中国科学院数学与系统科学研究院期刊网

15 November 2021, Volume 64 Issue 6
    

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  • Xiao Ping XU, Yan Yue SHI
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 881-894. https://doi.org/10.12386/A2021sxxb0074
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    We mainly study the robust stability for linear time-varying systems within the framework of nest algebra. We consider the robust stability when the system and controller are subject to independent uncertainties measured by the gap metric, and a sufficient condition is obtained by using the trigonometric structure of the graphs about the plant and the controller. Furthermore, we also obtain some sufficient conditions for the simultaneously robust stability of several linear time-varying systems. The numerical example shows that our conclusion is effective.

  • Ying ZHANG, Cong Ming PENG
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 895-908. https://doi.org/10.12386/A2021sxxb0075
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    In this paper, we consider the periodic Cauchy problem of an integrable two-component Camassa-Holm system, which can be regarded as a two-component extension of the modified Camassa-Holm equation. First, the periodic peakons are obtained in explicit formulas. Then the precise blow-up scenarios of strong solutions and several conditions on the initial data that produce blow-up of the induced solutions are described in detail.

  • Hong Yan XU, Lian Zhong YANG
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 909-932. https://doi.org/10.12386/A2021sxxb0076
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    By making use of the Nevanlinna theory and difference Nevanlinna theory of several complex variables, we investigate several Fermat type systems of partial differential difference equations, and obtain a series of results about the existence and the forms of entire solutions of such systems, which are some improvements and generalization of the previous results given by Cao, Gao, Liu et al. We also give some examples to show that there exists significant differences in the forms of transcendental entire solutions with finite order of the systems of the equations with between several complex variables and single complex variable.

  • Yue Hu WANG, Cong Jun ZHANG
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 933-946. https://doi.org/10.12386/A2021sxxb0077
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    We introduce a class of order-theoretic approaches for studying the fractional differential variational inequalities. By using the order-theoretic fixed point the-orems, we prove the existence of maximal solution and minimal solution to fractional differential variational inequalities on Hilbert lattices, and obtain some new results. Our order-theoretic approaches adopted for this kind of problems are fundamentally different from the recent literatures, in which the main tools are the topological fixed point theorems and discrete approximation methods. These order-theoretic methods can effectively weaken the continuity of the involved mappings.

  • Yi YU Jian, Cai SUN
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 947-958. https://doi.org/10.12386/A2021sxxb0078
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    We mainly determine the compatible left-symmetric algebra structures on the deformed bms3 algebra with some natural grading conditions by classified the compatible left-symmetric algebra structures on the deformed bms3 algebra.

  • Li Na LIU, Li Ming TANG
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 959-966. https://doi.org/10.12386/A2021sxxb0079
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    In this paper, using the minimal faithful representation of Qn, we characterize some subgroups of automorphism groups of Qn, including inner automorphism groups, central automorphism groups, involution automorphism groups and outer automorphism groups.

  • Xin Li ZHANG, Da Xiong PIAO
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 967-978. https://doi.org/10.12386/A2021sxxb0080
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    By using Moser's twist theorem, under some smoothness conditions, we prove the existence of infinitely many invariant tori and so the Lagrange stability for the sublinear asymmetric Duffing equations x"+a(x+)1/3-b(x-)1/3+φ(x)=p(t), where the perturbation term φ(x) is bounded, while the forced term p(t) is periodic in t.

  • Yong Qin XIE, Jiang Wei ZHANG, Chuang Xia HUANG
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 979-990. https://doi.org/10.12386/A2021sxxb0081
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    In this paper, the method (or technique) of bi-spaces contractive semigroup method(see Theorem 2.10) is presented in a general setting as an alternative approach to the study the asymptotic behavior of nonlinear evolutionary equation. As an application, we consider reaction-diffusion equations with fading memory, and prove the asymptotic compactness of the semigroup on H01(Ω)×Lμ2(R; H01(Ω)) with initial data in L2(Ω)×Lμ2(R; H01(Ω)). Thus the bi-spaces global attractor A is confirmed. Furthermore, by using the new decomposition technique, we demonstrate the asymptotic regularity of the solution to obtain the contractive function. It is noteworthy that the nonlinearity f satisfies the polynomial growth of arbitrary order and bi-spaces global attractor AD(ALμ2(R; D(A)).

  • Sheng Yu GUAN, Chuan Fu YANG, Murat SAT
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 991-998. https://doi.org/10.12386/A2021sxxb0082
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    We provide a method for solving inverse Sturm-Liouville problem on the double loop graph. We deduce asymptotic of eigenvalues for double loop graph with the standard matching condition at the contact vertex, and then reconstruct the unknown potential by the Riesz basis constructed from the subspectrum, and finally present the uniqueness theorem and reconsbruction algorithm.

  • Shi You SUI, Wei Jiao XU
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 999-1004. https://doi.org/10.12386/A2021sxxb0083
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    We consider the number of limit cycles bifurcating from the center of quadratic reversible system (r6) with non-Morsean point under quadratic perturbations. It is proved that the sharper bound is 2, which verifies the conjecture given by[Iliev I. D., Perturbations of quadratic centers, Bull. Sci. Math., 1998, 122:107-161].
  • Jin Bao JIAN, Peng Jie LIU, Xian Zhen JIANG
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 1005-1026. https://doi.org/10.12386/A2021sxxb0084
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    The researches on the alternating direction method of multiplier method (ADMM) for solving two-block optimization have been gradually mature and perfect. However, the studies on ADMM for solving nonconvex multi-block optimization are relatively few. In this paper, we first propose a partially symmetric regularized ADMM for nonconvex multi-block optimization with linear constraints. Second, under appropriate assumptions including the region of the two parameters in the updating formulas for the multiplier, the global convergence of the proposed method is proved. Third, when the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz (KL) property, the strong convergence of the method is proved. Furthermore, when the associated KL property function has a special structure, the sublinear and linear convergence rate of the method are obtained. Finally, some preliminary numerical experiments are carried out, and this shows that the proposed method is numerically effective.

  • Xin Yue CHENG, Yan Nian GONG
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 1027-1036. https://doi.org/10.12386/A2021sxxb0085
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    We study the Randers metrics of weakly isotropic scalar curvature. We prove that a Randers metric of weakly isotropic scalar curvature must be of isotropic S-curvature. Further, we prove that a conformally flat Randers metric of weakly isotropic scalar curvature is either Minkowskian or Riemannian.
  • Mei FU, Hao Dong HU
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 1037-1042. https://doi.org/10.12386/A2021sxxb0086
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    We translate a recurrence relation into a generating function and expand the product of two bivariate Eulerian polynomials in terms of the complete homogeneous symmetric functions.

  • Ting LUO, Chuan Xi ZHU
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 1043-1054. https://doi.org/10.12386/A2021sxxb0087
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    In this paper, the new concept of tripled coincidence point and weakly compatible for a pair of mappings F:X×X×XX, g:XX in cone bmetric spaces are introduced. Under not necessary normal conditions of cone, some tripled coincidence for contractive mappings and tripled common fixed point problems of weakly compatible mappings are studied. The obtained results generalize some coupled common fixed point theorems in corresponding literatures. Finally, an example is given to illustrate our main results.

  • Tao XU, Xiao Min DONG, He Guo LIU
    Acta Mathematica Sinica, Chinese Series. 2021, 64(6): 1055-1060. https://doi.org/10.12386/A2021sxxb0088
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    An automorphism α of a group G is called class preserving if α(g) ∈ gG for all gG, where gG denotes the conjugacy class of g in G. These automorphisms form a normal subgroup of the automorphism group Aut(G) of G which we denote by Autc(G). In this paper, an upper bound of the order of Autc(G) of an extension of a finite cyclic group by a finite nilpotent group is determined. Meanwhile, an upper bound of the order of Autc(G) of an extension of a finite p-group by a finite nilpotent group is given.