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Totally real minimal 2-spheres in quaternionic projective space

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Science China Mathematics 2005年第3期48卷 341-349页

作者： HE Yijun wang changping LMAM School of Mathematical Sciences Peking University Beijing 100871 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J, K} of complex structures on HPn satisfying U = -JI = K,JK = -KJ = /, KI = -IK = J. A surface M(?) HPn is called totally real, if at each point p ∈M the tangent plane TPM is perpendicular to I(TPM), J(TPM) and K(TPM). It is known that any surface M(?)RPn(?) HPn is totally real, where RPn (?) HPn is the standard embedding of real projective space in HPn induced by the inclusion R in H, and that there are totally real surfaces in HPn which don't come from this way. In this paper we show that any totally real minimal 2-sphere in HPn is isometric to a full minimal 2-sphere in Rp2m (?) RPn(?) HPn with 2m≤n. As a consequence we show that the Veronese sequences in KP2m (m≥1) are the only totally real minimal 2-spheres with constant curvature in the quaternionic projective space.

关键词： quaternionic projective space, totally real surfaces, minimal surfaces.

Time-like Willmore surfaces in Lorentzian 3-space

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Science China Mathematics 2006年第1期49卷 75-85页

作者： DENG Yanjuan wang changping LMAM School of Mathematical Sciences Peking University Beijing 100871 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

Let R13 be the Lorentzian 3-space with inner product (, ). Let Q3 be the conformal compactification of R13, obtained by attaching a light-cone C∞ to R13 in infinity. Then Q3 has a standard conformal Lorentzian structure with the conformal transformation group O(3,2)/{±1}. In this paper, we study local conformal invariants of time-like surfaces in Q3 and dual theorem for Willmore surfaces in Q3. Let M (?) R13 be a time-like surface. Let n be the unit normal and H the mean curvature of the surface M. For any p ∈ M we define S12(p) = {X ∈ R13 (X - c(P),X - c(p)) = 1/H(p)2} with c(p) = P+ 1/H(p)n(P) ∈ R13. Then S12 (p) is a one-sheet-hyperboloid in R3, which has the same tangent plane and mean curvature as M at the point p. We show that the family {S12(p),p ∈ M} of hyperboloid in R13 defines in general two different enveloping surfaces, one is M itself, another is denoted by M (may be degenerate), and called the associated surface of M. We show that (i) if M is a time-like Willmore surface in Q3 with non-degenerate associated surface M, then M is also a time-like Willmore surface in Q3 satisfying M = M; (ii) if M is a single point, then M is conformally equivalent to a minimal surface in R13.

关键词： Lorentzian 3-space, Willmore surfaces, conformal Gauss map, dual theorem.

Conformally flat Lorentzian hypersurfaces in R_1~4 with three distinct principal curvatures

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Science China Mathematics 2018年第5期61卷 897-916页

作者： Xiaozhen wang changping wang Zhenxiao Xie School of Mathematics and Computer Science Fujian Normal University Fujian Provincial Key Laboratory of Mathematical Analysis and Its Application Fujian Normal University Department of Mathematics China University of Mining and Technology (Beijing)

A three dimensional Lorentzian hypersurface x : M_1~3→ R_1~4 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, and this property is preserved under the conformal transformation of R_1~4. Using the projective light-cone model, for those whose shape operators have three distinct real eigenvalues, we calculate the integrability conditions by constructing a scalar conformal invariant and a canonical moving frame in this paper. Similar to the Riemannian case, these hypersurfaces can be determined by the solutions to some system of partial differential equations.

关键词： conformally flat Lorentzian hypersurfaces conformal geometry of Lorentzian space forms integrability equations

增强探测信息可观测性的主动防御滑模协同突防制导律

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导弹与航天运载技术（中英文） 2024年第2期 51-58页

作者：王昌平方峰王振亚彭冬亮谢俊伟杭州电子科技大学自动化学院杭州310018 中国运载火箭技术研究院北京100076

针对敌方来袭拦截弹制导策略未知的主动防御协同突防场景,考虑目标弹-防御弹单向和双向协同配合模式,采用滑模控制方法提出了兼顾拦截弹探测信息可观测性和防御弹反拦截精度的协同突防制导律。构建了融合空间探测构型需求和拦截成功必... 详细信息

针对敌方来袭拦截弹制导策略未知的主动防御协同突防场景,考虑目标弹-防御弹单向和双向协同配合模式,采用滑模控制方法提出了兼顾拦截弹探测信息可观测性和防御弹反拦截精度的协同突防制导律。构建了融合空间探测构型需求和拦截成功必要条件的滑模面,分别应用双幂次趋近律和带状态反馈的指数型趋近律,推导了目标弹-防御弹的单/双向协同制导律。相较于单向协同,双向协同通过引入加速度代价函数,应用最优化方法优化了协同突防制导律,目标弹通过协作机动帮助防御弹降低打击来袭拦截弹的过载需求。仿真结果表明,协同滑模突防制导律可确保目标弹和防御弹达到期望的空间探测构型,并能够精准地打击来袭拦截弹。

关键词：主动防御协同制导滑模控制可观测性

基于改进Yolov3的H型钢喷号识别系统研究

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冶金动力 2024年第3期 63-66,74页

作者：高磊徐洪汪昌平马鞍山钢铁股份有限公司长材事业部安徽马鞍山243000

随着工业生产智能化程度不断提升,智能视频识别技术被逐渐广泛应用于工业生产中。针对马钢重型H型钢生产线精整区存在的工艺复杂、物料跟踪困难问题,提出一种在矫直机后用喷码机在钢坯上喷印批号、在堆垛区域人工检查台位置安装一套字... 详细信息

随着工业生产智能化程度不断提升,智能视频识别技术被逐渐广泛应用于工业生产中。针对马钢重型H型钢生产线精整区存在的工艺复杂、物料跟踪困难问题,提出一种在矫直机后用喷码机在钢坯上喷印批号、在堆垛区域人工检查台位置安装一套字符识别装置来识别批号并实现物料跟踪的方法。根据喷印字符相对较小且没有大小形态变化的特性,改进了Yolov3模型结构,设计5个不同尺度的卷积特征图,并与残差网络中相应尺度的特征图进行融合,形成最终的特征金字塔执行字符识别任务。试验结果表明,该方法的识别准确率能达到99.5%以上,可在工程上进行应用。

关键词：重型H型钢物料跟踪字符识别 Yolov3

Conformal CMC-Surfaces in Lorentzian Space Forms

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Chinese Annals of Mathematics,Series B 2007年第3期28卷 299-310页

作者： Changxiong NIE Xiang MA changping wang Lab of Mathematics and Applied Mathematics School of Mathematical Sciences Peking University Beijing 100871 China

Let Q^3 be the common conformal compactification space of the Lorentzian space forms Q^3 1 ,S^3 1,We study the conformal geometry of space-like surfaces in Q^3 ,It is shown that any conformal CMC-surface in Q^3 must be conformally equivalent to a constant mean curvature surface in R^3 1,or,H^3 1,We also show that if x ：M→Q^3 is a space-like Willmore surface whose conformal metric g has constant curvature K,the either K = -1 and x is conformally equivalent to a minimal surface in R^3 1,or K=0 and x is conformally equivalent to the surface H^1（1/√2）×H^1（1/√2） in H^3 1.

关键词： Conformal geometry Willmore surfaces Lorentzian space

Time-Like Conformal Homogeneous Hypersurfaces with Three Distinct Principal Curvatures

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Chinese Annals of Mathematics,Series B 2020年第5期41卷 679-696页

作者： Yanbin LIN Ying LU changping wang School of Mathematics and Statistics Minnan Normal UniversityZhangzhou 363000FujianChina School of Mathematical Sciences Xiamen UniversityXiamen 361005FujianChina College of Mathematics and Informatics Fujian Normal UniversityFuzhou 350117China

A hypersurface x(M)in Lorentzian space R41 is called conformal homogeneous,if for any two points p,q on M,there exists,a conformal transformation of R41,such that(x(M))=x(M),(x(p))=x(q).In this paper,the authors give a complete classifica-tion for regular time-like conformal homogeneous hypersurfaces in R41 with three distinct principal curvatures.

关键词： Lorentzian metric Conformal metric Conformal space form Conformal homogeneous Time-like hypersurface

Wintgen ideal submanifolds with a low-dimensional integrable distribution

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Frontiers of Mathematics in China 2015年第1期10卷 111-136页

作者： Tongzhu LI Xiang MA changping wang Department of Mathematics Beijing Institute of Technology Beijing 100081 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China College of Mathematics and Computer Science Fujian Normal University Fuzhou 350108 China

Submanifolds in space forms satisfy the well-known DDVV inequality. A submanifold attaining equality in this inequality pointwise is called a Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are investigated in this paper using the framework of MSbius geometry. We classify Wintgen ideal submanfiolds of dimension rn ≥ 3 and arbitrary codimension when a canonically defined 2-dimensional distribution D2 is integrable. Such examples come from cones, cylinders, or rotational submanifolds over super-minimal surfaces in spheres, Euclidean spaces, or hyperbolic spaces, respectively. We conjecture that if D2 generates a k-dimensional integrable distribution Dk and k 〈 m, then similar reduction theorem holds true. This generalization when k = 3 has been proved in this paper.

关键词： Wintgen ideal submanifold DDVV inequality super-conformalsurface super-minimal surface

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地质实验测试中高品位铁的测定

化工管理 2024年第6期 63-66页

作者：王长萍蔡万山甘肃有色金属地质勘查局白银矿产勘查院甘肃白银730900

文章介绍了一种新的测铁方法——重铬酸钾法,其利用盐酸对样品进行加热分解后,让铁矿石中的铁变成氧化铁,并用氯化亚锡将Fe^(3+)转化为Fe^(2+),以钨酸钠为指示试剂,再用三氯化钛将余下的小部分Fe^(3+)转化成Fe^(2+)至颜色变成钨蓝色,然... 详细信息

文章介绍了一种新的测铁方法——重铬酸钾法,其利用盐酸对样品进行加热分解后,让铁矿石中的铁变成氧化铁,并用氯化亚锡将Fe^(3+)转化为Fe^(2+),以钨酸钠为指示试剂,再用三氯化钛将余下的小部分Fe^(3+)转化成Fe^(2+)至颜色变成钨蓝色,然后用重铬酸钾标准液将其氧化,直至蓝色变淡到无色为止,之后加入配制好的硫磷混酸,以二苯胺磺酸钠作为指示剂,再用重铬酸钾溶液滴定,最后对铁矿石中的铁含量进行分析计算。对试验结果的准确度、精密度进行数据统计分析,并同时进行方法比对试验,结果表明该方法操作简便、分析速度快、灵敏度高、具有良好的准确度和精密度,并且此次试验方法与国家标准方法的测定结果没有显著性差异。

关键词：地质实验测试高品位铁重铬酸钾法