中国科学院数学与系统科学研究院期刊网

15 June 2021, Volume 37 Issue 6
    

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  • Min CAI, Li Qun XIAO, Shu Wei LI
    Acta Mathematica Sinica. 2021, 37(6): 835-853. https://doi.org/10.1007/s10114-021-0151-x
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    In some situations, the failure time of interest is defined as the gap time between two related events and the observations on both event times can suffer either right or interval censoring. Such data are usually referred to as doubly censored data and frequently encountered in many clinical and observational studies. Additionally, there may also exist a cured subgroup in the whole population, which means that not every individual under study will experience the failure time of interest eventually. In this paper, we consider regression analysis of doubly censored data with a cured subgroup under a wide class of flexible transformation cure models. Specifically, we consider marginal likelihood estimation and develop a two-step approach by combining the multiple imputation and a new expectation-maximization (EM) algorithm for its implementation. The resulting estimators are shown to be consistent and asymptotically normal. The finite sample performance of the proposed method is investigated through simulation studies. The proposed method is also applied to a real dataset arising from an AIDS cohort study for illustration.

  • Tian LIANG
    Acta Mathematica Sinica. 2021, 37(6): 854-872. https://doi.org/10.1007/s10114-021-9359-z
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    Let n ≥ 2, β ∈ (0, n) and Ω ⊂ Rn be a bounded domain. Support that φ:[0, ∞)→[0, ∞) is a Young function which is doubling and satisfies

    If Ω is a John domain, then we show that it supports a (φn/(n-β), φ)β-Poincaré inequality. Conversely, assume that Ω is simply connected domain when n=2 or a bounded domain which is quasiconformally equivalent to some uniform domain when n ≥ 3. If Ω supports a (φn/(n-β), φ)β-Poincaré inequality, then we show that it is a John domain.

  • Satyajit SAHOO, Namita DAS, Nirmal Chandra ROUT
    Acta Mathematica Sinica. 2021, 37(6): 873-892. https://doi.org/10.1007/s10114-021-9514-6
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    In this article, we refine certain earlier existing bounds for Berezin number of operator matrices. We also prove some new Berezin number inequalities for general n×n operator matrices. Further, we establish several upper bounds for Berezin number and generalized Euclidean Berezin number for off-diagonal operator matrices. Finally, some interesting examples are discussed.

  • Jin Chuan HOU, Jin Fei CHAI
    Acta Mathematica Sinica. 2021, 37(6): 893-910. https://doi.org/10.1007/s10114-021-0427-1
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    The separability and the entanglement (that is, inseparability) of the composite quantum states play important roles in quantum information theory. Mathematically, a quantum state is a trace-class positive operator with trace one acting on a complex separable Hilbert space. In this paper, in more general frame, the notion of separability for quantum states is generalized to bounded positive operators acting on tensor product of Hilbert spaces. However, not like the quantum state case, there are different kinds of separability for positive operators with different operator topologies. Four types of such separability are discussed; several criteria such as the finite rank entanglement witness criterion, the positive elementary operator criterion and PPT criterion to detect the separability of the positive operators are established; some methods to construct separable positive operators by operator matrices are provided. These may also make us to understand the separability and entanglement of quantum states better, and may be applied to find new separable quantum states.

  • Nan ZHAO, Jiang ZHOU
    Acta Mathematica Sinica. 2021, 37(6): 911-925. https://doi.org/10.1007/s10114-021-0251-7
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    Applying the new class of multiple weights Apθ, we establish some weighted norm inequalities for certain classes of multilinear operators in the Morrey-type spaces. In addition, the new multiple weighted norm inequalities for multilinear commutators of T with the new BMO functions BMOθ are also obtained.

  • Yu Lei WANG, He Guo LIU
    Acta Mathematica Sinica. 2021, 37(6): 926-940. https://doi.org/10.1007/s10114-021-9509-3
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    Let p be an odd prime, and let k be a nonzero nature number. Suppose that nonabelian group G is a central extension as follows
    1→G'→G→Zpk×…×Zpk,
    where G'≌ Zpk, and ζG/G' is a direct factor of G/G'. Then G is a central product of an extraspecial pk-group E and ζG. Let|E|=p(2n+1)k and|ζG|=p(m+1)k. Suppose that the exponents of E and ζG are pk+l and pk+r, respectively, where 0 ≤ l, rk. Let AutG' G be the normal subgroup of Aut G consisting of all elements of Aut G which act trivially on the derived subgroup G', let AutG/ζG,ζGG be the normal subgroup of Aut G consisting of all central automorphisms of G which also act trivially on the center ζG, and let AutG/ζG,ζG/G'G be the normal subgroup of Aut G consisting of all central automorphisms of G which also act trivially on ζG/G'. Then (i) The group extension 1→AutG' G→Aut G→Aut G'→1 is split. (ii) AutG' G/AutG/ζG,ζGGG1×G2, where Sp(2n-2, Zpk)?HG1 ≤ Sp(2n, Zpk), H is an extraspecial pk-group of order p(2n-1)k and (GL(m-1, Zpk)?Zpk(m-1))?Zpk(m) ≤ G2 ≤ GL(m, Zpk)?Zpk(m). In particular, G1=Sp(2n -2, Zpk)?H if and only if l=k and r=0; G1=Sp(2n, Zpk) if and only if lr; G2=(GL(m -1, Zpk)?Zpk(m-1))?Zpk(m) if and only if r=k; G2=GL(m, Zpk)?Zpk(m) if and only if r=0. (iii) AutG' G/AutG/ζG,ζG/G'GG1×G3, where G1 is defined in (ii); GL(m-1, Zpk)?Zpk(m-1)G3 ≤ GL(m, Zpk). In particular, G3=GL(m -1, Zpk)?Zpk(m-1) if and only if r=k; G3=GL(m, Zpk) if and only if r=0. (iv) AutG/ζG,ζG/G'G≌AutG/ζG,ζGG ? Zpk(m). If m=0, then AutG/ζG,ζGG=Inn G≌Zpk(2n); If m > 0, then AutG/ζG,ζGG≌Zpk(2nm)×Zpk-r(2n), and AutG/ζG,ζGG/Inn G≌Zpk(2n(m-1))×ZZpk-r(2n).

  • Xue Qi WANG
    Acta Mathematica Sinica. 2021, 37(6): 941-956. https://doi.org/10.1007/s10114-021-0194-z
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    In this article, we classify 1-connected 8-dimensional Poincaré complexes, topological manifolds and smooth manifolds whose integral homology groups are isomorphic to those of S3×S5. A topic related to a paper of Escher and Ziller is also discussed.

  • Li Nan ZHONG, Jian Guo HONG, Hao ZHAO
    Acta Mathematica Sinica. 2021, 37(6): 957-970. https://doi.org/10.1007/s10114-021-0001-x
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    In this paper, we determine some nontrivial secondary Adams differentials on the fourth line ExtA4,* (Z/p, Z/p) of the classical Adams spectral sequence. Specially, among these differentials, two of them are obtained via the matrix Massey products.

  • Yan Yan CUI, Yong Hong XIE, He Ju YANG, Yu Ying QIAO
    Acta Mathematica Sinica. 2021, 37(6): 971-991. https://doi.org/10.1007/s10114-021-9380-2
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    This paper is mainly about holomorphic mappings associated with conic regions which are closely connected with k-ST(α). We introduce new subclasses of starlike (spirallike) functions, namely, Scp(k, α) (Scp(k, α, β)), and discuss their coefficient estimates and the Fekete-Szegö-Goluzin's problem. Then we generalize Scp(k, α, β) on the unit ball Bn in Cn, that is, k-conic spirallike mappings of type β and order α. We obtain the growth, covering and distortion theorems of the generalized mappings. Besides that, we construct k-conic spirallike mappings of type β and order α on Bn through Sc(k, α, β) by the generalized Roper-Suffridge extension operators.

  • Lin SUN
    Acta Mathematica Sinica. 2021, 37(6): 992-1004. https://doi.org/10.1007/s10114-021-9335-7
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    A proper vertex coloring of a graph is acyclic if every cycle uses at least three colors. A graph G is acyclically k-choosable if for any list assignment L={L(v):vV (G)} with|L(v)| ≥ k for all vV (G), there exists a proper acyclic vertex coloring φ of G such that φ(v) ∈ L(v) for all vV (G). In this paper, we prove that if G is a planar graph and contains no 5-cycles and no adjacent 4-cycles, then G is acyclically 6-choosable.