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A Note on Weak Open cs-images of Metric Spaces

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Chinese Quarterly Journal of Mathematics 2005年第3期20卷 265-268页

作者： li ke-dian liANG Hong-liang Department of Mathematics and Information Science Zhangzhou Normal University Zhangzhou 363000 China Department of Mathematics Shangqiu Teacher＇s College Shangqiu 476000 China

In this paper, we prove that a space with a compact Countable weak base if and only if it is a weak open cs-image of a metric space.

关键词： Metric spaces weak bases cs-mappings

cs＊-regular Families and Metrization Theorems

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Chinese Quarterly Journal of Mathematics 2009年第4期24卷 609-613页

作者： li ke-dian XU Hua-wei Department of Mathematics and Information Science Zhangzhou Normal University Zhangzhou363000 China Department of Mathematics Shangqiu Teacher＇s College Shangqiu 476000 China

In this paper, we proved that a sequential space has a cs＊-regular cs＊-network （or a cs＊-regular weak base） is metrizable, which generalized related results in [6], [12] and [14].

关键词： cs*-regular families network weak base metrizable spaces

On Spaces with a Locally Countable sn-network

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Chinese Quarterly Journal of Mathematics 2010年第4期25卷 495-499页

作者： KANG Bi-fang YAN Ming-gang li ke-dian Department of Mathematics and Informantion Science Zhangzhou Normal UniversityZhangzhou 363000China Adult Education College Shangqiu Vocational and Technical CollegeShangqiu 476000China

In this paper,spaces with a locally countable sn-network are *** is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable *** its application,almost-open and closed mappings（or finite-to-one and closed mapping） preserve locally countable sn-networks,and a perfect preimage theorem on spaces with a locally countable sn-network is established.

关键词： locally countable family sn-network k-network cs-network

The Completeness of Cone Metric Spaces

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Chinese Quarterly Journal of Mathematics 2013年第4期28卷 565-572页

作者： li ke-dian Department of Mathematics and Information Science Zhangzhou Normal University Zhangzhou 363000China

Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection propert... 详细信息

关键词： compactness completeness cauchy sequence cone metric space

Interval-Valued Intuitionistic Fuzzy-Rough Sets

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浙江海洋学院学报（自然科学版） 2010年第5期29卷 496-506页

作者： WU Yan-hua li ke-dian Department of Mathematics Physics and Information Science Zhangzhou Normal University Zhangzhou Fujian 363000 P. R. China

This paper combines interval-valued intuitionistic fuzzy sets and rough *** studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets mode... 详细信息

关键词： Interval-valued intuitionistic fuzzy sets Interval-valued intuitionistic fuzzy rough sets Hamming distance Approximation roughness

Digital generation of super-Gaussian perfect vortex beams via wavefront shaping with globally adaptive feedback

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High Power Laser Science and Engineering 2024年第1期12卷 42-51页

作者： Rui Ma ke Hai Luo Jing Song He Wei li Zhang dian Yuan Fan Anderson S.L.Gomes Jun liu International Collaborative Laboratory of 2D Materials for Optoelectronics Science and Technology of Ministry of Education Institute of Microscale OptoelectronicsShenzhen UniversityShenzhenChina Institute for Advanced Study Shenzhen UniversityShenzhenChina Fiber Optics Research Centre School of Information and Communication EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina Departamento de Física Universidade Federal de PernambucoRecife-PEBrazil

High-intensity vortex beams with tunable topological charges and low coherence are highly demanded in applications such as inertial confinement fusion(ICF) and optical communication. However, traditional optical vortices featuring nonuniform intensity distributions are dramatically restricted in application scenarios that require a high-intensity vortex beam owing to their ineffective amplification resulting from the intensity-dependent nonlinear effect. Here, a low-coherence perfect vortex beam(PVB) with a topological charge as high as 140 is realized based on the super-pixel wavefront-shaping technique. More importantly, a globally adaptive feedback algorithm(GAFA) is proposed to efficiently suppress the original intensity fluctuation and achieve a flat-top PVB with dramatically reduced beam speckle contrast. The GAFA-based flat-top PVB generation method can pave the way for high-intensity vortex beam generation,which is crucial for potential applications in ICF, laser processing, optical communication and optical trapping.

关键词： digital micromirror device flat-top beam orbital angular momentum perfect vortex beam random fiber laser

The Sequence-covering Compact Images of Paracompact Locally Compact Spaces

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Northeastern Mathematical Journal 2000年第4期16卷 463-468页

作者：李进金李克典 Zhangzhou Teachers'College Shangqiu Teachers'College

This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally... 详细信息

关键词： sequence covering mapping compact covering mapping compact mapping quotient mapping paracompact locally compact space cs cover sn cover cs* cover

Global Stability of a Viral Infection Model with Defectively Infected Cells and Latent Age

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Chinese Annals of Mathematics,Series B 2024年第4期45卷 555-572页

作者： Jianquan li Yuming CHEN Peijun ZHANG dian ZHANG School of Computer Science Xijing University Department of Mathematics Wilfrid Laurier University Xi'an key Laboratory of Human-Machine Integration and Control Technology for Intelligent Rehabilitation Xijing University Equal contributor.Department of Immunology Xi'an Medical University

The authors propose and analyze a viral infection model with defectively infected cells and age of the latently infected cells. The existence of steady states is determined by the basic reproduction number of virus. With the Lyapunov's direct method, they establish a threshold dynamics of the model with the basic reproduction number of virus as the threshold parameter. To achieve it, a novel procedure is proposed. Its novelties are two-folded. On one hand, the coefficients involved in the specific forms of the used Lyapunov functionals for the two feasible steady states are determined by the same set of inequalities. On the other hand, for the infection steady state, a new approach is proposed to check whether the derivative of the Lyapunov functional candidate along solutions is negative(semi-)definite or not. This procedure not only simplifies the analysis but also exhibits the relationship between the two Lyapunov functionals for the two feasible steady states. Moreover, the procedure is expected to be applicable for other similar models.

关键词： Age structure Basic reproduction number Equilibrium Global stability Lyapunov direct method Viral infection model

Strong Edge Coloring of Outerplane Graphs with Independent Crossings

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 467-477页

作者： ke-Jie li Xin ZHANG School of Mathematics and Statistics Xidian UniversityXi’an 710071China

The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of the same *** outerplane graph with independent crossings is a graph embedded in the plane in such a way that all vertices are on the outer face and two pairs of crossing edges share no common end *** is proved that every outerplane graph with independent crossings and maximum degreeΔhas strong chromatic index at most 4Δ-6 if Δ≥4,and at most 8 ifΔ≤*** bounds are sharp.

关键词： outer-1-planar graph IC-planar graph strong edge coloring crossing