Abstract C 34 H 26 N 6 Ni 2 O 8 , monoclinic, P 1 / n (no. 14), a = 12.4072(8) Å, b 13.5186(10) c 19.4750(14) β 92.902(2)°, V 3262.3(4) Å 3 Z 4, R gt ( F ) 0.0304, w ref 0.0809, T 223 K.

let $r$ be a commutative ring and $m$ be an $r$-module with $t(m)$ as subset,   the set of torsion elements. the total graph of the module denoted   by $t(gamma(m))$, is the (undirected) graph with all elements of   $m$ as vertices, and for distinct elements  $n,m in m$, the   vertices $n$ and $m$ are adjacent if and only if $n+m in t(m)$. in this paper we   study the domination number of $t(ga...

In the title compound, C(13)H(10)ClNO, the central C-N bond has considerable double-bond character and the N-O bond indicates a formal negative charge on the O atom. The mol-ecule is stabilized by an intra-molecular C-H⋯O hydrogen bond. The geometry about the C=N bond is Z [C-C-N-O torsion angle = -4.2 (3)°] and the phenyl and benzene rings are trans-oriented around the C=N bond. The phenyl and...

(1) d/dxX(z) = A{z)X{z), where X(z) is an n x 1 column vector and A(z) is an n x n matrix of singlevalued meromorphic functions in a neighbourhood of the (isolated) singular point 0. Sometimes we write A instead of A(z) but we always consider a matrix of functions with such a notation unless explicitly stated otherwise. Each fundamental solution matrix for (1) can be represented near zero as (2...

for a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, dewan et al [k. k. dewan, n. singh and a. mir, extension of some polynomial inequalities to the polar derivative, j. math. anal. appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). in this paper we improve and extend the above inequality. our result generalizes certai...

Abstract. In this paper we derive an explicit formula for the number of representations of an integer by the sextenary form x + y + z + 7s + 7t + 7u. We establish the following intriguing inequalities 2b(n) ≥ a7(n) ≥ b(n) for n 6= 0, 2, 6, 16. Here a7(n) is the number of partitions of n that are 7-cores and b(n) is the number of representations of n +2 by the sextenary form (x + y + z + 7s + 7t...

Let $R$ be an associative ring with identity. An element $x in R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if there exist $g in G$, $n in mathbb{Z}$ and $r in R$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). A ring $R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if every element of $R$ is $mathbb{Z}G$-regular (resp. strongly $...