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- 저자 : Al-Ghafri, Bushra Rashid (검색결과 2 건)
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DIFFERENCES OF DIFFERENTIAL OPERATORS BETWEEN WEIGHTED-TYPE SPACES
Al Ghafri, Mohammed Said,Manhas, Jasbir Singh Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.3
Let 𝓗(𝔻) be the space of analytic functions on the unit disc 𝔻. Let 𝜓 = (𝜓<sub>j</sub>)<sup>n</sup><sub>j=0</sub> and 𝚽 = (𝚽<sub>j</sub>)<sup>n</sup><sub>j=0</sub> be such that 𝜓<sub>j</sub>, 𝚽<sub>j</sub> ∈ 𝓗(𝔻). The linear differential operator is defined by T<sub>𝜓</sub>(f) = ∑<sup>n</sup><sub>j=0</sub> 𝜓<sub>j</sub>f<sup>(j)</sup>, f ∈ 𝓗(𝔻). We characterize the boundedness and compactness of the difference operator (T<sub>𝜓</sub> - T<sub>𝚽</sub>)(f) = ∑<sup>n</sup><sub>j=0</sub> (𝜓<sub>j</sub> - 𝚽<sub>j</sub>) f<sup>(j)</sup> between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (non compact) differential operators such that their difference is bounded (compact).
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Waly, Mostafa Ibrahim,Al-Ghafri, Bushra Rashid,Guizani, Nejib,Rahman, Mohammad Shafiur Asian Pacific Journal of Cancer Prevention 2015 Asian Pacific journal of cancer prevention Vol.16 No.8
Plants and their by-products offer a diverse mixture of chemical constituents like natural antioxidants. Date-pits are rich in phenolic compounds that have antioxidant potential. The main objective of this study was to investigate the protective effect of a date-pit extract (DPE) against AOM-induced colonic carcinogenicity and oxidative stress. Thirty-two weanling male Sprauge-Dawley rats were randomly divided into four groups (eight rats in each group). All rats were fed basic diet and water ad libitum, and randomly distributed per treatment groups as follows: negative controls injected with normal saline once a week for two weeks, a cancer group injected intra-peritoneally with azoxymethane (15mg/kg body weight) for two consecutive weeks, and DPE treated groups receiving the extract via the oral route (1.5ml/day) for the entire experiment in the presence or absence of AOM injection. Results showed that DPE contained phytonutrients that were capable of inhibiting chemically-induced oxidative stress in the rat colonic cells. In those animals that consumed DPE, a protective effect was observed against AOM-induced oxidative stress in rat colonic cells as evident by a significant decrease in MDA and oxidized DCF formation in AOM injected and DPE fed groups. It is concluded that DPE has potential antioxidant and anticarcinogenic properties.
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