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Asymptotic coefficients and errors for Chebyshev polynomial approximations with weak endpoint singularities: Effects of different bases

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Science China Mathematics 2023年第1期66卷 191-220页

作者： xiaolong zhang John P.Boyd MOE-LCSM School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China Department of Climate&Space Sciences and Engineering University of MichiganAnn ArborMI 48109USA

When one solves differential equations by a spectral method,it is often convenient to shift from Chebyshev polynomials Tn(x) with coefficients anto modified basis functions that incorporate the boundary *** homogeneous Dirichlet boundary conditions,u(±1)=0,popular choices include the "Chebyshev difference basis" ζn(x)≡Tn+2(x)-Tn(x) with coefficients here denoted by bnand the "quadratic factor basis" Qn(x)≡(1-x2)Tn(x) with coefficients *** u(x) is weakly singular at the boundary,then the coefficients andecrease proportionally to O(A(n)/nκ) for some positive constant κ,where A(n) is a logarithm or a *** prove that the Chebyshev difference coefficients bndecrease more slowly by a factor of 1/n while the quadratic factor coefficients cndecrease more slowly still as O(A(n)/nκ-2).The error for the unconstrained Chebyshev series,truncated at degree n=N,is O(|A(N)|/Nκ) in the interior,but is worse by one power of N in narrow boundary layers near each of the *** having nearly identical error norms in interpolation,the error in the Chebyshev basis is concentrated in boundary layers near both endpoints,whereas the error in the quadratic factor and difference basis sets is nearly uniformly oscillating over the entire interval in ***,for Chebyshev polynomials,the values of their derivatives at the endpoints are O(n2),but only O(n) for the difference ***,we give the asymptotic coefficients and rigorous error estimates of the approximations in these three bases,solved by the least squares *** also find an interesting fact that on the face of it,the aliasing error is regarded as a bad thing;actually,the error norm associated with the downward curving spectral coefficients decreases even faster than the error norm of infinite *** the premise is under the same basis,and when involving different bases,it may not be established yet.

关键词： Chebyshev polynomial interpolation endpoint singularities least squares method

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Addressing the strength-ductility trade-off in a cast Al-Li-Cu alloy—Synergistic effect of Sc-alloying and optimized artificial ageing scheme

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Journal of Materials Science & Technology 2022年第1期96卷 212-225页

作者： Jinshuo zhang Guohua Wu Liang zhang xiaolong zhang Chunchang Shi Xin Tong National Engineering Research Center of Light Alloy Net Forming and State Key Laboratory of Metal Matrix Composites School of Materials Science andEngineeringShanghai Jiao Tong UniversityShanghai200240China Shanghai Innovation Institute for Materials Shanghai200444China

A dramatic improvement of strength and ductility of cast Al-2.5Li-1.5Cu-1Zn-0.5Mg-0.15 Zr alloy was obtained by the collaboration of Sc-alloying and optimized ageing *** and independent influence of Sc-alloying and different ageing temperatures were *** results revealed that a substantial increase was realized in the hardness of Sc-containing alloy,and the ageing response time was only influenced by ageing *** and heterogeneousδ'(Al_(3)Li),wideδ'-precipitation free zones(δ'-PFZs),and a large amount of T_(1)(Al_(2)CuLi)precipitates were observed in Sc-containing alloy aged at 175℃,which resulted in superior yield strength and poor *** Sc-containing alloy obtained an excellent combination of ductility(elongation=8.2%)and tensile strength(ultimate strength=565 MPa)suffered to 150℃ ageing for 64 *** increase in the elongation was mainly due to the combined effect of grain refining,much finerδ',and extremely narrowδ'-PFZs(<10 nm),while the higher strength was mainly attributed to the formation of Al_(3)(Sc,Zr,Li)composite particles and a large amount of S'(Al_(2)CuMg)***,the enhancement of the different ageing temperature(150℃ and 175℃)on the mechanical properties of the alloys without Sc addition was not obvious.

关键词： Cast Al-Li-Cu alloy δ’-PFZs Mechanical properties Cu-containing phases Microstructure evolutions

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单叶蔷薇基因组SSR标记开发与应用

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中南林业科技大学学报 2024年第6期44卷 186-196页

作者：张雪云张晓龙李娜孔青洋于超潘会堂张启翔罗乐北京林业大学花卉种质创新与分子育种北京市重点实验室北京100083 北京林业大学国家花卉工程技术研究中心北京100083 北京林业大学城乡生态环境北京实验室北京100083 北京林业大学园林环境教育部工程研究中心北京100083 北京林业大学林木花卉遗传育种教育部重点实验室北京100083 北京林业大学林木资源高效生产全国重点实验室北京100083 北京林业大学园林学院北京100083

【目的】单叶蔷薇是蔷薇属唯一的单叶物种,目前已被列为国家二级濒危保护植物,开发高效的分子标记可以为单叶蔷薇居群遗传多样性分析、克隆生长格局等研究提供重要的数据支撑,为其居群遗传资源的保育提供理论指导。【方法】利用Krait v... 详细信息

【目的】单叶蔷薇是蔷薇属唯一的单叶物种,目前已被列为国家二级濒危保护植物,开发高效的分子标记可以为单叶蔷薇居群遗传多样性分析、克隆生长格局等研究提供重要的数据支撑,为其居群遗传资源的保育提供理论指导。【方法】利用Krait v1.3软件对单叶蔷薇全基因组序列中1~6核苷酸重复的SSR位点进行搜索并分析其序列特征,进而采用Primer Premier3.0软件设计引物。选取16个单叶蔷薇样本通过琼脂糖凝胶电泳和毛细管电泳检验引物的有效性和多态性。最后用POPGENE32软件和PowerMarker3.25软件对高多态性引物扩增产物数据进行遗传参数分析,利用软件NTSYS-pc2.10对16个单叶蔷薇样本进行聚类分析。【结果】单叶蔷薇基因组序列上共识别出142 083个SSR位点,其中二核苷酸重复类型数目最多,占比46.95%。单核苷酸至六核苷酸重复型中占比最高的基序类型分别为A/T、AT/AT、AAG/CTT、AAAT/ATTT、AAAAT/ATTTT和AAAAAG/CTTTTT,充分表明A/T为优势碱基。单叶蔷薇基因组SSR序列长度变化范围为12~1 026 bp,不同的核苷酸重复类型均呈现长度越长数量越少的规律,区间长度为10~15 bp的SSR位点数量最多,占比47.42%。合成的140对引物中112对可以获得清晰的目的条带,引物有效率为80%;最后筛选出多态性高、稳定性好的14对引物在16份单叶蔷薇样本中检测到等位基因58个,PIC值在0.314 3~0.675 9之间,等位基因数(Na)、有效等位基因数(Ne)、Shannon信息指数(I)及PIC值平均分别为4.142 9、2.576 9、1.080 8和0.529 2。Pearson相关分析结果表明所筛选引物的PIC值与SSR长度间并无显著相关性。通过聚类分析发现,筛选出的14对引物能够将基于不同居群的单叶蔷薇进行较好地区分,遗传相似系数在0.45~0.86之间。【结论】利用单叶蔷薇全基因组大规模开发的SSR标记数量丰富且类型多样,筛选出的高多态性SSR位点将为后续单叶蔷薇居群遗传多样性研究发挥重要作用。

关键词：单叶蔷薇 SSR 标记开发多态性

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Research on knowledge acquisition method about the IF/THEN rules based on rough set theory

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Journal of Systems Engineering and Electronics 2008年第3期19卷 628-634,F0003页

作者： Liu Daohua Yuan Sicong zhang xiaolong Wang Fazhan School of Mechanical & Electronic Engineering Xi'an Univ. of Architecture & Technology Xi'an 710055 P. R. China Dept. of Computer Science Xinyang Normal Univ. Xinyang 464000 P. R. China

The basic principles of IF/THEN rules in rough set theory are analyzed first, and then the automatic process of knowledge acquisition is given. The numerical data is qualitatively processed by the classification of membership functions and membership degrees to get the normative decision table. The regular method of relations and the reduction algorithm of attributes are studied. The reduced relations are presented by the multi-representvalue method and its algorithm is offered. The whole knowledge acquisition process has high degree of automation and the extracted knowledge is true and reliable.

关键词： rough set theory knowledge's automatic gain IF/THEN rule attribute reduction multi-dimensionalrepresentative value.

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HFO-1234ze(E)/CO_(2)混合气体工频击穿及分解特性实验研究

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高压电器 2024年第3期60卷 161-169页

作者：田双双李晓涵张英张小龙柯锟靳小平袁子安兰佳琪湖北工业大学新能源及电网装备安全监测湖北省工程研究中心武汉430068 贵州电网有限责任公司电力科学研究院贵阳550000 国网重庆市电力公司检修分公司重庆404100

近年来,由于HFO-1234ze(E)具备良好的环保特性和优良的绝缘性能,被认为有较大潜力应用于中低压设备中。目前针对该气体的试验探究相对比较少。文中首先计算了不同气压下HFO-1234ze(E)/CO_(2)混合气体的液化温度,然后利用气体绝缘性能测... 详细信息

近年来,由于HFO-1234ze(E)具备良好的环保特性和优良的绝缘性能,被认为有较大潜力应用于中低压设备中。目前针对该气体的试验探究相对比较少。文中首先计算了不同气压下HFO-1234ze(E)/CO_(2)混合气体的液化温度,然后利用气体绝缘性能测试平台,分别探究了气压、混合比对HFO-1234ze(E)/CO_(2)混合气体绝缘特性的影响,并讨论实际工程应用中的最优混合比和气压值,再采用气相色谱质谱联用仪(GC-MS)对分解产物进行定性分析,同时对分解产物进行了仿真计算。研究结果表明在不同均匀场的条件下,HFO-1234ze(E)/CO_(2)混合气体的绝缘性能均随着混合比的提升而提高,击穿电压呈近似线性增长;在混合比保持不变的条件下,提高气压能够显著改善HFO-1234ze(E)/CO_(2)混合气体绝缘性能;同时在0.3 MPa条件下,20%~25%体积分数的HFO-1234ze(E)不仅具有良好的绝缘水平,而且受到电场不均匀度的影响相对较小,适用于实际工程应用。HFO-1234ze(E)/CO_(2)混合气体具有良好的自恢复绝缘特性,分解的产物主要为氢氟化碳(HFC)和碳氢化合物(HC),仿真结果表明分解产物较为稳定。综合实验和仿真计算结果表明HFO-1234ze(E)/CO_(2)混合气体有潜力替代SF6气体应用中低压绝缘设备中。

关键词：环保气体 HFO-1234ze(E)混合气体电场不均匀度绝缘特性

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Cursor caging:enhancing focus targeting in interactive fisheye views

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Science China(Information Sciences) 2013年第5期56卷 115-130页

作者： SONG HongZhi FU Yi zhang Liang zhang xiaolong(Luke) College of Informatics South China Agricultural University College of Information Sciences and Technology Pennsylvania State University307D IST BuildingUniversity ParkPA 16802USA

Fisheye view is an effective approach to visualizing and navigating large data sets by offering both local details and global context in the same ***,by using different magnification factors for detail and context information,fisheye view also leads to new usability issues,one of which is the focus targeting *** challenge happens when a user tries to select a target to either shift the focus to a new place or chooses the *** of the magnification factors applied to the fisheye view,the target moves when the cursor moves,and consequently,the moving distance the cursor actually needs to travel to reach the target does not match the distance between the cursor and target shown on the *** accuracy and efficiency can be *** paper analyzes the mechanism of this difficulty and proposes a new technique,cursor caging,as a method to alleviate the focus targeting difficulty in interactive fisheye *** technique extends the fisheye magnification approach from one element to a focal region,which can contain several elements,and allows the mouse cursor to move freely inside this region without affecting the magnification of objects inside the focal *** addition to the mathematical representation of this technique,we also develop two designs that incorporate the cursor caging concept in fisheye views,and describe a usability study on the *** results showed that cursor caging can significantly improve the task completion time and reduce the error rate in focusing targeting tasks.

关键词： fisheye view non-linear magnification focus targeting formal analysis cursor caging

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Bionic Stepping Motors Driven by Piezoelectric Materials

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Journal of Bionic Engineering 2023年第3期20卷 858-872页

作者： Shupeng Wang Shihui Zhou xiaolong zhang Pengyun Xu Zhihui zhang Luquan Ren Key Laboratory of Bionic Engineering(Ministry of Education) Jilin UniversityChangchun130022China Department of Mechanical and Electrical Engineering Ocean University of ChinaQingdao266100China

By imitating the behavioral characteristics of some typical animals, researchers develop bionic stepping motors to extend the working range of piezoelectric materials and utilize their high accuracy advantage as well. A comprehensive review of the bionic stepping motors driven by piezoelectric materials is presented in this work. The main parts of stepping piezoelectric motors, including the feeding module, clamping module, and other critical components, are introduced elaborately. We classify the bionic stepping piezoelectric motors into inchworm motors, seal motors, and inertia motors depending on their main structure modules, and present the mutual transformation relationships among the three types. In terms of the relative position relationships among the main structure modules, each of the inchworm motors, seal motors, and inertia motors can further be divided into walker type, pusher type, and hybrid type. The configurations and working principles of all bionic stepping piezoelectric motors are reported, followed by a discussion of the advantages and disadvantages of the performance for each type. This work provides theoretical support and thoughtful insights for the understanding, analysis, design, and application of the bionic stepping piezoelectric motors.

关键词： Bionic stepping piezoelectric motor Inchworm motor Seal motor Inertia motor Walker type Pusher type Hybrid type

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Strengthening effect of super typhoon Rammasun(2014)on upwelling and cold eddies in the South China Sea

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Journal of Oceanology and Limnology 2021年第2期39卷 403-419页

作者： Xue LI xiaolong zhang Dongyang FU Shan LIAO Guangdong Ocean Remote Sensing and Information Engineering Technology Research Center Guangdong Ocean UniversityZhanjiang 524088China State Key Laboratory of Marine Environmental Science College of Ocean and Earth SciencesXiamen UniversityXiamen 361102China Marine Resources Big Data Center of South China Sea Southern Marine Science and Engineering Guangdong LaboratoryZhanjiang 524088China Meteorological Bureau Yan’an 716000China School of Cybersecurity Sichuan UniversityChengdu 610065China

Typhoon is one of the frequent natural disasters in coastal regions of *** shown in many studies,the impact of typhoons on the South China Sea(SCS)should not be *** typhoon Rammasun(2014)was studied that formed in the northwestern Pacific,passed through the SCS,then landed in the Leizhou *** sensing data and model products were used to analyze the spatiotemporal variations of the cold eddies,upwelling,sea surface temperature,mixed layer depth,rainfall,sea surface salinity,suspended sediment concentration,and surface-level *** confirm the constant presence of upwelling and cold eddies in the southeast of Hainan(north of the Zhongsha Islands)and the southeast of Vietnam in *** addition,we found the strengthening effect of super typhoon Rammasun on the upwelling and cold eddies in the *** major reasons for the continuous decrease in sea surface temperature and the slow regaining of seawater temperature were the enhanced upwelling and vertical mixing caused by the *** increasing of the surface runoff in the Indochina Peninsula was mainly affected by the typhoon,with some contribution for the southeast of Vietnam’s cold eddy and upwelling.

关键词： cold eddies sea surface temperature(SST) South China Sea(SCS) typhoon Rammasun upwelling

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厂房建筑光伏项目开发、设计与施工探讨

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现代建筑电气 2024年第4期15卷 51-56页

作者：陈志刚田鑫张小龙中天西北建设投资集团有限公司陕西西安710055 西安高铁东城建设发展有限公司陕西西安710038 华融贵阳置业有限责任公司贵州贵阳550000

以某厂房项目为例,详尽对比分析了厂房建筑光伏发电的不同开发设计形式、系统构成、安装工艺以及关键节点控制,对光伏发电量进行仿真计算并与实测数据对比分析,为厂房建筑光伏发电项目应用和研究提供参考与借鉴。

关键词：光伏发电光伏建筑一体化光伏组件并网

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Bionics-based Optimization of Step-climbing Gait in a Novel Mini-RHex Robot

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Journal of Bionic Engineering 2022年第3期19卷 616-628页

作者： Xingguo Song Jiajun Pan xiaolong zhang Chunjun Chen Danshan Huang Mechanical Engineering School Southwest Jiaotong UniversityChengdu610031China 41st Detachment Unit 32272Chinese People’s Liberation ArmyDeyang618408China

RHex-style robots can perform manifold moving gaits in different applications,but they have always faced a challenge of climbing up high *** this paper,the bionics-based gait optimization in an RHex-style robot is proposed for climbing steps at different heights,which even enables the robot to climb up the step with 4.2 times of the leg ***,a thoracic flexion is designed in the robot,and an algorithm of adjusting body inclination is proposed to perform the rising stage after placing front legs on top of step,which can be applied in different RHex-style robots with different ***,when the thoracic flexion is implemented,the robot can climb the higher step with the proposed ***,to climbing the higher steps,a claw-shape legs-based algorithm is proposed for robot reaching the higher step and climbing it *** the vital rising stage,when the front legs of the robot have reached the top of the step,the robot can bend the front body downward with its thoracic flexion like a cockroach,and then lift the front and middle legs alternately to move COM up and forward onto the *** simulation analysis is utilized to verify the feasibility of the proposed ***,the step-climbing experiments at different heights are performed in our robot to compare with the existing *** results of simulations and experiments show the superiority of the proposed algorithms for the improved robot due to climbing up the higher steps.

关键词： Mini-RHex robot Climbing gait Thoracic flexion Gait optimization Claw-shape legs

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