Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

This paper considers the problem of electing a leader ina dynamic ring in which processors are permitted to fail and recoverduring election. e( n log n + I;, ) messages, when counting only messagessent by functional processors, are shown to be necessary and sufficientfor dynamic ring election, where I;v is the number of processor recoveriesexperienced.

In this paper, we give a new method for constructing LCD codes. We employ group rings and well known map that sends ring elements to subring of the n×n matrices obtain Our construction guarantees our codes are also codes, namely, ideals in ring. show with certain condition on element v, one can construct non-trivial Moreover, by adding more constraints reversible. present many examples binary w...

In the title complex, [V(C(18)H(11)ClN(2)O(2))(CH(3)O)O(CH(3)OH)], the V(V) ion is coordinated by a tridendate 3-chloro-N'-(2-oxidonaphthalen-1-ylmethylidene)benzohydrazidate ligand, one oxido ligand and by O atoms from a methanol and a methoxide ligand, forming a distorted octa-hedral geometry. The dihedral angle between the benzene ring and the naphthyl-ene ring system is 6.4 (3)°. The deviat...

how to cite this article: shetty g, avabratha k.s, rai b.s. ring-enhancing lesions in the brain: a diagnostic dilemma. iran j child neurol. 2014 summer;8(3): 61-64. abstract the most common radiological abnormality seen in young indian patients with epilepsy is single small enhancing (ring/disc) computed tomographic (ct) lesions. the two most common differential diagnosis of this lesion in clin...

the effect of alkyl substituents on the c-phenyl and/or the n-phenyl ring of benzophenylhydroxamic acid on their molecular structure and hydrogen bonding has been investigated. the predominant configuration in chcl3 is determined by steric and electronic effects. substituents on the c-phenyl ring favor the cis configuration, while substituents in the n-phenyl ring favor a trans configuration. t...

let r be a commutative ring with identity and m be a unitary r-module. let : s(m) −! s(m) [ {;} be a function, where s(m) is the set of submodules ofm. suppose n  2 is a positive integer. a proper submodule p of m is called(n − 1, n) − -prime, if whenever a1, . . . , an−1 2 r and x 2 m and a1 . . . an−1x 2p(p), then there exists i 2 {1, . . . , n − 1} such that a1 . . . ai−1ai+1 . . . an−1x...

It is well-known (see [1]) that for a Heisenberg magnet symmetry operators and symmetry classes can be defined in a very similar way as for tensors (see e.g. [2, 3, 4]). Newer papers which consider the action of permutations on the Hilbert space H of the Heisenberg magnet are [5, 6, 7, 8]. We define symmetry classes and commutation symmetries in the Hilbert space H of the 1D spin-1/2 Heisenberg...

The effect of alkyl substituents on the C-phenyl and/or the N-Phenyl ring of benzophenylhydroxamic acid on their molecular structure and hydrogen bonding has been investigated. The predominant configuration in CHCl3 is determined by steric and electronic effects. Substituents on the C-phenyl ring favor the cis configuration, while substituents in the N-phenyl ring favor a trans c...