this paper, we will prove the following theorem, Let R be a ring with 1 having
a reverse derivation d ≠ 0 such that, for each x R, either d(x) = 0 or d(x) is
invertible in R, then R must be one of the following: (i) a division ring D, (ii) D 2 ,
the ring of 2×2 matrices over D, (iii) D[x]/(x ) 2
where char D = 2, d (D) = 0 and
d(x) = 1 + ax for some a in the center Z of D. Furthermore, if 2R ≠ 0 then R = D 2 is
possible if and only if D does not contain all quadratic extensions of Z, the center of
D.
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... Show MoreMultiple linear regressions are concerned with studying and analyzing the relationship between the dependent variable and a set of explanatory variables. From this relationship the values of variables are predicted. In this paper the multiple linear regression model and three covariates were studied in the presence of the problem of auto-correlation of errors when the random error distributed the distribution of exponential. Three methods were compared (general least squares, M robust, and Laplace robust method). We have employed the simulation studies and calculated the statistical standard mean squares error with sample sizes (15, 30, 60, 100). Further we applied the best method on the real experiment data representing the varieties of
... Show MoreFor extraction chloro anion complexes of Cd2+ and Hg2+ used many organic agents as extractant according to liquid ion exchange method such as α-Naphthyl amine (α-NA), 4-Amino benzoic acid (4-ABA), 2-[(4-Carboxy methyl phenyl) azo]-4,5-diphenyl imidazole (4CMePADPI) and Cryptand (C222). This study includes definition hydrochloric acid concentration in aqueous phase and shaking with organic phase necessary for extraction as well as shaking time, organic solvent effect, interferences and alkaline salt effect. Thermodynamic showed the ion exchange reaction was exothermic for α-NA, C222 and endothermic for 4-ABA, 4-CMePADPI for extraction CdCl4=, but for extraction HgCl4= was exothermic with 4-ABA, 4CMePADPI and C222 but
... Show MoreObjectives: To identify the frequency and types of microsatellite instability among a group of sporadic CRC patients and to correlate the findings with clinicopathological characteristics. Methods: During an 8-month period, all patients with sporadic CRC who attended to two teaching hospitals in Baghdad, Iraq were recruited to this cross-sectional study regardless of age, sex, ethnicity, or tumor characteristics. Demographic, clinical, and histopathological features were recorded. DNA was extracted from FFPE-blocks of the resected tumors and normal tissues. PCR amplification of five microsatellite mononucleotide repeat loci (BAT25, BAT26, NR-21, NR-24, and MONO-27) and 2 pentanucleotide repeat control markers (Penta C and Pent
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