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Acta Mathematica Sinica,Chinese Series
2017, Vol.33 Num.12
Online: 2017-12-15

1587 Wen Qiang SHEN
Rees-Shishikura's Theorem for Geometrically Finite Rational Maps
In this paper, we generalize Rees-Shishikura's theorem to the class of geometrically finite rational maps.
2017 Vol. 33 (12): 1587-1596 [Abstract] ( 10 ) [HTML 1KB] [PDF 197KB] ( 39 )
1597 Xiao Qing LU, Liang Wen LIAO, Jun WANG
On Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations
We consider transcendental meromorphic solutions with N(r, f)=S(r, f) of the following type of nonlinear differential equations:#br#fn+Pn-2(f)=p1(z)eα1(z)+p2(z)eα2(z),#br#where n ≥ 2 is an integer, Pn-2(f) is a differential polynomial in f of degree not greater than n-2 with small functions of f as its coefficients, p1(z), p2(z) are nonzero small functions of f, and α1(z), α2(z) are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of meromorphic solutions and their possible forms of the above equation. Our results extend and improve some known results obtained most recently.
2017 Vol. 33 (12): 1597-1608 [Abstract] ( 4 ) [HTML 1KB] [PDF 222KB] ( 55 )
1609 Hamid Reza MORADI, Mohsen Erfanian OMIDVAR
Complementary Inequalities to Improved AM-GM Inequality

Following an idea of Lin, we prove that if A and B are two positive operators such that 0 < mI ≤ Am'I ≤ M'I ≤ BMI, then

where K(h)=((h+1)2)/(4h) and h =M/m and Φ is a positive unital linear map.

2017 Vol. 33 (12): 1609-1616 [Abstract] ( 5 ) [HTML 1KB] [PDF 182KB] ( 17 )
1617 Jing Lan PENG, Yun Hua ZHOU
Sub-additive Topological and Measure-theoretic Tail Pressures
In this paper, we give some definitions of the topological tail pressures for sub-additive potentials and prove that they are equivalent if the potentials are continuous. Under some assumptions, we get a variational principle which exhibits the relationship between topological tail pressure and measure-theoretic tail entropy. Finally, we define a new measure-theoretic tail pressure for sub-additive potentials and some interesting properties of it are obtained.
2017 Vol. 33 (12): 1617-1631 [Abstract] ( 4 ) [HTML 1KB] [PDF 224KB] ( 14 )
1632 Xiao Li GUO, Yue Yang MEN
On Partial Regularity of Suitable Weak Solutions to the Stationary Fractional Navier-Stokes Equations in Dimension Four and Five
In this paper, we investigate the partial regularity of suitable weak solutions to the multidimensional stationary Navier-Stokes equations with fractional power of the Laplacian (-Δ)α (n/6 ≤ α < 1 and α ≠1/2). It is shown that the n + 2 -6α (3 ≤ n ≤ 5) dimensional Hausdorff measure of the set of the possible singular points of suitable weak solutions to the system is zero, which extends a recent result of Tang and Yu[19] to four and five dimension. Moreover, the pressure in ε-regularity criteria is an improvement of corresponding results in[1, 13, 18, 20].
2017 Vol. 33 (12): 1632-1646 [Abstract] ( 16 ) [HTML 1KB] [PDF 244KB] ( 20 )
1647 Mei Fang CHENG, Hui Hui LIU, Ai Wen SUN
Mapping Properties of Certain Oscillatory Integrals on Modulation Spaces
Suppose β1 > α1 ≥ 0, β2 > α2 ≥ 0 and (k, j) ∈ R2. In this paper, we mainly investigate the mapping properties of the operator#br#Tα,βf(x, y, z)=∫Q2 f(x -t, y -s, z -tksj)e-2πit-β1s-β2t-1-α1s-1-α2dtds#br#on modulation spaces, where Q2=[0, 1] ×[0, 1] is the unit square in two dimensions.
2017 Vol. 33 (12): 1647-1658 [Abstract] ( 4 ) [HTML 1KB] [PDF 245KB] ( 18 )
1659 Mei Yun LIU, Jin Chuan HOU
Strong 3-Commutativity Preserving Maps on Standard Operator Algebras
Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B(X). A map Φ:AA is said to be strong 3-commutativity preserving if[Φ(A), Φ(B)]3=[A, B]3 for all A, BA, where[A, B]3 is the 3-commutator of A, B defined by[A, B]3=[[[A, B], B], B] with[A, B]=AB -BA. The main result in this paper is shown that, if Φ is a surjective map on A, then Φ is strong 3-commutativity preserving if and only if there exist a functional h:A → F and a scalar λ ∈ F with λ4=1 such that Φ(A)=λA + h(A)I for all AA.
2017 Vol. 33 (12): 1659-1670 [Abstract] ( 5 ) [HTML 1KB] [PDF 220KB] ( 11 )
1671 Xun Xiang GUO
Similarity and Parameterizations of Dilations of Pairs of Dual Group Frames in Hilbert Spaces
In this paper, firstly, in order to establish our main techniques we give a direct proof for the existence of the dilations for pairs of dual group frames. Then we focus on proving the uniqueness of such dilations in certain sense of similarity and giving an operator parameterization of the dilations of all pairs of dual group frames for a given group frame. We show that the operators which transform different dilations are of special structured lower triangular.
2017 Vol. 33 (12): 1671-1683 [Abstract] ( 4 ) [HTML 1KB] [PDF 216KB] ( 36 )
1684 Jie Sheng XIAO, Guang Fu CAO
Wandering Subspaces and Quasi-wandering Subspaces in the Hardy-Sobolev Spaces
In this paper, we prove that for -(1/2) ≤ β ≤ 0, suppose M is an invariant subspaces of the Hardy-Sobolev spaces Hβ2(D) for Tzβ, then MzM is a generating wandering subspace of M, that is, M=[MzM]Tzβ. Moreover, any non-trivial invariant subspace M of Hβ2(D) is also generated by the quasi-wandering subspace PMTzβM, that is, M=[PMTzβM]Tzβ.
2017 Vol. 33 (12): 1684-1692 [Abstract] ( 4 ) [HTML 1KB] [PDF 201KB] ( 13 )
1693 Hui Min CHANG
Cluster Structures in 2-Calabi-Yau Triangulated Categories of Dynkin Type with Maximal Rigid Objects
In this paper, we consider two kinds of 2-Calabi-Yau triangulated categories with finitely many indecomposable objects up to isomorphisms, called An,t=Db(KA(2t+1)(n+1)-3)/τt(n+1)-1[1], where n, t ≥ 1, and Dn,t=Db(KD2t(n+1))/τ(n+1)φn, where n, t ≥ 1, and φ is induced by an automorphism of D2t(n+1) of order 2. Except the categories An,1, they all contain non-zero maximal rigid objects which are not cluster tilting. An,1 contain cluster tilting objects. We define the cluster complex of An,t (resp. Dn,t) by using the geometric description of cluster categories of type A (resp. type D). We show that there is an isomorphism from the cluster complex of An,t (resp. Dn,t) to the cluster complex of root system of type Bn. In particular, the maximal rigid objects are isomorphic to clusters. This yields a result proved recently by Buan-Palu-Reiten:Let RAn,t, resp. RDn,t, be the full subcategory of An,t, resp. Dn,t, generated by the rigid objects. Then RAn,tRAn,1 and RDn,tRAn,1 as additive categories, for all t ≥ 1.
2017 Vol. 33 (12): 1693-1704 [Abstract] ( 4 ) [HTML 1KB] [PDF 250KB] ( 10 )
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