Mohammad Salahuddin Khan

On * -bimultipliers, Generalized * -biderivations and Related Mappings

In this paper we dene the notions of left -bimultiplier, -bimultiplier and generalized -biderivation, and to prove that if a semiprime -ring admits a left - bimultiplier M, then M maps R R into Z(R). In Section 3, we discuss the applications of theory of -bimultipliers. Further, it was shown that if a semiprime -ring R admits a symmetric generalized -biderivation G : R R ! R with an associated nonzero symmet- ric -biderivation B : R R ! R, then G maps R R into Z(R). As an application, we establish corresponding results in the setting of C -algebra.

On rings and algebras with derivations

Let R be an associative ring with center Z(R). The objective of this paper is to discuss the commutativity of a semiprime ring R which admits a derivation d such that d([xm,yn]) ± [xm,yn] ∈ Z(R) for all x,y ∈ R or d([xm,yn]) ∈ Z(R) for all x,y ∈ R or d(xm ∘ yn) ∈ Z(R) for all x,y ∈ R, where m and n are fixed positive integers. Finally, we apply these purely ring theoretic results to obtain commutativity of Banach algebra via derivation.

Onion Peel Ethylacetate Fraction and Its Derived Constituent Quercetin 4′-O-β-D Glucopyranoside Attenuates Quorum Sensing Regulated Virulence and Biofilm Formation

The resistance and pathogenesis of bacteria could be related to their ability to sense and respond to population density, termed quorum sensing (QS). Inhibition of the QS system is considered as a novel strategy for the development of antipathogenic agents, especially for combating drug-resistant bacterial infections. In the present study, the anti-QS activity of Onion peel ethylacetate fraction (ONE) was tested against Chromobacterium violaceum CV12472 and Pseudomonas aeruginosa PAO1. ONE inhibit the QS-mediated virulence factors production such as violacein in C. violaceum and elastase, pyocyanin in P. aeruginosa. Further, the treatment with sub-MICs of ONE significantly inhibited the QS-mediated biofilm formation, EPS (Extracellular polymeric substances) production and swarming motility. Further, quercetin 4′-O-β-D glucopyranoside (QGP) was isolated from ONE and its anti-QS potential was confirmed after observing significant inhibition of QS-controlled virulence factors such as violacein, elastase, pyocyanin and biofilm formation in test pathogens. Molecular docking analysis predicted that QGP should be able to bind at the active sites of Vfr and LasR, and if so blocks the entry of active sites in Vfr and LasR.

Effect of different chickpea varieties on development of the pulse beetle, Callosobruchus chinensis (L.).

Studies conducted on growth and development of the pulse beetle, Callosobruchus chinensis ( L.) on 11 chickpea varieties in Department of Entomology, G.B. Pant University of Agriculture and Technology Pantnagar during JuneSeptember, 2014 revealed that the fecundity of the pulse beetle female varied significantly on different chickpea varieties, minimum being on PBG 1 (59.0 eggs/100 seeds ) and maximum on PKG 1 (81.0 eggs/100 seeds). The development period for eggs (5.33-7.0 days), larva (17.0-18.67 days) and pupa (5.67-7.33 days) on different varieties did not differ significantly however, significant variation in the total development period from eggs to adult (28.6732.33 days) was recorded in different varieties. Similarly the growth index of the pulse beetle varied significantly on various varieties (0.52-0.71). The results of study showed that the chickpea variety PKG 1 was most suitable for growth and development of the pulse beetle. How to view point the article : Ahmad, Mohammad Abbas, Khan, M.S. and Agnihotri, Meena (2016). Effect of different chickpea varieties on development of the pulse beetle, Callosobruchus chinensis (L.). Internat. J. Plant Protec., 9(1) : 233-236.

A Characterization of Generalized Derivations on Prime Rings

Let R be a noncommutative prime ring, U be the left Utumi quotient ring of R, and k, m, n, r be fixed positive integers. If there exist a generalized derivation G and a derivation g (which is independent of G) of R such that [G(xm)xn + xng(xm), xr]k = 0, for all x ∈ R, then there exists a ∈ U such that G(x) = ax, for all x ∈ R. As a consequence of the result in the present article, one may obtain Theorem 1 in Demir and Argaç [10].

Commutativity of rings involving additive mappings

Abstract Let R be an associative ring. In the present paper, we investigate commutativity of a ring admitting an additive mapping F satisfying any one of the following properties: (i) F ([x, y]2 ) = F ([x2 , y2 ]), (ii) F ((x ◦ y)2 ) = F (x2 ◦ y2 ), (iii) F ((xy)n ) = F (xn yn ), (iv) F (xm yn ) = F (yn xm ), (v) (F (x)F (y))n = (F (y)F (x))n for all x, y ∈ R, where m and n are positive integers greater than 1. Moreover, some related results are also discussed. Finally, some examples are given to demonstrate that the restrictions imposed on the hypotheses of the various results are not superfluous.