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A new construction for involutions over finite fields

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Frontiers of Mathematics in China 2022年第4期17卷 553-565页

作者： Zhaohui ZHANG Qunying LIAO College of Mathematical Science Sichuan Normal UniversityChengdu610066China

In 2020,Niu et al.[Cryptogr.Commun.,2020,12(2):165–185]studied the fixed points of involutions over the finite field with q-elements.This paper further discusses the relationship between the fixed points set and the non-fixed points set of two involutions f_(1)(x)and f_(2)(x)over the finite field F_(q),and then obtains a necessary and sufficient condition for that the composite function f_(1)■f_(2)(x)is also an involution over F_(q).In particular,a special class of involutions over some finite fields is determined completely.

关键词： Permutation polynomial involution fixed point non-fixed point

On Constacyclic Codes over Zp1p2…pt

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Chinese Annals of Mathematics,Series B 2019年第4期40卷 555-566页

作者： Derong XIE Qunying LIAO College of Mathematical Science Sichuan Normal University

Let t ≥ 2 be an integer, and let p1, ···, ptbe distinct primes. By using algebraic properties, the present paper gives a sufficient and necessary condition for the existence of non-trivial self-orthogonal cyclic codes over the ring Zp1p2···ptand the corresponding explicit enumerating formula. And it proves that there does not exist any self-dual cyclic code over Zp1p2···pt.

关键词： Ideal Isomorphism Constacyclic code Self-orthogonal code Self-orthogonal cyclic code

Differential Operator Approach to■quantum Groups and Their Oscillator Representations

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1360-1374页

作者： Zhao Bing FAN Ji Cheng GENG Shao Long HAN College of Mathematical Science Harbin Engineering UniversityHarbin 150001P.R.China

For a quasi-split Satake diagram,we define a modified q-Weyl algebra,and show that there is an algebra homomorphism between it and the corresponding■quantum group.In other words,we provide a differential operator approach to■quantum groups.Meanwhile,the oscillator representations of■quantum groups are obtained.The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.

关键词： ■quantum group differential operator oscillator representation crystal basis

Incipient fault diagnosis on active disturbance rejection control

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science China(Information sciences) 2022年第9期65卷 301-302页

作者： Darong HUANG Xingxing HUA Bo MI Yang LIU Zhenyuan ZHANG college of Information science and Engineering Chongqing Jiaotong University college of mathematical and Statistics Chongqing Jiaotong University

Dear editor,The incipient fault diagnosis method has received great attention in recent decades owing to the increasing demand for reliability and safety in industrial processes [1, 2]. A controller of active disturbance rejection control (ADRC)can effectively separate the incipient fault from the disturbance. Therefore, studying the incipient fault estimation has become a necessarily imminent research topic in this new frontier.

关键词： Active disturbance rejection control Fault diagnosis Disturbance abrupt incipient fault soft incipient fault

A Collaboration Network Model with Multiple Evolving Factors

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Chinese Physics Letters 2016年第4期33卷 159-162页

作者：徐秀莲刘春平何大韧 college of Physics science and Technology Yangzhou University College of Mathematical Science Yangzhou University

To describe the empirical data of collaboration networks, several evolving mechanisms have been proposed, which usually introduce different dynamics factors controlling the network growth. These models can reasonably reproduce the empirical degree distributions for a number of we11-studied real-world collaboration networks. On the basis of the previous studies, in this work we propose a collaboration network model in which the network growth is simultaneously controlled by three factors, including partial preferential attachment, partial random attachment and network growth speed. By using a rate equation method, we obtain an analytical formula for the act degree distribution. We discuss the dependence of the act degree distribution on these different dynamics factors. By fitting to the empirical data of two typical collaboration networks, we can extract the respective contributions of these dynamics factors to the evolution of each networks.

关键词： of de on in A Collaboration Network Model with Multiple Evolving Factors that with from for is been RDP

Complete moment convergence for ND random variables under the sub-linear expectations

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Applied Mathematics(A Journal of Chinese Universities) 2023年第3期38卷 444-457页

作者： FENG Feng-xiang WANG Ding-cheng WU Qun-ying college of science Guilin University of TechnologyGuilin 541004China School of mathematical science University of Electronic Science and TechnologyChengdu 611731China

In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of r... 详细信息

关键词： complete convergence complete moment convergence ND random variables sub-linear expectation

New application to Riccati equation

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Chinese Physics B 2010年第8期19卷 88-95页

作者：套格图桑斯仁道尔吉李姝敏 College of Mathematical Science Inner Mongolia Normal University College of Mathematical Science Bao Tou Teachers' College

To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamotc-Sivashinsky equation and the set of （2＋1）-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.

关键词： Riccati equation formula of nonlinear superposition nonlinear evolution equation exact solution

Infinite Sequence Soliton-Like Exact Solutions of (2 + 1)-Dimensional Breaking Soliton Equation

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Communications in Theoretical Physics 2011年第6期55卷 949-954页

作者： Taogetusang Sirendaoerji 李姝敏 College of Mathematical Science Inner Mongolia Normal University College of Mathematical Science Bao Tou Teachers' College

寻求新无限的顺序象 soliton 一样非线性的进化方程的准确答案(旧姓) 由在辅助方程方法上开发建设和机械化的二个特征，秒种椭圆形的方程高度被学习并且新类型答案和 B ? cklund 转变被获得。( 2+1 )然后，维的碎 soliton 方程作为一个... 详细信息

寻求新无限的顺序象 soliton 一样非线性的进化方程的准确答案(旧姓) 由在辅助方程方法上开发建设和机械化的二个特征，秒种椭圆形的方程高度被学习并且新类型答案和 B ? cklund 转变被获得。( 2+1 )然后，维的碎 soliton 方程作为一个例子和它的无限的顺序被选象soliton一样准确解决方案在符号的计算系统 Mathematica 的帮助下被构造，它包括无限的顺序 Jacobi 椭圆形的类型的光滑的象soliton一样解决方案， Jacobi 椭圆形的类型的无限的顺序协议 soliton 解决方案和指数的函数类型和三角形的功能的无限的顺序山峰 soliton 解决方案打字。

关键词：破裂孤子方程无限序列精确解 Mathematica Backlund变换 Jacobi 非线性演化方程符号计算系统

Rogue waves of the sixth-order nonlinear Schr?dinger equation on a periodic background

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Communications in Theoretical Physics 2022年第5期74卷 5-13页

作者： Wei Shi Zhaqilao college of Mathematics science Inner Mongolia Normal University Center for Applied mathematical science

In this paper, we construct the rogue wave solutions of the sixth-order nonlinear Schr?dinger equation on a background of Jacobian elliptic functions dn and cn by means of the nonlinearization of a spectral problem and Darboux transformation approach. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.

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