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We study the connections between one-sided Hopf algebras and one-sided quantum quasigroups, tracking the four possible invertibility conditions for the left and right composite morphisms that combine comultiplications and multiplications in these structures. The genuinely one-sided structures exhibit precisely two of the invertibilities, while it emerges that imposing one more condition often entails the validity of all four. A main result shows that under appropriate conditions, just one of the invertibility conditions is su?cient for the existence of a one-sided antipode. In the left Hopf algebra which is a variant of the quantum special linear group of two-dimensional matrices, it is shown explicitly that the right composite is not injective, and the left composite is not surjective. 相似文献
3.
For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates. 相似文献
4.
Hanene Zemmouri Sonda Ammar Amel Boumendjel Mahfoud Messarah Abdelfattah El Feki Mohamed Bouaziz 《Arabian Journal of Chemistry》2019,12(8):1954-1963
The aqueous and hydroalcoholic extracts of borage (Borago officinalis) leaves from Annaba region (Algeria) were preliminary analyzed for their phenolic profile (total phenolics, total flavonoids, total flavonols, total tannins and total anthocyanins). These extracts were evaluated for their antioxidant properties by different methods such as DPPH radical scavenging, test NBT and total antioxidant activity. The two extracts have exhibited a high antiradical capacity. Indeed, the ethanolic extract showed the lower IC50 values and the highest amount of phenolics (94.09 ± 1.72 mg gallic acid/g dry extract). Using LC-MS/MS analysis, it was possible to identify phenolic acids, flavonoids, sterol and for the first time oleuropein was identified in the aqueous extract of the plant. The obtained results have demonstrated that phenolic compounds are the major contributor to the antioxidant activity of plants. 相似文献
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《Mathematische Nachrichten》2018,291(13):2024-2044
In this paper we study the maximal function and local means characterizations and the non‐smooth atomic decomposition of the Triebel–Lizorkin type spaces with variable exponents . These spaces were recently introduced by Yang et al. and cover the Triebel–Lizorkin spaces with variable exponents as well as the classical Triebel–Lizorkin spaces , even the case when . Moreover, covered by this scale are also the Triebel–Lizorkin‐type spaces with constant exponents which, in turn cover the Triebel–Lizorkin–Morrey spaces. As an application we obtain a pointwise multiplier assertion for those spaces. 相似文献
7.
Fausto De Mari 《代数通讯》2018,46(4):1709-1715
In this paper (generalized) soluble groups for which the set of all non-modular subgroups satisfies some weak chain condition are described. Groups satisfying weak chain conditions on non-permutable subgroups are also considered. 相似文献
8.
G. Peruginelli 《代数通讯》2018,46(11):4724-4738
We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring. 相似文献
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本文证明了左n-角范畴的稳定化范畴具有n-角结构,并证明了当n为奇数时,左n-角范畴的Grothendieck群与其稳定化范畴的Grothendieck群同构. 相似文献