中国科学院数学与系统科学研究院期刊网

15 March 2022, Volume 38 Issue 3
    

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  • Ana María BOTERO
    Acta Mathematica Sinica. 2022, 38(3): 465-486. https://doi.org/10.1007/s10114-022-0383-4
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    In previous work of the author, a top intersection product of toric b-divisors on a smooth complete toric variety is defined. It is shown that a nef toric b-divisor corresponds to a convex set and that its top inetersection number equals the volume of this convex set. The goal of this article is to extend this result and define an intersection product of sufficiently positive toric b-classes of arbitrary codimension. For this, we extend the polytope algebra of McMullen to the so called convex-set algebra and we show that it embeds in the toric b-Chow group. In this way, the convex-set algebra can be viewed as a ring for an intersection theory for sufficiently positive toric b-classes. As an application, we show that some Hodge type inequalities are satisfied for the convex set algebra.
  • Yan Xia REN, Ren Ming SONG, Zhen Yao SUN, Jian Jie ZHAO
    Acta Mathematica Sinica. 2022, 38(3): 487-498. https://doi.org/10.1007/s10114-022-0559-y
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    This paper is a continuation of our recent paper (Electron. J. Probab., 24(141), (2019)) and is devoted to the asymptotic behavior of a class of supercritical super Ornstein-Uhlenbeck processes (Xt)t≥0 with branching mechanisms of infinite second moments. In the aforementioned paper, we proved stable central limit theorems for Xt(f) for some functions f of polynomial growth in three different regimes. However, we were not able to prove central limit theorems for Xt(f) for all functions f of polynomial growth. In this note, we show that the limiting stable random variables in the three different regimes are independent, and as a consequence, we get stable central limit theorems for Xt(f) for all functions f of polynomial growth.
  • Jin Ge YAO, Jing Bo DOU
    Acta Mathematica Sinica. 2022, 38(3): 499-509. https://doi.org/10.1007/s10114-022-0345-x
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    In this paper we classify the positive solutions of the divergent equation with Neumann boundary on the upper half space\begin{equation*} \begin{cases} -{\rm div}(t^\alpha \nabla u)=t^{\beta}f(u), &(y,t)\in\mathbb{R}^{n+1}_+,\\ \displaystyle\lim_{t \to 0^+} t^\alpha\frac{\partial u}{\partial t}=0 \end{cases}\end{equation*}by the method of moving spheres and Kelvin transformations, where $n\ge 1, \ \alpha> 0,\, \beta>-1, \ \frac{n-1}{n+1}\beta\le\alpha<\beta+2,$ and $f :(0,\infty)\rightarrow(0,\infty)$ is non-negative continuous function satisfying some conditions. This equation arises from a weighed Sobolev inequality involving divergent operator ${\rm div}(t^\alpha \nabla u)$ on the upper half space.
  • Wen Peng ZHANG, Yuan Yuan MENG
    Acta Mathematica Sinica. 2022, 38(3): 510-518. https://doi.org/10.1007/s10114-022-0541-8
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    The main purpose of this article is to study the calculating problem of the sixth power mean of the two-term exponential sums, and give an interesting calculating formula for it. At the same time, the paper also provides a new and effective method for the study of the high order power mean of the exponential sums.
  • Zobo Vincent de Paul ABLÉ, Justin FEUTO
    Acta Mathematica Sinica. 2022, 38(3): 519-546. https://doi.org/10.1007/s10114-022-0572-1
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    In this paper, carrying on with our study of the Hardy-amalgam spaces $\mathcal H^{(q,p)}$ and $\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ ($0< q,p <\infty$), we give a characterization of their dual spaces whenever $0< q\leq 1$ and $q\leq p<\infty$. Moreover, when $0< q\leq p\leq 1$, these characterizations coincide with those obtained in our earlier papers.
  • Hong Jun LIU, Xiao Jun HUANG, Yue FAN
    Acta Mathematica Sinica. 2022, 38(3): 547-559. https://doi.org/10.1007/s10114-022-1003-z
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    The aim of this paper is to investigate the relationship between relative quasisymmetry and quasimöbius in quasi-metric spaces, and show that a homeomorphism f is η-quasisymmetric relative to A if and only if it is θ-quasimöbius relative to A between two both bounded quasi-metric spaces, where A ? X and X is a quasi-metric space.
  • Juan WANG, Lian Ying MIAO, Jin Bo LI, Yun Long LIU
    Acta Mathematica Sinica. 2022, 38(3): 560-570. https://doi.org/10.1007/s10114-022-0097-7
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    An acyclic colouring of a graph G is a proper vertex colouring such that every cycle uses at least three colours. For a list assignment L = {L(v)|vV(G)}, if there exists an acyclic colouring ρ such that ρ(v) ∈ L(v) for each vV(G), then ρ is called an acyclic L-list colouring of G. If there exists an acyclic L-list colouring of G for any L with ∣L(v)∣≥ k for each vV (G), then G is called acyclically k-choosable. In this paper, we prove that every graph with maximum degree Δ ≤ 7 is acyclically 13-choosable. This upper bound is first proposed. We also make a more compact proof of the result that every graph with maximum degree Δ ≤ 3 (resp., Δ ≤ 4) is acyclically 4-choosable (resp., 5-choosable).
  • An Kang YU, Ya Juan YANG, Bao De LI, Ai Ting WANG
    Acta Mathematica Sinica. 2022, 38(3): 571-590. https://doi.org/10.1007/s10114-022-0648-y
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    In 2011, Dekel et al. developed highly geometric Hardy spaces $H^p(\Theta)$, for the full range $0< p\leq 1$, which are constructed by continuous multi-level ellipsoid cover $\Theta$ of $\mathbb{R}^n$ with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level. The authors obtain the finite atomic decomposition characterization of Hardy spaces $H^p(\Theta)$ and as an application, the authors prove that given an admissible triplet $(p,\,q,\,l)$ with $1\le q \leq \infty$, if $T$ is a sublinear operator and uniformly bounded elements of some quasi-Banach space $\mathcal{B}$ for maps all $(p,\,q,\,l)$-atoms with $q<\infty$ (or all continuous $(p,q,l)$-atoms with $q=\infty$), then $T$ uniquely extends to a bounded sublinear operator from $H^{p}(\Theta)$ to $\mathcal{B}.$ These results generalize the known results on the anisotropic Hardy spaces of Bownik et al.
  • Gui Lin JI, Chang Jian LIU, Peng Heng LI
    Acta Mathematica Sinica. 2022, 38(3): 591-611. https://doi.org/10.1007/s10114-022-0513-z
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    In this paper, the bifurcation of limit cycles for planar piecewise smooth systems is studied which is separated by a straight line. We give a new form of Abelian integrals for piecewise smooth systems which is simpler than before. In application, for piecewise quadratic system the existence of 10 limit cycles and 12 small-amplitude limit cycles is proved respectively.
  • Qi YAN, Xian An JIN
    Acta Mathematica Sinica. 2022, 38(3): 612-622. https://doi.org/10.1007/s10114-022-1031-8
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    In this article we show that any embedded graph has a checkerboard colourable twual, which is equivalent to having a bipartite twual. We also obtain that any Eulerian embedded graph has a checkerboard colourable partial Petrial, answering questions posed by Ellis-Monaghan and Moffatt [Trans. Amer. Math. Soc., 364, 1529–1569 (2012)].