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半正定多项式的一个降次有理平方和表示算法

系统科学与数学 2024年第5期44卷 1241-1271页

作者：黄勇曾振柄杨路饶永生广州大学计算科技研究院广州510006 广东省数学教育软件工程技术研究中心广州510006 上海大学理学院数学系上海200444 中国科学院成都计算机应用研究所成都610041

文章给出一个构造性算法,将一元半正定多项式表示为一些次数递降的多项式的平方和,当输入的多项式的系数是有理数时,该算法构造的降次多项式的系数也是有理数.文章还把这种方法推广到多元多项式情况,即如果该多项式有平方和表示,使用文... 详细信息

文章给出一个构造性算法,将一元半正定多项式表示为一些次数递降的多项式的平方和,当输入的多项式的系数是有理数时,该算法构造的降次多项式的系数也是有理数.文章还把这种方法推广到多元多项式情况,即如果该多项式有平方和表示,使用文章方法也能得到该半正定多元多项式的一个特殊的平方和分解.

关键词：半正定多项式平方和表示降次多项式平方和有理平方和

Design and implementation of web-based dynamic geometry drawing technology

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The Journal of China Universities of Posts and Telecommunications 2019年第6期26卷 43-53页

作者： Guan Hao rao yongsheng Xu Zhangtao Chengdu Institute of Computer Application Chinese Academy of SciencesChengdu 610041China University of Chinese Academy of Sciences Beijing 100049China Institute of Computing Science and Technology Guangzhou UniversityGuangzhou 510006China School of Mathematics and Statistics Central China Normal UniversityWuhan 430079China

Dynamic geometry software, as a piece of computer-assisted instruction(CAI) software, is closely and deeply associated with mathematics, and is widely applied to mathematics teaching activities in primary and secondary schools. Meanwhile, web technology also has become an important technology for assisting education and teaching. This paper expounds a web-based dynamic geometry software development process, and analyses specific requirements regarding graphical application programming interface(API) required by dynamic geometry software. With experiments and comparison on the two different hypertext markup language(HTML)5 graphical API technologies, i.e., scalable vector graphics(SVG) and Canvas, on different apparatuses and browsers, we draw the conclusion that it is more suitable to adopt Canvas as the graphical API technology for the web-based dynamic geometry software, thus further proposed the principles and methods for an object-oriented Canvas design. The dynamic geometry software based on the newly-designed Canvas has technical advantages and educational value, well incorporating aesthetic education into mathematics education.

关键词： web Canvas dynamic geometry subject tools

On the asymptotic expressions of critical energy barrier in Prandtl-Tomlinson model

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International Journal of Smart and Nano Materials 2019年第2期10卷 107-115页

作者： Rong-Guang Xu Yuan Xiang Qi rao yongsheng Leng Department of Mechanical and Aerospace Engineering The George Washington UniversityWashingtonDCUSA

The Prandtl-Tomlinson(PT)model is the most widely used and successful minimalistic model to describe atomistic scale friction.It can describe the thermally activated,stress assistant process which shows stick-slip frictional behavior.The relationship between the energy barrier and lateral force is critical to determine how the frictional force depends on velocity and temperature.There is some confusion in the literature to derive such relationship.The underlying assumption and approximations are not stated in a clear way and the rigorous derivations are missing.This study discusses the asymptotic behavior of the energy barrier as the support-spring coupling lowers it to zero and gives a detailed derivation of the asymptotic expression of the energy barrier within the framework of PT model.

关键词： Prandtl-Tomlinson model friction stick-slip friction force microscope

Moving target localization for multistatic passive radar using delay, Doppler and Doppler rate measurements

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Journal of Systems Engineering and Electronics 2020年第5期31卷 939-949页

作者： ZHAO yongsheng HU Dexiu ZHAO Yongjun LIU Zhixin Data and Target Engineering Institute PLA Strategic Support Force Information Engineering UniversityZhengzhou 450001China

Time delay and Doppler shift between the echo signal and the reference signal are two most commonly used measurements in target localization for the passive radar. Doppler rate, which can be obtained from the extended cross ambiguity function, offers an opportunity to further enhance the localization accuracy. This paper considers using the measurement Doppler rate in addition to measurements of time delay and Doppler shift to locate a moving target. A closed-form solution is developed to accurately and efficiently estimate the target position and velocity.The proposed solution establishes a pseudolinear set of equations by introducing some additional variables, imposes weighted least squares formulation to yield a rough estimate, and utilizes the function relation among the target location parameters and additional variables to improve the estimation accuracy. Theoretical covariance and Cramer-rao lower bound(CRLB) are derived and compared, analytically indicating that the proposed solution attains the CRLB. Numerical simulations corroborate this analysis and demonstrate that the proposed solution outperforms existing methods.

关键词： target localization multistatic passive radar time delay Doppler shift Doppler rate

Moving target localization in distributed MIMO radar with transmitter and receiver location uncertainties

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Chinese Journal of Aeronautics 2019年第7期32卷 1705-1715页

作者： yongsheng ZHAO Dexiu HU Yongjun ZHAO Zhixin LIU National Digital Switching System Engineering and Technological Research Center (NDSC)

In this paper, the problem of moving target localization from Bistatic Range(BR) and Bistatic Range Rate(BRR) measurements in a Multiple-Input Multiple-Output(MIMO) radar system having widely separated antennas is investigated. We consider a practically motivated scenario,where the accurate knowledge of transmitter and receiver locations is not known and only the nominal values are available for processing. With the transmitter and receiver location uncertainties,which are usually neglected in MIMO radar systems by prior studies, taken into account in the measurement model, we develop a novel algebraic solution to reduce the estimation error for moving target localization. The proposed algorithm is based on the pseudolinear set of equations and two-step weighted least squares estimation. The Cramer-rao Lower Bound(CRLB) is derived in the presence of transmitter and receiver location uncertainties. Theoretical accuracy analysis demonstrates that the proposed solution attains the CRLB, and numerical examples show that the proposed solution achieves significant performance improvement over the existing algorithms.

关键词： Bistatic range Bistatic range rate Location uncertainty MIMO radar Target localization Two-step weighted least squares

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动态数学数字资源开放平台的研究与设计

哈尔滨工业大学学报 2019年第5期51卷 14-22页

作者：管皓秦小林饶永生中国科学院大学北京100049 中国科学院成都计算机应用研究所成都610041 广州大学计算科技研究院广州510006

数字教育资源的共建共享行动已成为当前教育信息化的重要内容和研究热点.经过多年的研究和建设,数字教育资源其价值并未得到充分的利用,反而出现所谓的"资源孤岛"和"数字废墟".究其原因主要是由于现有的资源平台建设未具有足够的开放性... 详细信息

数字教育资源的共建共享行动已成为当前教育信息化的重要内容和研究热点.经过多年的研究和建设,数字教育资源其价值并未得到充分的利用,反而出现所谓的"资源孤岛"和"数字废墟".究其原因主要是由于现有的资源平台建设未具有足够的开放性以及学科相关性.基于PaaS结构提出了教育资源开放平台模型,并结合动态几何、计算机代数、几何定理自动推理等技术,采用微服务架构设计并实现了一种动态数学教学资源开放平台.该开放平台具有深入数学学科、开放资源与能力定制化、分级授权等特点.利用OAuth2.0技术作为主要的授权流程,为第三方应用和用户提供认证授权、分级定制化的动态数学内容素材和能力.给出该开放平台的相关特点及总体设计,介绍了面向应用及用户权限的分层策略与认证流程及开放资源与工具的定制化流程.根据性能分析,表明该平台已广泛应用于教学活动中.目前该开放平台已为电子教材、通用演示软件及在线备课平台等多个第三方应用提供服务,得到了广泛应用.

关键词：数字教育资源动态数学微服务架构 OAuth2.0 开放平台

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基于吴方法的几何定理证明的恒等式方法

中国科学：数学 2021年第1期51卷 289-300页

作者：邹宇彭翕成饶永生广州大学计算科技研究院广州510006 华中师范大学国家数字化学习工程技术研究中心武汉430079

多年来通常认为以吴方法为代表的几何定理机器证明的坐标法给出的证明不可读,或不是图灵意义下的类人解答.其实,只要对吴氏的算法做不多的改进,即将命题的结论多项式表示为其条件多项式的线性组合,就能获得不依赖于理论、算法和大量计... 详细信息

多年来通常认为以吴方法为代表的几何定理机器证明的坐标法给出的证明不可读,或不是图灵意义下的类人解答.其实,只要对吴氏的算法做不多的改进,即将命题的结论多项式表示为其条件多项式的线性组合,就能获得不依赖于理论、算法和大量计算过程的恒等式明证.这样的恒等式可以转化为其他更简明且更有直观几何意义的点几何形式或向量及其他形式,从而获得多种证明方法.这也证明了点几何恒等式明证方法对等式型几何命题的普遍有效性.

关键词：吴方法几何定理证明恒等式方法点几何

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‘户太八号’桃红葡萄酒色泽与香气物质分析

中外葡萄与葡萄酒 2023年第6期 85-91页

作者：陈巧迎饶博涵王凌云张永刚陶永胜陕西国际商贸学院管理学院陕西西安712000 西北农林科技大学葡萄酒学院陕西杨凌712100 商洛市特色产业与休闲农业指导中心陕西商洛726000 陕西丹凤葡萄酒有限公司陕西丹凤726200

以‘户太八号’葡萄为原料,采用常规工艺酿造桃红葡萄酒,利用CIELab颜色空间技术进行色泽评价,用光谱法检测花色苷类化合物;采用SPME-GC-MS定性定量分析酒样香气成分,运用气味活性值(OAV)评价香气物质活性,分析其香气贡献;葡萄酒香气特... 详细信息

以‘户太八号’葡萄为原料,采用常规工艺酿造桃红葡萄酒,利用CIELab颜色空间技术进行色泽评价,用光谱法检测花色苷类化合物;采用SPME-GC-MS定性定量分析酒样香气成分,运用气味活性值(OAV)评价香气物质活性,分析其香气贡献;葡萄酒香气特征采用经培训的品评小组感官评价。结果表明,酒样呈淡红、微带浅黄色,对颜色起主要贡献的是聚合花色苷和辅花色苷;共测量挥发性物质39种,其中品种香气成分10种,发酵香气成分29种。OAV分析表明,品种香气物质中仅β-大马酮和3-甲硫基-1-丙醇气味活性较高(OAV>1),其他为潜在的气味贡献成分(0.1

关键词：户太八号桃红葡萄酒 CIELab颜色空间香气感官分析

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SGARP中符号计算模块的实现及其应用

计算机研究与发展 2014年第6期51卷 1341-1351页

作者：张景中张传军郑焕饶永生邹宇广州大学计算机科学与教育软件学院广州510006 电子科技大学计算机科学与工程学院成都610054 贵州省教育科学院贵阳550001

可持续发展的几何自动推理平台(sustainable geometry automated reasoning platform,SGARP)支持用户按需添加或修改几何定理机器证明所涉及的几何对象、谓词、定理和规则,以发展多种多样基于规则的机器自动推理或人机交互推理方法.为... 详细信息

可持续发展的几何自动推理平台(sustainable geometry automated reasoning platform,SGARP)支持用户按需添加或修改几何定理机器证明所涉及的几何对象、谓词、定理和规则,以发展多种多样基于规则的机器自动推理或人机交互推理方法.为进一步提高SGARP的推理能力和扩展其适用范围,提出一种在SGARP中实现符号计算功能的快捷方法,并成功添加了质点法和解析法推理模块.质点法可证明希尔伯特交点类几何命题,解析法能用于辅助证明各种类型有一定难度的几何定理,如著名的Thebault定理.对这两种方法用基于Web的机器证明测试用的几何问题库(thousands of geometric problems for geometric theorem provers,TGTP)中180道几何题进行评估,均在合理时间内给出令人满意的可读机器证明,表明升级后的SGARP能更好地满足用户学习与发展几何机器推理的需求.

关键词：可由用户持续发展的几何自动推理平台(SGARP) 几何定理机器证明符号计算 Python语言质点法 Thebault定理