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Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor
Yannan CHEN, Shenglong HU, Liqun QI, Wennan ZOU
Front. Math. China. 2019, 14 (1): 1-16.
https://doi.org/10.1007/s11464-019-0748-x
Third order three-dimensional symmetric and traceless tensors play an important role in physics and tensor representation theory. A minimal integrity basis of a third order three-dimensional symmetric and traceless tensor has four invariants with degrees two, four, six, and ten, respectively. In this paper, we show that any minimal integrity basis of a third order three-dimensional symmetric and traceless tensor is also an irreducible function basis of that tensor, and there is no syzygy relation among the four invariants of that basis, i.e., these four invariants are algebraically independent.
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Relative homological dimensions in recollements of triangulated categories
Yonggang HU, Hailou YAO
Front. Math. China. 2019, 14 (1): 25-43.
https://doi.org/10.1007/s11464-019-0751-2
Let be a proper class of triangles in a triangulated category , and let () be a recollement of triangulated categories. Based on Beligiannis's work, we prove that and have enough -projective objects whenever does. Moreover, in this paper, we give the bounds for the -global dimension of in a recollement () by controlling the behavior of the -global dimensions of the triangulated categories and : In particular, we show that the niteness of the -global dimensions of triangulated categories is invariant with respect to the recollements of triangulated categories.
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New characterizations of Musielak–Orlicz–Sobolev spaces via sharp ball averaging functions
Sibei YANG, Dachun YANG, Wen YUAN
Front. Math. China. 2019, 14 (1): 177-201.
https://doi.org/10.1007/s11464-019-0744-1
We establish a new characterization of the Musielak–Orlicz–Sobolev space on ; which includes the classical Orlicz–Sobolev space, the weighted Sobolev space, and the variable exponent Sobolev space as special cases, in terms of sharp ball averaging functions. Even in a special case, namely, the variable exponent Sobolev space, the obtained result in this article improves the corresponding result obtained by P. Hästö and A. M. Ribeiro [Commun. Contemp. Math., 2017, 19: 1650022] via weakening the assumption into , which was conjectured to be true by Hästö and Ribeiro in the aforementioned same article.
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12 articles
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