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    Properties and Applications of the Core Inverse of an Even-Order Tensor
    Hongxing Wang,Xiaoyan Zhang
    Acta mathematica scientia,Series A    2021, 41 (1): 1-14.  
    Abstract85)   HTML6)    PDF(pc) (326KB)(103)       Save

    Tensor generalized inverse is one of the important contents of tensor theory research. In this paper, based on the research of tensor generalized inverse in recent years, we obtain some properties of the core inverse of tensor with the Einstein product, a tensor partial ordering based on the core inverse and the least-squares solution of $ {{\cal A}} {*}{{\cal X}}={{\cal B}}$ under condition ${{\cal X}}\in{\Bbb {\cal R}}({{\cal A}}) $.

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    Inverse Spectral Problem for the Diffusion Operator from a Particular Set of Eigenvalues
    Qing Cao,Xiaochuan Xu
    Acta mathematica scientia,Series A    2021, 41 (3): 577-582.  
    Abstract77)   HTML13)    PDF(pc) (316KB)(108)       Save

    In this paper, we study the inverse spectral problem for the diffusion operator on a finite interval with the Robin-Dirichlet boundary conditions, and prove that a particular set of eigenvalues can uniquely determine the diffusion operator, and give the reconstruction algorithm.

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    A Partial Inverse Problem for the Sturm-Liouville Operator on Quantum Graphs with a Loop
    Shengyu Guan,Dongjie Wu,Sat Murat,Chuanfu Yang
    Acta mathematica scientia,Series A    2021, 41 (2): 289-295.  
    Abstract52)   HTML2)    PDF(pc) (278KB)(56)       Save

    This deals with the Sturm-Liouville operator on the quantum graphs with a loop. Given the potential on a part of edges, we try to recover the remaining potential from the subspectrum. The uniqueness theorem and a constructive algorithm for the solution of this partial inverse problem are provided.

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    Behaviour of Meromorphic Solutions of Complex Functional-Differential Equations
    Manli Liu,Lingyun Gao
    Acta mathematica scientia,Series A    2020, 40 (5): 1121-1131.  
    Abstract51)   HTML1)    PDF(pc) (359KB)(72)       Save

    The aim of this paper is twofold. Firstly, we consider the existence of solutions to a type of complex functional-differential equations

    (w')nw(n)=awn+1(g)+bw+d

    in complex variables. We obtain g is linear when w is a transcendental meromorphic function and a≠0, b, d are constants. In addition, due to the different properties between equations and system of equations, it is meaningful to research systems of equations, this paper is also concerned with a type of system of functional equations, properties of meromorphic solutions are obtained under some proper conditions. Examples are constructed to show that our results are accurate.

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    Construction of the Planar Bodies with Constant Width
    Deyan Zhang,Botao Duan
    Acta mathematica scientia,Series A    2021, 41 (1): 15-28.  
    Abstract50)   HTML2)    PDF(pc) (490KB)(84)       Save

    Firstly, a class of planar curves "lever wheel" and their arm functions are defined, and the parameter representation of the lever wheel is established in this paper. Secondly, it is shown that the lever wheel is an equivalent characterization of the constant width curve. Finally, it is proven that the Reuleaux polygons are a class of lever wheels with piecewise constant arm functions, and Reuleaux polygons with even edges are constructed.

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    Boundness of Riesz Transforms on Hardy Spaces Associated with Schrödinger Operators on the Heisenberg Group
    Xuan Chen
    Acta mathematica scientia,Series A    2021, 41 (1): 46-62.  
    Abstract39)   HTML5)    PDF(pc) (359KB)(54)       Save

    Let $L=-\Delta_{{\Bbb H}^{n}}+V $ be a Schrödinger operator on the Heisenberg group ${\Bbb H}^{n} $, where $V $ is a nonnegative potential belonging to the reverse Hölder class. By the molecular decomposition of the Hardy space $ H_{L}^{p}({\Bbb H}^{n})$, we obtain the $ H^p_L$-boundedness of the Riesz transform associated with $L $.

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    Meromorphic Solutions of Finite Order to the Equation $f^{n}+f^{m}(z+c)=e^{Az+B}$
    Minfeng Chen,Zongsheng Gao,Zhibo Huang
    Acta mathematica scientia,Series A    2021, 41 (4): 913-920.  
    Abstract39)   HTML4)    PDF(pc) (303KB)(38)       Save

    In this paper, we study the meromorphic solutions of finite order to the difference equations $f^{n}(z)+f^{m}(z+c)=e^{Az+B}$ $(c\neq 0)$ over the complex plane ${\mathbb C}$ for integers $n, m$, and $A, B, c\in {\mathbb C}$.

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    The Problem of the Radii of a Harmonic Linear Differential Operator
    Zhenyong Hu,Qihan Wang,Boyong Long
    Acta mathematica scientia,Series A    2020, 40 (5): 1163-1174.  
    Abstract36)   HTML0)    PDF(pc) (309KB)(28)       Save

    For harmonic mappings $ f_{i}(z)=h_{i}(z)+\overline{g_{i}(z)}$($ i=1, 2$) defined in the unit disk satisfying the given coefficient conditions, we consider the radii of full convexity and full starlikeness of order $\alpha $ for the convex combination $ (1-t)L^{\epsilon}_{f_{1}}+tL^{\epsilon}_{f_{2}}$, where $ L^{\epsilon}_{f_{i}}=z\frac{\partial f_{i}}{\partial z}-\epsilon\overline{z}\frac{\partial f_{i}}{\partial\overline{z}}(|\epsilon|=1)$ denotes the differential operator of $ f_{i}$. In addition, we obtain the radii of fully convex and full starlikeness of order $\alpha $ for convolution of harmonic mappings under the differential operator. All results are sharp.

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    Stabilities of K- Frames and Tight K- Frames Under the Operator Perturbation
    Dandan Du,Yucan Zhu
    Acta mathematica scientia,Series A    2021, 41 (1): 29-38.  
    Abstract34)   HTML1)    PDF(pc) (311KB)(43)       Save

    In this paper, we discuss the stabilities of K-frames and tight K-frames under the operator perturbation. Firstly, we provide an equivalent characterization of the operator perturbation for a K-frame by using a bounded linear operator $T $ from ${{\cal H}_1} $ to ${{\cal H}_2} $. We also give a simple way to construct new K-frames from two existing Bessel sequences. Meanwhile, we make a discussion on the construction for K-frames from given ones. In the end, we obtain a necessary and sufficient condition to generate tight K-frames from two old Bessel sequences. Our results generalize and improve the remarkable results which had been obtained by Casazza and Christensen.

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    Global Existence and Blowup Phenomena for a Semilinear Wave Equation with Time-Dependent Damping and Mass in Exponentially Weighted Spaces
    Changwang Xiao,Fei Guo
    Acta mathematica scientia,Series A    2020, 40 (6): 1568-1589.  
    Abstract32)   HTML3)    PDF(pc) (437KB)(26)       Save

    We consider the global small data solutions and blowup to the Cauchy problem for a semilinear wave equation with time-dependent damping and mass term as well as power nonlinearity. On one hand, if the power of the nonlinearity $p >p_F(N)=1+ \frac 2N$, it is proved that solutions with small initial data exist for all time in exponentially weighted energy spaces. On the other hand, if the power satisfies <p\leq p_F(\alpha, n)=1+\frac{2(1+\alpha)}{N(1+\alpha)-2\alpha}~(0<\alpha<1)$, for some special chosen parameters it is shown that solutions must blow up in finite time provided that the initial data satisfy some integral sign conditions.

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    The Novel (2+1)-Dimensional Supersymmetric Integrable Equations
    Fang Chen,Zeyu Sun,Minru Chen,Zhaowen Yan
    Acta mathematica scientia,Series A    2020, 40 (5): 1132-1141.  
    Abstract31)   HTML1)    PDF(pc) (294KB)(25)       Save

    Base on the super Lie algebra osp(2/2), we construct the (2+1)-dimensional supersymmetric integrable equations by means of two approaches. One of the technique is in terms of homogeneous spaces of super-Lie algebra, and in the other one, extending the dimension of the system has been used. Moreover, we derive the Bäcklund transformations for the (2+1)-dimensional supersymmetric integrable equations.

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    Approximation Properties of a New Bernstein-Bézier Operators with Parameters
    Qiulan Qi,Dandan Guo
    Acta mathematica scientia,Series A    2021, 41 (3): 583-594.  
    Abstract31)   HTML1)    PDF(pc) (309KB)(30)       Save

    In this paper, a new generalized Bernstein-Bézier type operators is constructed. The estimates of the moments of these operators are investigated. The rate of convergence in terms of modulus of continuity is given. Then, the equivalent theorem of these operators is studied.

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    The Non-Existence of Solutions of a Certain type of Nonlinear Complex Differential-Difference Equations
    Shuqing Lin,Junfan Chen
    Acta mathematica scientia,Series A    2021, 41 (1): 69-80.  
    Abstract30)   HTML2)    PDF(pc) (334KB)(47)       Save

    In this paper, we study transcendental entire solutions of a certain type of complex differential-difference equations where $P(z) $ and $Q(z) $ are non-zero polynomials, $\alpha(z) $ is polynomial, $ m$ and $n $ are positive integers, $ \eta\in{\Bbb C}\setminus\{0\}$. Several sufficient conditions on the non-existence of transcendental entire solutions of such equations are supplied.

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    Generalized Uncertainty Principle in Fock-Type Spaces
    Haigui Wu,Yuxia Liang
    Acta mathematica scientia,Series A    2020, 40 (6): 1409-1419.  
    Abstract30)   HTML0)    PDF(pc) (353KB)(76)       Save

    The unilateral weighted shift operator is used to construct a general self-adjoint operator pairs in this paper. We obtained the formula of generalized Uncertainty Principle in Fock-type spaces and presented conditions ensuring the equality. This result contains the classical Uncertainty Principle deduced from the derivation and multiplication operators, which can provide some theoretical basis for the solutions to related hot problems in quantum mechanics and other frontal subjects.

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    Existence and Uniqueness of Positive Solutions to an Unstirred Chemostat with Toxins
    Haixia Li
    Acta mathematica scientia,Series A    2020, 40 (5): 1175-1185.  
    Abstract29)   HTML0)    PDF(pc) (392KB)(39)       Save

    A food chain model in the unstirred chemostat with toxins is studied. The stability of the trivial solution and semi-trivial solution is analyzed by means of the stability theory, and a priori estimate of positive solution is given by the maximum principle and the super and sub-solution method. Then, by using the fixed point index theory, the sufficient conditions for the existence of positive solutions are achieved. Finally, the effect of the toxins on the dynamic behavior is discussed by virtue of the perturbation theory and bifurcation theory, and the stability and uniqueness of positive solutions are obtained. The results show that the species can coexist when the growth rates of the microorganisms u and v are larger in the presence of the toxins. Furthermore, if the effect of the toxins is sufficiently large, the system has unique stable positive solution when the growth rate of the microorganism v belongs to a certain range.

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    A Formal Analysis on the Large Ericksen Number Limit for the Incompressible Hyperbolic Ericksen-Leslie System of Liquid Crystals
    Feng Cheng
    Acta mathematica scientia,Series A    2021, 41 (1): 126-141.  
    Abstract28)   HTML0)    PDF(pc) (428KB)(19)       Save

    In this paper, we consider the parameterized incompressible hyperbolic Ericksen-Leslie system of liquid crystals. Formally, letting the parameter vanish, we prove that the limit system admits a local classical solution. Moreover, we formally obtained an estimate on the difference between the parameterized Ericksen-Leslie's incompressible hyperbolic liquid crystal model and the corresponding limit system, which corresponds to a formal energy estimate of the difference of the classical solutions in $L^2$ space.

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    The Boundedness of Pseudodifferential Operators on $H^p(\omega)$
    Yongming Wen,Xianming Hou
    Acta mathematica scientia,Series A    2021, 41 (2): 303-312.  
    Abstract28)   HTML4)    PDF(pc) (325KB)(27)       Save

    This paper gives the boundedness of a class of pseudodifferential operators $T_\sigma$ on weighted Hardy spaces $H^p(\omega)$, which improves the previous known results.

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    Bergman Type Operators on Logarithmic Weight General Function Spaces in Cn
    Pengcheng Tang,Si Xu,Xuejun Zhang
    Acta mathematica scientia,Series A    2020, 40 (5): 1151-1162.  
    Abstract28)   HTML0)    PDF(pc) (365KB)(24)       Save

    Let B be the unit ball in Cn. In this paper, the authors characterize the boundedness of the Bergman type operators Ta, b on the logarithmic weight general function spaces F(p, q, s, k) or from spaces A(p, q, s, k) to spaces L(p, q, s, k).

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    Approximate Controllability of Hilfer Fractional Integro-Differential Equations Using Sequence Method
    Jingyun Lv,Xiaoyuan Yang
    Acta mathematica scientia,Series A    2020, 40 (5): 1282-1294.  
    Abstract28)   HTML3)    PDF(pc) (339KB)(42)       Save

    Existing works on approximate controllability of fractional differential equations often assume that the nonlinear item is uniformly bounded and the corresponding fractional linear system is approximate controllable, which is, however, too constrained. In this paper, we omit these two assumptions and investigate the approximate controllability of Hilfer fractional integro-differential equations using sequence method.

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    Homogenization of the Oscillating Robin Mixed Boundary Value Problems
    Juan Wang,Jie Zhao
    Acta mathematica scientia,Series A    2021, 41 (1): 81-90.  
    Abstract28)   HTML3)    PDF(pc) (346KB)(20)       Save

    In this paper, we study the convergence rates of solutions for homogenization of the oscillating Robin mixed boundary value problems. The main difficulty of this work is due to the oscillating factor on the Robin boundary as well as boundary discrepancies. Thanks to the duality approach, we could handle the oscillatory integral. As a consequence, we establish the rates of convergence in $H^{1} $ and $L^{2} $, which depends on the dimension explicitly. This work may be regarded as an extension of the duality approach as well as smoothing operators for oscillating Robin mixed boundary value problems.

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