let a; b; k 2 k and u ; v 2 u(k). we show for any idempotent e 2 k, ( a 0 b 0 ) is e-clean i ( a 0 u(vb + ka) 0 ) is e-clean and if ( a 0 b 0 ) is 0-clean, ( ua 0 u(vb + ka) 0 ) is too.

let $r$ be a 2-torsion free ring and $u$ be a square closed lie ideal of $r$. suppose that $alpha, beta$ are automorphisms of $r$. an additive mapping $delta: r longrightarrow r$ is said to be a jordan left $(alpha,beta)$-derivation of $r$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin r$. in this paper it is established that if $r$ admits an additive mapping $g : rlongrigh...

in this work, new biodegradable abcba type pentablock copolymers with different mole ratio of l-lactide and ppdo-b-peg-b-ppdo triblock copolymer were synthesized and characterized. in the first step, ppdo-b-peg-b-ppdo triblock copolymer was synthesized via a ring-opening polymerization of p-dioxanone (pdo) monomer with poly (ethylene glycol) (peg) using stannous octoate (sn(oct)2) as the cataly...

results the mean udva (logmar) improved significantly from 1.13 ± 0.21 preoperatively to 0.24 ± 0.13 postoperatively (p < 0.001), and the mean cdva (logmar) improved significantly from 0.39 ± 0.12 to 0.19 ± 0.09 (p < 0.001). the mean cylinder of manifest refraction decreased significantly by 4.00 diopter (d) (p < 0.001). the mean spherical equivalent error (se) decreased significantly from −6.0...

purpose: to assess the stability of visual and refractive outcomes that was compared between three and 12 months after myoring implantation in moderate and severe keratoconus methods: this study included 54 eyes of 50 patients (27 males and 23 females) with stage ii and iii keratoconus who underwent myoring (dioptex gmbh) implantation. clinical outcomes including uncorrected distance visual acu...

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 ar...

here, we propose an optical filter and an optical power splitter based on two-dimensionalphotonic crystal all circular ring resonators. these structures are made of a square lattice ofsilicon rods with the refractive index n1=3.464 surrounded by air (with refractive indexn2=1). first, we have designed the filter and by using that, we designed a power splitter. thetransmission efficiency and qua...

the regioselective ring opening of styrene oxide using elemental iodine and bromine in the presence of disulfides as new catalysts was studied. the conductivity titration and uv spectroscopy were used to study the interaction of iodine with these catalysts. the results indicate that disulfide 11 is efficient in polyiodide formation, and can catalyze this reaction in excellent yield and high reg...

‎let $i$ denote an ideal of a noetherian ring $r$‎. ‎the purpose of‎ ‎this article is to introduce the concepts of quintasymptotic‎ ‎sequences over $i$ and quintasymptotic cograde of $i$‎, ‎and to show that they play a role analogous to quintessential sequences‎ ‎over $i$ and quintessential cograde of $i$‎. ‎we show that‎, ‎if $r$ is‎ ‎local‎, ‎then the quintasymptotic cograde of $i$ is una...