In this paper,we study f-harmonicity of some special maps from or into a doubly warped product manifold.First we recall some properties of doubly twisted product manifolds.After showing that the inclusion maps from Ri...In this paper,we study f-harmonicity of some special maps from or into a doubly warped product manifold.First we recall some properties of doubly twisted product manifolds.After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M ×（μ,λ） N can not be proper f-harmonic maps,we use projection maps and product maps to construct nontrivial f-harmonic maps.Thus we obtain some similar results given in [21],such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps.Furthermore,we investigate non-trivial f-harmonicity of the product of two harmonic maps.展开更多
Accurate cropland information is critical for agricultural planning and production,especially in foodstressed countries like China.Although widely used medium-to-high-resolution satellite-based cropland maps have been...Accurate cropland information is critical for agricultural planning and production,especially in foodstressed countries like China.Although widely used medium-to-high-resolution satellite-based cropland maps have been developed from various remotely sensed data sources over the past few decades,considerable discrepancies exist among these products both in total area and in spatial distribution of croplands,impeding further applications of these datasets.The factors influencing their inconsistency are also unknown.In this study,we evaluated the consistency and accuracy of six cropland maps widely used in China in circa 2020,including three state-of-the-art 10-m products(i.e.,Google Dynamic World,ESRI Land Cover,and ESA WorldCover)and three 30-m ones(i.e.,GLC_FCS30,GlobeLand 30,and CLCD).We also investigated the effects of landscape fragmentation,climate,and agricultural management.Validation using a ground-truth sample revealed that the 10-m-resolution WorldCover provided the highest accuracy(92.3%).These maps collectively overestimated Chinese cropland area by up to 56%.Up to 37%of the land showed spatial inconsistency among the maps,concentrated mainly in mountainous regions and attributed to the varying accuracy of cropland maps,cropland fragmentation and management practices such as irrigation.Our work shed light on the promotion of future cropland mapping efforts,especially in highly inconsistent regions.展开更多
With the continuous development of China’s education,the social requirements for high school teaching are constantly improving.The teaching of high school mathematics is a key point in the high school curriculum,but ...With the continuous development of China’s education,the social requirements for high school teaching are constantly improving.The teaching of high school mathematics is a key point in the high school curriculum,but also a major difficulty.Due to the strong logic and abstraction of the content of high school mathematics,some students find it very difficult to learn.In order to solve this problem,high school mathematics teachers can make use of mind maps to teach,so that students can exercise their thinking ability,and realize the improvement of comprehensive ability in mathematics.This paper analyzes the shortcomings of high school mathematics classrooms under the background of new curriculum reform and discusses the significance and methods of applying mind maps in high school mathematics classrooms,so as to put forward reasonable suggestions for realizing the efficient teaching of high school mathematics.展开更多
Both bi-harmonic maps and f-harmonic maps have some nice physical motivation and applications.Motivated largely by f-tension field not involving Riemannian curvature tensor, we attempt to formalize some large objects ...Both bi-harmonic maps and f-harmonic maps have some nice physical motivation and applications.Motivated largely by f-tension field not involving Riemannian curvature tensor, we attempt to formalize some large objects so as to broaden the notions of f-tension field and bi-tension field. We introduce a very large generalization of harmonic maps called f-bi-harmonic maps as the critical points of f-bi-energy functional, and then derive the Euler-Lagrange equation of f-bi-energy functional given by the vanishing of f-bi-tension field.Subsequently, we study some properties of f-bi-harmonic maps between the same dimensional manifolds and give a non-trivial example. Furthermore, we also study the basic properties of f-bi-harmonic maps on a warped product manifold so that we could find some interesting and complicated examples.展开更多
Lidar and visual data are affected heavily in adverse weather conditions due to sensing mechanisms,which bring potential safety hazards for vehicle navigation.Radar sensing is desirable to build a more robust navigati...Lidar and visual data are affected heavily in adverse weather conditions due to sensing mechanisms,which bring potential safety hazards for vehicle navigation.Radar sensing is desirable to build a more robust navigation system.In this paper,a cross-modality radar localisation on prior lidar maps is presented.Specifically,the proposed workflow consists of two parts:first,bird's-eye-view radar images are transferred to fake lidar images by training a generative adversarial network offline.Then with online radar scans,a Monte Carlo localisation framework is built to track the robot pose on lidar maps.The whole online localisation system only needs a rotating radar sensor and a pre-built global lidar map.In the experimental section,the authors conduct an ablation study on image settings and test the proposed system on Oxford Radar Robot Car Dataset.The promising results show that the proposed localisation system could track the robot pose successfully,thus demonstrating the feasibility of radar style transfer for metric robot localisation on lidar maps.展开更多
Owing to the limitation of a large genome size(~13 Gb),the genetic and gene mapping studies on faba bean(Vicia faba L.)are lagging far behind those for other legumes.In this study,we selected three purified faba bean ...Owing to the limitation of a large genome size(~13 Gb),the genetic and gene mapping studies on faba bean(Vicia faba L.)are lagging far behind those for other legumes.In this study,we selected three purified faba bean lines(Yundou 8137,H0003712,and H000572)as parents and constructed two F2 populations.These two F2 populations,namely 167 F2 plants in Pop1(Yundou 8137×H0003712)and 204 F2 plants in Pop2(H000572×Yundou 8137),were genotyped using a targeted next-generation sequencing(TNGS)genotyping platform,and two high-density single nucleotide polymorphisms(SNP)genetic linkage maps of faba bean were constructed.The map constructed from Pop1 contained 5103 SNPs with a length of 1333.31 cM and an average marker density of 0.26 cM.The map constructed from Pop2 contained 1904 SNPs with a greater length of 1610.61 cM.In these two F2 populations,QTL mapping identified 98 QTLs for 14 agronomic traits related to the flowers,pods,plant types and grains.The two maps were then merged into an integrated genetic linkage map containing 6895 SNPs,with a length of 3324.48 cM.These results not only lay the foundation for fine mapping and map-based cloning of related genes,but can also accelerate the molecular marker-assisted breeding of faba bean.展开更多
We were interested, along this work, in the phenomena of the quintessence and the inflation due to the F-harmonic maps, in other words, in the functions of the scalar field such as the exponential and trigo-harmonic m...We were interested, along this work, in the phenomena of the quintessence and the inflation due to the F-harmonic maps, in other words, in the functions of the scalar field such as the exponential and trigo-harmonic maps. We showed that some F-harmonic map such as the trigonometric functions instead of the scalar field in the lagrangian, allow, in the absence of term of potential, reproduce the inflation. However, there are other F-harmonic maps such as exponential maps which can’t produce the inflation;the pressure and the density of this exponential harmonic field being both of the same sign. On the other hand, these exponential harmonic fields redraw well the phenomenon of the quintessence when the variation of these fields remains weak. The problem of coincidence, however remains.展开更多
基金Partially supported by Guangxi Natural Science Foundation (2011GXNSFA018127)
文摘In this paper,we study f-harmonicity of some special maps from or into a doubly warped product manifold.First we recall some properties of doubly twisted product manifolds.After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M ×（μ,λ） N can not be proper f-harmonic maps,we use projection maps and product maps to construct nontrivial f-harmonic maps.Thus we obtain some similar results given in [21],such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps.Furthermore,we investigate non-trivial f-harmonicity of the product of two harmonic maps.
基金supported by NSFC (Grant Nos.11971358,11571259,11771339)Hubei Provincial Natural Science Foundation of China (No.2021CFB400)+1 种基金Fundamental Research Funds for the Central Universities (No.2042019kf0198)the Youth Talent Training Program of Wuhan University。
文摘In this article,we prove that a quasi-isometric map between rank one symmetric spaces is within bounded distance from an f-harmonic map.
基金This work was supported by the National Natural Science Foundation of China(72221002,42271375)the Strategic Priority Research Program(XDA28060100)the Informatization Plan Project(CAS-WX2021PY-0109)of the Chinese Academy of Sciences.
文摘Accurate cropland information is critical for agricultural planning and production,especially in foodstressed countries like China.Although widely used medium-to-high-resolution satellite-based cropland maps have been developed from various remotely sensed data sources over the past few decades,considerable discrepancies exist among these products both in total area and in spatial distribution of croplands,impeding further applications of these datasets.The factors influencing their inconsistency are also unknown.In this study,we evaluated the consistency and accuracy of six cropland maps widely used in China in circa 2020,including three state-of-the-art 10-m products(i.e.,Google Dynamic World,ESRI Land Cover,and ESA WorldCover)and three 30-m ones(i.e.,GLC_FCS30,GlobeLand 30,and CLCD).We also investigated the effects of landscape fragmentation,climate,and agricultural management.Validation using a ground-truth sample revealed that the 10-m-resolution WorldCover provided the highest accuracy(92.3%).These maps collectively overestimated Chinese cropland area by up to 56%.Up to 37%of the land showed spatial inconsistency among the maps,concentrated mainly in mountainous regions and attributed to the varying accuracy of cropland maps,cropland fragmentation and management practices such as irrigation.Our work shed light on the promotion of future cropland mapping efforts,especially in highly inconsistent regions.
文摘With the continuous development of China’s education,the social requirements for high school teaching are constantly improving.The teaching of high school mathematics is a key point in the high school curriculum,but also a major difficulty.Due to the strong logic and abstraction of the content of high school mathematics,some students find it very difficult to learn.In order to solve this problem,high school mathematics teachers can make use of mind maps to teach,so that students can exercise their thinking ability,and realize the improvement of comprehensive ability in mathematics.This paper analyzes the shortcomings of high school mathematics classrooms under the background of new curriculum reform and discusses the significance and methods of applying mind maps in high school mathematics classrooms,so as to put forward reasonable suggestions for realizing the efficient teaching of high school mathematics.
基金supported by the Science and Technology Research Project of Guangxi Universities(Grant No.2015ZD038)the Key Scientific Research Project of Guangxi University for Nationalities(Grant No.2012MDZD033)
文摘Both bi-harmonic maps and f-harmonic maps have some nice physical motivation and applications.Motivated largely by f-tension field not involving Riemannian curvature tensor, we attempt to formalize some large objects so as to broaden the notions of f-tension field and bi-tension field. We introduce a very large generalization of harmonic maps called f-bi-harmonic maps as the critical points of f-bi-energy functional, and then derive the Euler-Lagrange equation of f-bi-energy functional given by the vanishing of f-bi-tension field.Subsequently, we study some properties of f-bi-harmonic maps between the same dimensional manifolds and give a non-trivial example. Furthermore, we also study the basic properties of f-bi-harmonic maps on a warped product manifold so that we could find some interesting and complicated examples.
文摘背景:腰椎小关节炎是引起下腰痛的一个主要原因,目前主要依靠MRI进行初步定性诊断,但仍有一定漏诊、误诊的概率发生,因此MR T2^(*)mapping成像技术有望成为定量检查腰椎小关节炎软骨损伤的重要检测手段。目的:探讨MR T2^(*)mapping成像技术在定量分析腰椎小关节炎软骨损伤退变中的应用价值。方法:收集南京医科大学第四附属医院2020年4月至2022年3月门诊或住院合并下腰痛共110例患者,设为病例组;同时招募无症状志愿者80例,设为对照组。对所有纳入对象L1-S1的小关节行3.0 T MR扫描,获取T2^(*)mapping横断位图像和T2WI图像,分别对所有小关节软骨进行Weishaupt分级及T2^(*)值测量,收集数据并行统计学分析。不同小关节Weishaupt分级之间小关节软骨T2^(*)值比较采用单因素方差分析。结果与结论:①经统计分析发现,病例组腰椎小关节软骨T2^(*)值(17.6±1.5)ms明显较对照组(21.4±1.3)ms降低,差异有显著性意义(P<0.05);②在病例组中,随着腰椎小关节Weishaupt分级增加,小关节软骨T2^(*)值也呈逐渐下降趋势,且这种差异有显著性意义(P<0.05);③提示T2^(*)mapping能够较好地显示腰椎小关节软骨损伤的早期病理变化,腰椎小关节软骨的T2^(*)值能够定量评估腰椎小关节的软骨损伤程度;T2^(*)mapping成像技术能为影像学诊断腰椎小关节炎软骨早期损伤提供很好的理论依据,具有重要的临床应用价值。
基金National Key R&D Program of China,Grant/Award Number:2020YFB1313300National Nature Science Foundation of China under Grant,Grant/Award Number:61903332Hong Kong Center for Construction Robotics(InnoHK center supported by Hong Kong ITC)。
文摘Lidar and visual data are affected heavily in adverse weather conditions due to sensing mechanisms,which bring potential safety hazards for vehicle navigation.Radar sensing is desirable to build a more robust navigation system.In this paper,a cross-modality radar localisation on prior lidar maps is presented.Specifically,the proposed workflow consists of two parts:first,bird's-eye-view radar images are transferred to fake lidar images by training a generative adversarial network offline.Then with online radar scans,a Monte Carlo localisation framework is built to track the robot pose on lidar maps.The whole online localisation system only needs a rotating radar sensor and a pre-built global lidar map.In the experimental section,the authors conduct an ablation study on image settings and test the proposed system on Oxford Radar Robot Car Dataset.The promising results show that the proposed localisation system could track the robot pose successfully,thus demonstrating the feasibility of radar style transfer for metric robot localisation on lidar maps.
基金supported by the National Key R&D Program of China(2019YFD1001300 and 2019YFD1001303)the Construction of Molecular Database of Faba Bean and Pea and Identification of Maize Germplasm Project,Ministry of Agriculture and Rural Affairs,China(19200030)+3 种基金the Yunnan Key R&D Program,China(202202AE090003)the earmarked fund for China Agriculture Research System(CARS-08)the Crop Germplasm Resources Protection(2130135)the Major Agricultural Science and Technology Program of Chinese Academy of Agricultural Sciences(CAAS-XTCX20190025)。
文摘Owing to the limitation of a large genome size(~13 Gb),the genetic and gene mapping studies on faba bean(Vicia faba L.)are lagging far behind those for other legumes.In this study,we selected three purified faba bean lines(Yundou 8137,H0003712,and H000572)as parents and constructed two F2 populations.These two F2 populations,namely 167 F2 plants in Pop1(Yundou 8137×H0003712)and 204 F2 plants in Pop2(H000572×Yundou 8137),were genotyped using a targeted next-generation sequencing(TNGS)genotyping platform,and two high-density single nucleotide polymorphisms(SNP)genetic linkage maps of faba bean were constructed.The map constructed from Pop1 contained 5103 SNPs with a length of 1333.31 cM and an average marker density of 0.26 cM.The map constructed from Pop2 contained 1904 SNPs with a greater length of 1610.61 cM.In these two F2 populations,QTL mapping identified 98 QTLs for 14 agronomic traits related to the flowers,pods,plant types and grains.The two maps were then merged into an integrated genetic linkage map containing 6895 SNPs,with a length of 3324.48 cM.These results not only lay the foundation for fine mapping and map-based cloning of related genes,but can also accelerate the molecular marker-assisted breeding of faba bean.
文摘We were interested, along this work, in the phenomena of the quintessence and the inflation due to the F-harmonic maps, in other words, in the functions of the scalar field such as the exponential and trigo-harmonic maps. We showed that some F-harmonic map such as the trigonometric functions instead of the scalar field in the lagrangian, allow, in the absence of term of potential, reproduce the inflation. However, there are other F-harmonic maps such as exponential maps which can’t produce the inflation;the pressure and the density of this exponential harmonic field being both of the same sign. On the other hand, these exponential harmonic fields redraw well the phenomenon of the quintessence when the variation of these fields remains weak. The problem of coincidence, however remains.
