To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relati...To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.展开更多
The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation b...The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation between the form invariance and the Noether symmetry is studied.展开更多
To study the invariance of numerical character of matrix products and their statistical applications by matrix theory and linear model theory. Necessary and sufficient conditions are established for the product AB -C...To study the invariance of numerical character of matrix products and their statistical applications by matrix theory and linear model theory. Necessary and sufficient conditions are established for the product AB -C to have its numerical characters invariant with respect to every minimum norm g inverse, respectively. The algebraic results derived are then applied to investigate relationships among BLUE, WLSE and OLSE under the general Gauss? Markoff model.展开更多
The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with ...The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with the Noether symmetry and the Lie symmetry is discussed.展开更多
Background:Valid and reliable measures of depressive symptoms are crucial for understanding risk factors,outcomes,and interventions across rural and urban settings.Despite this need,the longitudinal invariance of thes...Background:Valid and reliable measures of depressive symptoms are crucial for understanding risk factors,outcomes,and interventions across rural and urban settings.Despite this need,the longitudinal invariance of these measures over time remains understudied.This research explores the structural components of the Center for Epidemiological Studies Depression Scale(CES-D)and examines its consistency across various living environments and temporal stability in a cohort of Chinese teenagers.Method:In the initial phase,1,042 adolescents furnished demographic details and undertook the CES-D assessment.After a three-month interval,967 of these participants repeated the CES-D evaluation.The study employed Confirmatory factor analysis(CFA)to scrutinize the scale’s structural integrity.We investigated factorial invariance by conducting a twopronged CFA:one comparing urban vs.rural backgrounds,and another contrasting the results from the initial assessment with those from the follow-up.Results:The CES-D demonstrated adequate reliability in both rural and urban high school student samples.The preliminary four-factor model applied to the CES-D demonstrated a good fit with the collected data.Invariance tests,including multigroup analyses comparing rural and urban samples and longitudinal assessments,confirmed the scale’s invariance.Conclusions:The results suggest that the CES-D serves as a reliable instrument for evaluating depressive symptoms among Chinese adolescents.Its applicability is consistent across different living environments and remains stable over time.展开更多
Recently,human motion prediction has gained significant attention and achieved notable success.However,current methods primarily rely on training and testing with ideal datasets,overlooking the impact of variations in...Recently,human motion prediction has gained significant attention and achieved notable success.However,current methods primarily rely on training and testing with ideal datasets,overlooking the impact of variations in the viewing distance and viewing angle,which are commonly encountered in practical scenarios.In this study,we address the issue of model invariance by ensuring robust performance despite variations in view distances and angles.To achieve this,we employed Riemannian geometry methods to constrain the learning process of neural networks,enabling the prediction of invariances using a simple network.Furthermore,this enhances the application of motion prediction in various scenarios.Our framework uses Riemannian geometry to encode motion into a novel motion space to achieve prediction with an invariant viewing distance and angle using a simple network.Specifically,the specified path transport square-root velocity function is proposed to aid in removing the view-angle equivalence class and encode motion sequences into a flattened space.Motion coding by the geometry method linearizes the optimization problem in a non-flattened space and effectively extracts motion information,allowing the proposed method to achieve competitive performance using a simple network.Experimental results on Human 3.6M and CMU MoCap demonstrate that the proposed framework has competitive performance and invariance to the viewing distance and viewing angle.展开更多
In this article, generalized Birkhoff equations are put forward by adding supplementary terms to the Birkhoff equations. A conformal invariance of the Birkhoff equations can be used to study the generalized Birkhoff E...In this article, generalized Birkhoff equations are put forward by adding supplementary terms to the Birkhoff equations. A conformal invariance of the Birkhoff equations can be used to study the generalized Birkhoff Equations, and two examples are presented to illustrate the application of the results.展开更多
In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultan...In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.展开更多
This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differenti...This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.展开更多
This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the c...This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.展开更多
This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are g...This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.展开更多
This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding confor...This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.展开更多
This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigati...This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.展开更多
Background: Self-efficacy has been identified as an important determinant of youth's behavior change including physical activity(PA) participation. However, the dimensionality check of a PA self-efficacy scale has...Background: Self-efficacy has been identified as an important determinant of youth's behavior change including physical activity(PA) participation. However, the dimensionality check of a PA self-efficacy scale has rarely been conducted in China. The current study aims to examine(1) the unidimensionality of a shortened Chinese version of PA self-efficacy scale(S-PASESC);(2) the measurement invariance of S-PASESC across gender and levels of education;(3) the latent factor mean difference between gender and levels of education;(4) the direct effects of self-efficacy on PA by different gender and education levels; and(5) the comparisons of the direct effects of self-efficacy on PA across gender and education levels.Methods: The participants were 5 th through 11 th grade public school students recruited from 7 cities located in different geographic regions of China. The final data include a total of 3003 participants(49.7% boys) who have completed the scales.Results: Confirmatory factor analysis(CFA) test supported the unidimensionality of S-PASESC. The S-PASESC is invariant across gender and 3 levels of education at both configural, full metric, and full scalar levels. Findings from latent mean comparisons showed that boys reported higher PA self-efficacy than girls. Students' perceived PA self-efficacy tend to decrease from elementary to high school. Finally, self-efficacy positively related to PA by groups of different gender and education levels and the relationship between self-efficacy and PA is stronger among middle school boys than girls.Conclusion: Findings suggest S-PASESC is a valid scale for measuring Chinese students' PA self-efficacy.展开更多
The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new...The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is givea to illustrate the application of the results.展开更多
This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infini...This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.展开更多
Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativisti...Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D'Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.展开更多
In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is gi...In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.展开更多
Dear Editor,This letter is concerned with the attitude control for a novel tiltrotor unmanned aerial vehicle with two pairs of tiltable coaxial rotors and one rear rotor.An immersion and invariance-based adaptive atti...Dear Editor,This letter is concerned with the attitude control for a novel tiltrotor unmanned aerial vehicle with two pairs of tiltable coaxial rotors and one rear rotor.An immersion and invariance-based adaptive attitude controller for the tilt-rotor unmanned aerial vehicle is proposed.In the proposed control strategy,an adaptive update law is specially designed to compensate for the uncertainties of damping coefficients.The stability of the resulting closed-loop coaxial tiltrotor unmanned aerial vehicle(CTRUAV)system is proved by the Lyapunov methodology and LaSalle’s invariance theory.Finally。展开更多
A form invariance and a conserved quantity of the generalised Birkhoffian system are studied. First, a definition and a criterion of the form invariance are given. Secondly, through the form invariance, a new conserve...A form invariance and a conserved quantity of the generalised Birkhoffian system are studied. First, a definition and a criterion of the form invariance are given. Secondly, through the form invariance, a new conserved quantity can be deduced. Finally, an example is given to illustrate the application of the result.展开更多
文摘To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.
文摘The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation between the form invariance and the Noether symmetry is studied.
文摘To study the invariance of numerical character of matrix products and their statistical applications by matrix theory and linear model theory. Necessary and sufficient conditions are established for the product AB -C to have its numerical characters invariant with respect to every minimum norm g inverse, respectively. The algebraic results derived are then applied to investigate relationships among BLUE, WLSE and OLSE under the general Gauss? Markoff model.
文摘The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with the Noether symmetry and the Lie symmetry is discussed.
文摘Background:Valid and reliable measures of depressive symptoms are crucial for understanding risk factors,outcomes,and interventions across rural and urban settings.Despite this need,the longitudinal invariance of these measures over time remains understudied.This research explores the structural components of the Center for Epidemiological Studies Depression Scale(CES-D)and examines its consistency across various living environments and temporal stability in a cohort of Chinese teenagers.Method:In the initial phase,1,042 adolescents furnished demographic details and undertook the CES-D assessment.After a three-month interval,967 of these participants repeated the CES-D evaluation.The study employed Confirmatory factor analysis(CFA)to scrutinize the scale’s structural integrity.We investigated factorial invariance by conducting a twopronged CFA:one comparing urban vs.rural backgrounds,and another contrasting the results from the initial assessment with those from the follow-up.Results:The CES-D demonstrated adequate reliability in both rural and urban high school student samples.The preliminary four-factor model applied to the CES-D demonstrated a good fit with the collected data.Invariance tests,including multigroup analyses comparing rural and urban samples and longitudinal assessments,confirmed the scale’s invariance.Conclusions:The results suggest that the CES-D serves as a reliable instrument for evaluating depressive symptoms among Chinese adolescents.Its applicability is consistent across different living environments and remains stable over time.
基金supported by the Beijing Municipal Science and Technology Commission and Zhongguancun Science Park Management Committee,No.Z221100002722020National Nature Science Foundation of China,No.62072045Innovation Transfer Fund of Peking University Third Hospital,No.BYSYZHKC2021110。
文摘Recently,human motion prediction has gained significant attention and achieved notable success.However,current methods primarily rely on training and testing with ideal datasets,overlooking the impact of variations in the viewing distance and viewing angle,which are commonly encountered in practical scenarios.In this study,we address the issue of model invariance by ensuring robust performance despite variations in view distances and angles.To achieve this,we employed Riemannian geometry methods to constrain the learning process of neural networks,enabling the prediction of invariances using a simple network.Furthermore,this enhances the application of motion prediction in various scenarios.Our framework uses Riemannian geometry to encode motion into a novel motion space to achieve prediction with an invariant viewing distance and angle using a simple network.Specifically,the specified path transport square-root velocity function is proposed to aid in removing the view-angle equivalence class and encode motion sequences into a flattened space.Motion coding by the geometry method linearizes the optimization problem in a non-flattened space and effectively extracts motion information,allowing the proposed method to achieve competitive performance using a simple network.Experimental results on Human 3.6M and CMU MoCap demonstrate that the proposed framework has competitive performance and invariance to the viewing distance and viewing angle.
基金the National Natural Science Foundation of China(10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education,China(20040007022)
文摘In this article, generalized Birkhoff equations are put forward by adding supplementary terms to the Birkhoff equations. A conformal invariance of the Birkhoff equations can be used to study the generalized Birkhoff Equations, and two examples are presented to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant Nos 10372053,10572021 and 10772025)the National Natural Science Foundation of Henan province of China(Grant No 0311010900)
文摘In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022)
文摘This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022)
文摘This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.
基金supported by the National Natural Science Foundation of China (Grant No 10372053)the Natural Science Foundation of Henan Province,China (Grant Nos 082300410330 and 082300410370)
文摘This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant No10772025)the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China (Grant No 08KJB130002)
文摘This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.
基金Supported by National Natural Science Foundation of China under Grant No. 10972151the Natural Science Foundation of Higher Education Institution of Jiangsu Province under Grant No. 08KJB130002
文摘This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.
基金supported by a grant from the National Social Science Foundation of China (No. 13CTY031)
文摘Background: Self-efficacy has been identified as an important determinant of youth's behavior change including physical activity(PA) participation. However, the dimensionality check of a PA self-efficacy scale has rarely been conducted in China. The current study aims to examine(1) the unidimensionality of a shortened Chinese version of PA self-efficacy scale(S-PASESC);(2) the measurement invariance of S-PASESC across gender and levels of education;(3) the latent factor mean difference between gender and levels of education;(4) the direct effects of self-efficacy on PA by different gender and education levels; and(5) the comparisons of the direct effects of self-efficacy on PA across gender and education levels.Methods: The participants were 5 th through 11 th grade public school students recruited from 7 cities located in different geographic regions of China. The final data include a total of 3003 participants(49.7% boys) who have completed the scales.Results: Confirmatory factor analysis(CFA) test supported the unidimensionality of S-PASESC. The S-PASESC is invariant across gender and 3 levels of education at both configural, full metric, and full scalar levels. Findings from latent mean comparisons showed that boys reported higher PA self-efficacy than girls. Students' perceived PA self-efficacy tend to decrease from elementary to high school. Finally, self-efficacy positively related to PA by groups of different gender and education levels and the relationship between self-efficacy and PA is stronger among middle school boys than girls.Conclusion: Findings suggest S-PASESC is a valid scale for measuring Chinese students' PA self-efficacy.
文摘The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is givea to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10472040, 10572021 and 10772025)the Outstanding Young Talents Training Found of Liaoning Province of China (Grant No 3040005)
文摘This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.
基金The project supported by National Natural Science Foundation of China under Grant No. 19972010, and Natural Science Foundation of Henan Province under Grant Nos. 984053100 and 998040080
文摘Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D'Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.
文摘In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.
文摘Dear Editor,This letter is concerned with the attitude control for a novel tiltrotor unmanned aerial vehicle with two pairs of tiltable coaxial rotors and one rear rotor.An immersion and invariance-based adaptive attitude controller for the tilt-rotor unmanned aerial vehicle is proposed.In the proposed control strategy,an adaptive update law is specially designed to compensate for the uncertainties of damping coefficients.The stability of the resulting closed-loop coaxial tiltrotor unmanned aerial vehicle(CTRUAV)system is proved by the Lyapunov methodology and LaSalle’s invariance theory.Finally。
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10772025,10932002)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics
文摘A form invariance and a conserved quantity of the generalised Birkhoffian system are studied. First, a definition and a criterion of the form invariance are given. Secondly, through the form invariance, a new conserved quantity can be deduced. Finally, an example is given to illustrate the application of the result.
