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2021年 第36卷 第4期    刊出日期：2021-12-30

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在 Stein 流形中有界域的解析簇上积分表示及其应用

陈叔瑾

2021, 36(4):  331-355.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.001

摘要 ( 88 )   PDF (432KB) ( 64 )  

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In this paper, we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds (the two types bounded domains in [3] are regarded as its special cases). Secondly we get the integral formulas of the solution of \overline \partial-equationequation. And we use a new and unique method to give a uniform estimate of the solution of \overline \partial-equation, which is different from Henkin’s method.

一种求解未知噪音水平的低秩矩阵恢复问题有效算法

靳正芬, 王朵, 尚有林, 律金曼

2021, 36(4):  356-368.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.002

摘要 ( 110 )   PDF (363KB) ( 115 )  

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Recovering an unknown high dimensional low rank matrix from a small set of entries is widely spread in the fields of machine learning, system identification and image restoration, etc. In many practical applications, the few observations are always corrupted by noise and the noise level is also unknown. A novel model with nuclear norm and square root type estimator has been proposed, which does not rely on the knowledge or on an estimation of the standard deviation of the noise. In this paper, we firstly reformulate the problem to an equivalent variable separated form by introducing an auxiliary variable. Then we propose an efficient alternating direction method of multipliers(ADMM) for solving it. Both of resulting subproblems admit an explicit solution, which makes our algorithm have a cheap computing. Finally, the numerical results show the benefits of the model and the efficiency of the proposed method.

一个三阶 m 点边值问题的三个正解

宋雪, 杨赟瑞, 杨璐

2021, 36(4):  369-375.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.003

摘要 ( 96 )   PDF (335KB) ( 71 )  

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An existence criterion of triple positive solutions to a third-order m-point boundary value problem is established by Avery-Peterson fixed point theorem. At the same time, a corresponding example is given to illustrate the result.

涉及整函数差分的唯一性研究

邱仕林, 刘丹

2021, 36(4):  376-389.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.004

摘要 ( 71 )   PDF (365KB) ( 61 )  

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In this paper, we study the uniqueness of entire functions and prove the following theorem. Let f be a transcendental entire function of finite order. Then there exists at most one positive integer k, such that  f ( z )∆ ^k _c f ( z ) −R ( z ) has finitely many zeros, where R ( z ) is a non-vanishing rational function and c is a nonzero complex number. Our result is an improvement of the theorem given by Andasmas and Latreuch [1].

某些周期函数类的 N 宽度

王家玮, 吴嘎日迪

2021, 36(4):  390-394.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.005

摘要 ( 60 )   PDF (273KB) ( 53 )  

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This paper considers the Kolmogorov width, the Gelfand width and the Linear width of the periodic smooth functions with boundary conditions in Orlicz space. Further, the relationships among these three types of width are obtained.

Forchheimer 方程组的 Phragmén-Lindelöf 二择一结果

陈雪姣, 李远飞

2021, 36(4):  395-404.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.006

摘要 ( 87 )   PDF (307KB) ( 26 )  

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This paper investigates the spatial behavior of the solutions of the Forchheimer equations in a semi-infinite cylinder. Using the energy estimation method and the differential inequality technology, the differential inequality about the solution is derived. By solving this differential inequality, it is proved that the solutions grow polynomially or decay exponentially with spatial variables.

关于双曲三角形间的拟共形映射

赵蕾

2021, 36(4):  405-414.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.007

摘要 ( 63 )   PDF (372KB) ( 69 )  

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Quasiconformal mappings between hyperbolic triangles are considered. We give an explicit estimate of the dilation of the quasiconformal mappings, which generalizes Bishop’s results.


基本 C*-代数与 Haagerup 张量积

贺维骄

2021, 36(4):  415-418.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.008

摘要 ( 78 )   PDF (282KB) ( 47 )  

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 In this note, we give a new characterization of elementary C*-algebras in terms of completely compact maps and Haagerup tensor products.


利用特征结构配置方法修正质量和刚度矩阵

刘丽娜, 袁钰莹, 袁永新

2021, 36(4):  419-429.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.009

摘要 ( 57 )   PDF (285KB) ( 74 )  

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A novel numerical method is presented to update mass and stiffness matrices simultaneously with measured vibration data by means of the combined acceleration and displacement output feedback. By the method, the required displacement and acceleration output feedback gain matrices are determined, and thus the optimal approximation mass matrix and stiffness matrix which satisfy the required orthogonality relation and eigenvalue equation are found. The proposed method is computationally efficient and the updated mass and stiffness matrices are also symmetric and have the compact expressions. The numerical example shows that the proposed method is reliable and attractive.


环 F_p+vF_p+v²F_p 上常循环码的深度分布

李建豪, 吴化璋

2021, 36(4):  430-440.  doi:10.13371/j.cnki.chin.q.j.m.2021.04.010

摘要 ( 73 )   PDF (386KB) ( 70 )  

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 In this paper, we studied the depth spectrum and the depth distribution of constacyclic codes over the non-chain ring R = F_p+vF_p+v²F_p, where v³=v. By decomposing the linear codes C over R into the linear codes over the finite field Fp, three corresponding constacyclic codes C₁, C₂, C₃ over Fp were obtained. Furthermore, considering the depth spectrum of constacyclic codes over the finite filed Fp, and the relationship between constacyclic codes C₁, C₂, C₃ and C, the depth spectrum and the depth distribution of constacyclic codes over R were discussed.