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Oscillatory hyper Hilbert transforms along variable curves
Jiecheng CHEN, Dashan FAN, Meng WANG
Front. Math. China. 2019, 14 (4): 673-692.
https://doi.org/10.1007/s11464-019-0783-7
For n = 2 or 3 and , we study the oscillatory hyper Hilbert transformalong an appropriate variable curve in (namely, is a curve in for each fixed x), where . We obtain some boundedness theorems of , under some suitable conditions on and . These results are extensions of some earlier theorems. However, is not a convolution in general. Thus, we only can partially employ the Plancherel theorem, and we mainly use the orthogonality principle to prove our main theorems.
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Properties of core-EP order in rings with involution
Gregor DOLINAR, Bojan KUZMA, Janko MAROVT, Burcu UNGOR
Front. Math. China. 2019, 14 (4): 715-736.
https://doi.org/10.1007/s11464-019-0782-8
We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289–300] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Filomat, 2018, 32: 3073–3085]. We present new characterizations of the core-EP order in *-rings with identity and introduce the notions of the dual core-EP decomposition and the dual core-EP order in-rings.
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On Diophantine approximation with one prime and three squares of primes
Wenxu GE, Feng ZHAO, Tianqin WANG
Front. Math. China. 2019, 14 (4): 761-779.
https://doi.org/10.1007/s11464-019-0776-6
Let λ1, λ2, λ3, λ4 be non-zero real numbers, not all of the same sign, w real. Suppose that the ratios λ1/λ2, λ1/λ3 are irrational and algebraic. Then there are in.nitely many solutions in primes pj, j =1, 2, 3, 4, to the inequality . This improves the earlier result.
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Number of fixed points for unitary Tn−1-manifold
Shiyun WEN, Jun MA
Front. Math. China. 2019, 14 (4): 819-831.
https://doi.org/10.1007/s11464-019-0785-5
Let M be a 2n-dimensional closed unitary manifold with a Tn−1-action with only isolated fixed points. In this paper, we first prove that the equivariant cobordism class of a unitary Tn−1-manifold M is just determined by the equivariant Chern numbers [M],where ω= (i1, i2, ..., i6) are the multi-indexes for all i1, i2, ..., i6∈. Then we show that if Mdoes not bound equivariantly, then the number of fixed points is greater than or equal to , where denotes the minimum integer no less than n/6.
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