighted space. In passing, one establishes time derivative as a continuously invertible, normal operator admitting functional ...

A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also de...

A finitely generated $R$-module is said to be a module of type ($F_r$) if its $(r-1)$-th Fitting ideal is the zero ideal and its $r$-th Fitting ideal is a regular ideal. Let $R$ be a commutative ring and $N$ be a submodule of  $R^n$ which is generated by columns of  a matrix $A=(a_{ij})$ with $a_{ij}in R$ for all $1leq ileq n$, $jin Lambda$, where $Lambda $ is a (possibly infinite) index set.  ...

considerable interest has been focused on the triazole structure, which has been known to possess a broad spectrum of biological activities such as antitumor, anti-inflammatory, antimicrobial, antiviral, and anticonvulsant activities. before this, several heterocyclic compounds containing triazole were synthesized that had shown considerable anticonvulsant activity. as part of our continuous re...