The title compound, C(17)H(18)N(4), contains a pyrazolopyridine system fused with a seven-membered carbocyclic ring. The pyrazole ring is coplanar with the pyridine ring, while the phenyl ring is twisted by a dihedral angle of 14.38 (14)° with respect to the pyridine ring. The seven-membered ring displays a chair conformation. The packing is stabilized by N-H⋯N hydrogen bonds and N-H⋯π(arene) i...

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...

A new series of imidazo[2,1-b]thiazole analogs containing a methyl sulfonyl COX-2 pharmacophore was synthesized and evaluated for their COX-2 inhibitory activity. According to in-vitro COX-1/COX-2 inhibition data, all compounds (6a-g) were selective inhibitors of COX-2 isoenzyme with IC50 values in the highly potent 0.08-0.16 mM range. These results indicated that both potency and selectivity o...

A new series of imidazo[2,1-b]thiazole analogs containing a methyl sulfonyl COX-2 pharmacophore was synthesized and evaluated for their COX-2 inhibitory activity. According to in-vitro COX-1/COX-2 inhibition data, all compounds (6a-g) were selective inhibitors of COX-2 isoenzyme with IC50 values in the highly potent 0.08-0.16 mM range. These results indicated that both potency and selectivity o...

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

let $r$ be a commutative ring with zero-divisor set $z(r)$. the total graph of $r$, denoted by$t(gamma(r))$, is the simple (undirected) graph with vertex set  $r$ where two distinct vertices areadjacent if their sum lies in $z(r)$.this work considers minimum zero-sum $k$-flows for $t(gamma(r))$.both for $vert rvert$ even and the case when $vert rvert$ is odd and $z(g)$ is an ideal of $r$it is s...

A group of 1,3-biarylhydrazide derivatives possessing a COX-2 azido pharmacophore at the Para- position of the C-1 phenyl ring in conjunction with a N-3 phenyl or substituted-phenyl ring (4-F,4-Cl,4-OMe) were designed and synthesized based on nucleophilic substitution reaction. A molecular modelling study of these compounds showed that the designed molecules were well bound with the active site...

‎in a recent paper c‎. ‎miguel proved that the diameter of the commuting graph of the matrix ring $mathrm{m}_n(mathbb{r})$ is equal to $4$ if either $n=3$ or $ngeq5$‎. ‎but the case $n=4$ remained open‎, ‎since the diameter could be $4$ or $5$‎. ‎in this work we close the problem showing that also in this case the diameter is $4$.