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norm Equalities and Inequalities for Three Circulant Operator Matrices

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Acta Mathematica Sinica,English Series 2017年第4期33卷 571-590页

作者： Zhao Lin JIANG Yun Cheng QIAO Shu Dong WANG School of Sciences Linyi University Linyi 276005 P. R. China

In this paper, three new circulant operator matrices, scaled circulant operator matrices,diag-circulant operator matrices and retrocirculant operator matrices, are given respectively. Several norm equalities and inequalities for these operator matrices are proved. We show the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norm. Pinching type inequality is also given for weakly unitarily invariant norms. These results are closely related to the nice structure of these special operator matrices. Furthermore, some special cases and specific examples are also considered.

关键词： Operator matrix norm scaled circulant diag-circulant retrocirculant

Dual Quaternions and Dual Quaternion Vectors

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Communications on Applied Mathematics and Computation 2022年第4期4卷 1494-1508页

作者： Liqun Qi Chen Ling Hong Yan Department of Mathematics School of ScienceHangzhou Dianzi UniversityHangzhou 310018ZhejiangChina Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomKowloonHong KongChina Department of Electrical Engineering and Centre for Intelligent Multidimensional Data Analysis City University of Hong KongKowloonHong KongChina

We introduce a total order and an absolute value function for dual numbers.The absolute value function of dual numbers takes dual number values,and has properties similar to those of the absolute value function of real numbers.We define the magnitude of a dual quaternion,as a dual number.Based upon these,we extend 1-norm,co-norm,and 2-norm to dual quaternion vectors.

关键词： Dual number Absolute value function Dual quaternion Magnitude norm

Robustness of iterative learning control for a class offractional-order linear continuous-time switched systems in the sense of L^p norm

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Journal of Systems Engineering and Electronics 2019年第4期30卷 783-791页

作者： ZHANG Kejun PENG Guohua School of Natural and Applied Sciences Northwestern Polytechnical UniversityXi’an 710129China School of Math and Physical Sciences Xuzhou Institute of TechnologyXuzhou 221018China

For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the sense of L^p norm.When the systems are disturbed by bounded external noises,robustness of the PDα-type algorithm is firstly analyzed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral.Then,convergence of the algorithm is discussed for the systems without any external noise.The results demonstrate that,under some given conditions,both convergence and robustness can be guaranteed during the entire time interval.Simulations support the correctness of the theory.

关键词： fractional-order switched systems iterative learning control L^p norm

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

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IEEE/CAA Journal of Automatica Sinica 2019年第5期6卷 1116-1126页

作者： Yufang Chang Guisheng Zhai Bo Fu Lianglin Xiong the School of Electrical and Electronic Engineering Hubei University of TechnologyWuhan 430068China the Department of Mathematical Sciences Shibaura Institute of TechnologySaitama 337-8570Japan the School of Mathematics and Computer Science Yunnan Minzu UniversityKunming 650500China

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an outputdependent switching law by constructing a robust Luenberger observer for each subsystem.

关键词： Convex combination limear matrix inequalities (LMIs) norm bounded uncertainties output-dependent switching, quadratic stabilization state-dependent switching switched uncertain linear systems(SULS)

Finite Groups Whose norm Quotient Groups Have Cyclic Sylow Subgroups

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Journal of Mathematical Research with Applications 2022年第2期42卷 153-161页

作者： Songliang CHEN Yun FAN School of Mathematics and Big Data Guizhou Education University School of Mathematics and Statistics Central China Normal University

Let G be a finite group and N(G) be its norm. Then N(G) is a characteristic subgroup of G which normalizes every subgroup of G. In this paper, we will study the structure of G under one of the following conditions: 1) norm quotient group G/N(G) is cyclic; 2) all Sylow subgroups of G/N(G) are cyclic and in particular if the order of G/N(G) is a square-free number.

关键词： norm Dedekind group Hamiltonian group $\pi $-group structure of finite group Sylow subgroup

The Schwarzian Derivative of Harmonic Mappings in the Plane

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Chinese Annals of Mathematics,Series B 2020年第2期41卷 193-208页

作者： Liping NIE Zongxin YANG Institute of Mathematics and Informatics Jiangxi Normal UniversityNanchang 330022China

In this paper, the authors introduce a definition of the Schwarzian derivative of any locally univalent harmonic mapping defined on a simply connected domain in the complex plane. Using the new definition, the authors prove that any harmonic mapping f which maps the unit disk onto a convex domain has Schwarzian norm ||Sf||≤ 6. Furthermore, any locally univalent harmonic mapping f which maps the unit disk onto an arbitrary regular n-gon has Schwarzian norm||Sf||≤8/3.

关键词： Schwarzian derivative Schwarzian norm Harmonic mapping

Alternative Order Without Alternative norms?

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Fudan Journal of the Humanities and Social Sciences 2022年第2期15卷 227-246页

作者： Yong-Soo Eun Hanyang University SeoulRepublic of Korea

The Chinese government,especially under President Xi Jinping,is willing to propose an alternative to the existing US-led international order.Accordingly,new or alternative understandings of and approaches to the international order that are more finely attuned to China are increasingly sought,and it is therefore not surprising that the Chinese International Relations(IR)community is attempting to establish the conceptual or theoretical sources and normative rationales for an alternative international order by developing indigenous IR theories that reflect“Chinese characteristics”.However,whether China is able to define and actualise a“new normal”in international relations—whether,that is,it can have and exercise“normative power”—is contingent on the recognition of Chinese discourses of that alternative by other actors.A key question,then,is:if and to what extent are Chinese alternatives recognised beyond China?I address this question,with a focus on the issue of knowledge transmission and sharing in three large East Asian IR communities.More specifically,I analyse their conceptual,theoretical,and epistemological orientations.I also compare the orientations with American IR scholarship,using various forms of evidence,including the most recent Teaching,Research,and International Policy survey data.

关键词： China International order norm International relations(IR) Chinese IR Critical self-reflection

基于近似零范数稀疏恢复的迭代解法的三维重力反演（英文）

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Applied Geophysics 2018年第3期15卷 524-535页

作者：孟兆海徐学纯黄大年天津航海仪器研究所中国科学院地质与地球物理研究所中国科学院油气资源研究重点实验室北京100029 吉林大学地球科学学院吉林长春130012 吉林大学地球探测科学与技术学院吉林长春130012

重力反演是应用地球物理中一个经典的方法,可以获取地下空间的密度分布特征。本文研究了一种新的三维重力反演方法,以压缩感知中的稀疏恢复方法为基本原理。建立以零范数为约束的目标函数,采用近似零范数求解方法对目标函数进行迭代求... 详细信息

重力反演是应用地球物理中一个经典的方法,可以获取地下空间的密度分布特征。本文研究了一种新的三维重力反演方法,以压缩感知中的稀疏恢复方法为基本原理。建立以零范数为约束的目标函数,采用近似零范数求解方法对目标函数进行迭代求解。以重力正演模型为基础进行反演方法研究,建立包含深度加权函数的零范数的目标函数,采用相应的最优化数学方法进行求解,得到稀疏的反演结果。同时,为了得到具有实际地质意义的反演结果,采用惩罚函数将反演密度值约束在具有实际地球物理和地质意义范围内。采用本文提出的反演方法得到的反演目标异常源具有较为清晰的边界、深度信息和剩余密度分布信息。本文利用理论模型实验来验证反演方法效果,并将得到的反演结果与设计的理论模型对比分析说明三维反演方法的有效性和可靠性。为了进一步说明本文采用的反演方法的可靠性,将其应用到美国德克萨斯州采集的实际重力数据反演,并将反演结果与前人研究结果和该地区的测井资料进行对比分析,盐丘的深度为4.2km与测井得到深度4.4km基本上是一致的,说明研究的反演方法具有实际应用价值。

关键词： Three-dimensional gravity inversion sparse recovery approximate zero norm iterative method density constraint penalty function

Single color image super-resolution using sparse representation and color constraint

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Journal of Systems Engineering and Electronics 2020年第2期31卷 266-271页

作者： XU Zhigang MA Qiang YUAN Feixiang School of Computer and Communication Lanzhou University of TechnologyLanzhou 730050China

Color image super-resolution reconstruction based on the sparse representation model usually adopts the regularization norm(e.g.,L1 or L2).These methods have limited ability to keep image texture detail to some extent and are easy to cause the problem of blurring details and color artifacts in color reconstructed images.This paper presents a color super-resolution reconstruction method combining the L2/3 sparse regularization model with color channel constraints.The method converts the low-resolution color image from RGB to YCbCr.The L2/3 sparse regularization model is designed to reconstruct the brightness channel of the input low-resolution color image.Then the color channel-constraint method is adopted to remove artifacts of the reconstructed highresolution image.The method not only ensures the reconstruction quality of the color image details,but also improves the removal ability of color artifacts.The experimental results on natural images validate that our method has improved both subjective and objective evaluation.

关键词： color image sparse representation super-resolution L2/3 regularization norm color channel constraint