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In this paper, centralizing (semi-centralizing) and commuting (semi-commuting) derivations of semirings are characterized. The action of these derivations on Lie ideals is also discussed and as a consequence, some significant results are proved. In addition, Posner’s commutativity theorem is generalized for Lie ideals of semirings and this result is also extended to the case of centralizing (semi-centralizing) derivations of prime semirings. Further, we observe that if there exists a skew-commuting (skew-centralizing) derivation D of S, then D = 0. It is also proved that for any two derivations d 1 and d 2 of a prime semiring S with char S ≠ 2 and x d1 x d2 = 0, for all xS implies either d 1 = 0 or d 2 = 0.

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Abstract  

Extraction behavior of 1 × 10−2–0.1 M U(VI) from aqueous phases containing 0.86 M Th(IV) at 4 M HNO3 in 1.1 M tributyl phosphate (TBP) and 1.1 M N,N-dihexyl octanamide (DHOA) solutions in different diluents viz. n-dodecane, 10% 1-octanol + n-dodecane, and decahydronaphthalene (decalin) was studied. Third-phase formation was observed in both the extractants using n-dodecane as diluent. There was a gradual decrease in Th(IV) concentration in the third-phase (heavy organic phase, HOP) with increased aqueous U(VI) concentration [0.71 M (no U(VI))–0.61 M (0.1 M U(VI)) for TBP; 0.27 M (no U(VI))–0.22 M (0.1 M U(VI)) for DHOA]. The HOP volume in case of DHOA was ~2.2 times of that of TBP. Uranium concentration in HOP increased with its initial concentration in the aqueous phase [from 1.8 × 10−2 M (0.01 M U(VI))–0.162 M (0.1 M U(VI)) for TBP; from 1.4 × 10−2 M (0.01 M U(VI))–0.14 M (0.1 M U(VI)) for DHOA] suggesting that Th(IV) was being replaced by U(VI). An empirical correlation was developed for predicting the concentrations of uranium and thorium in HOP for both the extractants. No third-phase appeared during the extraction of uranium and thorium from the aqueous phases employing 10% 1-octanol + n-dodecane, or decalin as diluents, and therefore, were better choices as diluent for alleviating the third-phase formation during the reprocessing of spent thorium based fuels, and for the recovery of thorium from high-level waste solutions.

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Reversed-phase thin-layer chromatography (RP-TLC) is a sensitive, reliable, and reproducible technique, which can analyze a number of components simultaneously. This technique was exploited in the present study to identify the adulteration of vegetable oils (groundnut, soybean, and sunflower oil) in ghee, using the fact that β-sitosterol, an unsaponifiable matter, is present in vegetable oils, while absent in pure ghee. For this, RP-TLC of reference standards, unsaponifiable matter of pure ghee (cow and buffalo), pure vegetable oils, and the ghee adulterated with these vegetable oils (≥1%) was carried out on plates with different stationary phases, viz., RP-18, RP-8, and RP-2 plates using solvent system comprising of petroleum ether, acetonitrile, and methanol. The results revealed that adulteration of vegetable oils in ghee can easily be detected at a level of as low as 1 percent on RP-18 and RP-8 plates, while RP-2 plate did not offer any help in detection of adulteration. Thus, with the help of RP-TLC, a robust technique, the purity of ghee can be screened with respect to the presence of vegetable oils.

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Iron and zinc deficiency affects more than half of the world population due to low inherent micronutrient content of cereals and other staple foods. The micronutrient deficiency is further aggravated by poor availability of these minerals in calcareous soils and their uptake by crop plants. Series of available wheat-Aegilops addition lines were evaluated for identification of alien chromosomes carrying genes for high grain iron and zinc concentrations and release of mugineic acid(s) facilitating micronutrient uptake under their deficient conditions. Addition lines of chromosome 2Sv, 2Uv and 7Uv of Ae. peregrina, 2Sl and 7Sl of Ae. longissima and 2U of Ae. umbellulata were found to carry genes for high grain iron whereas the group 7 chromosomes had genes for higher grain zinc. Higher release of mugineic acid (MA) under iron deficient condition was observed in addition lines of chromosome 2Sv, 2Uv, 4Uv and 7Sv of Ae. peregrina, 2Sl and 6Sl of Ae. longissima and 2U and 5U of Ae. umbellulata. Higher grain and root iron concentration and MA(s) release under iron sufficient condition in the group 2 chromosome addition lines suggests that their high grain iron may be attributed to the higher uptake of the micronutrients through MA(s). These addition lines with two- to threefold high grain iron and zinc concentration could be used for precise introgression of genes into elite wheat cultivars for enhanced uptake of these micronutrients by wheat plants in problematic soils and their biofortification in grains.

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