The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices...The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.展开更多
Background:The validity and reliability of the Borg 6–20 rating of perceived exertion(RPE)scale has not been tested among Chinese people from China' Mainland.The purpose of this study was to test:1)The validity o...Background:The validity and reliability of the Borg 6–20 rating of perceived exertion(RPE)scale has not been tested among Chinese people from China' Mainland.The purpose of this study was to test:1)The validity of Leung Chinese version and Wang Chinese version of the Borg 6–20 RPE scale;2)The reliability of Wang Chinese version RPE scale;and 3)The agreement of these two Chinese versions of the RPE scale among young healthy adults from China' Mainland.Methods:A total of 26 subjects(11 males,15 females;age 22.7±3.0 yrs)volunteered to participate.They performed one(n=3),two(n=14),or three trials(n=9)of the Bruce treadmill protocol test within 9.0±5.1 days(validation trials),and 30.4±27.9 days(reliability trials).Power output,heart rate,oxygen consumption,and RPE were recorded.Results:RPE was significantly correlated with power output(Leung version rs≥0.75,Wang version rs≥0.73),heart rate(HR)(Leung version rs≥0.84,Wang version rs≥0.87),and oxygen consumption(VO2)(Leung version rs≥0.80,Wang version rs≥0.81)(all p<0.01).The overall test-retest interclass correlation was 0.94(p<0.01).No significant differences in correlations(RPE against power output,HR and VO_(2))between trials existed for the reliability tests of Wang version scale.No significant differences in correlations(RPE against power output,HR and VO_(2))between the two Chinese versions of RPE scale existed.Conclusion:Both Chinese RPE scales are valid among young healthy Chinese mandarin speaking adults.The Wang scale is reliable,and the Leung and Wang scales show superior agreement with each other.展开更多
基金Project supported by Hong Kong Baptist University RC’s Start-up Grant for New Academics,the Hong Kong Research Grant Council(Nos.PolyU 15302114,15300715,15301716,and 15300717)the National Natural Science Foundation of China(No.11372124)
文摘The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.
文摘Background:The validity and reliability of the Borg 6–20 rating of perceived exertion(RPE)scale has not been tested among Chinese people from China' Mainland.The purpose of this study was to test:1)The validity of Leung Chinese version and Wang Chinese version of the Borg 6–20 RPE scale;2)The reliability of Wang Chinese version RPE scale;and 3)The agreement of these two Chinese versions of the RPE scale among young healthy adults from China' Mainland.Methods:A total of 26 subjects(11 males,15 females;age 22.7±3.0 yrs)volunteered to participate.They performed one(n=3),two(n=14),or three trials(n=9)of the Bruce treadmill protocol test within 9.0±5.1 days(validation trials),and 30.4±27.9 days(reliability trials).Power output,heart rate,oxygen consumption,and RPE were recorded.Results:RPE was significantly correlated with power output(Leung version rs≥0.75,Wang version rs≥0.73),heart rate(HR)(Leung version rs≥0.84,Wang version rs≥0.87),and oxygen consumption(VO2)(Leung version rs≥0.80,Wang version rs≥0.81)(all p<0.01).The overall test-retest interclass correlation was 0.94(p<0.01).No significant differences in correlations(RPE against power output,HR and VO_(2))between trials existed for the reliability tests of Wang version scale.No significant differences in correlations(RPE against power output,HR and VO_(2))between the two Chinese versions of RPE scale existed.Conclusion:Both Chinese RPE scales are valid among young healthy Chinese mandarin speaking adults.The Wang scale is reliable,and the Leung and Wang scales show superior agreement with each other.
