The Dirac hierarchy of isospectral evolution equations associated with the Dirac spectral problem are studied in this paper. The commutator representations of Dirac hierarchy are first presented, and then through the ...The Dirac hierarchy of isospectral evolution equations associated with the Dirac spectral problem are studied in this paper. The commutator representations of Dirac hierarchy are first presented, and then through the nonlinearization of Lax pair the involutive solutions of Dirac hierarchy are obtained.展开更多
In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the repr...In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.展开更多
Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be...Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.展开更多
The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system an...The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system and showed that the time evolution equations for n≤3 obtained by nonlinearizing the time parts of Lax systems for AKNS hierarchy are Liouville integrable under the constraint of the spatial part.展开更多
Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and...Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and their uniqueness is proven. In previous works, the main research method for the study scalar singular integral operators and Riemann boundary value problems with Carlemann shift were operator identities, which allowed to eliminate shift and to reduce scalar problems to matrix problems without shift. In this study, the operator identities were used for the opposite purpose: to transform operators of multiplication by matrix-functions into scalar operators with Carlemann linear-fractional shift.展开更多
This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers ...This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations.展开更多
It is well known that, making use of isospectral technique of Lax, we can obtain involutive integrals of motion for some classical integrable systems. Flaschka first applied this Lax trick to the Toda lattice. Afterwa...It is well known that, making use of isospectral technique of Lax, we can obtain involutive integrals of motion for some classical integrable systems. Flaschka first applied this Lax trick to the Toda lattice. Afterwards, Moser gave the Lax pairs corresponding展开更多
In this paper, the behaviors of involutive bases under composition operation are studied. For two kinds of involutive bases, i.e., Pommaret bases, Janet bases, we study their behavior problems under composition. Some ...In this paper, the behaviors of involutive bases under composition operation are studied. For two kinds of involutive bases, i.e., Pommaret bases, Janet bases, we study their behavior problems under composition. Some further problems are also proposed.展开更多
In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface...In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.展开更多
Background:The concept of“involution”has garnered significant attention within China’s education system,encapsulating students’perceptions of intense and often fruitless academic competition.However,the impact of ...Background:The concept of“involution”has garnered significant attention within China’s education system,encapsulating students’perceptions of intense and often fruitless academic competition.However,the impact of perceived involution on students’psychological outcomes,particularly academic burnout,remains underexplored.This study examines the relationship between perceived involution and academic burnout among university students.Specifically,it examines whether anxiety mediates this relationship and whether self-control moderates the effect of perceived involution on anxiety.Methods:A cross-sectional survey was administered to 673 university students in China.Standardized scales were employed to measure perceived involution,anxiety,self-control,and academic burnout.Data analysis was performed using SPSS 26.0 and the PROCESS macro(version 4.2),incorporating mediation(Model 4)and moderation(Model 7)analyses with bootstrapping procedures.Results:Perceived involution was positively associated with academic burnout(β=0.25,p<0.01),accounting for approximately 6%of the variance,which indicates a small-to-moderate effect.Anxiety partially mediated this relationship,with a significant indirect effect(B=0.0013,95%CI[0.0003,0.0029]).Furthermore,self-control significantly moderated the association between perceived involution and anxiety(interactionβ=0.19,p=0.03),such that the positive effect of perceived involution on anxiety was attenuated among students with higher self-control.Although the effect sizes were modest,these findings suggest meaningful psychological and practical implications at the population level in highly competitive academic environments.Conclusion:These findings suggest that perceived involution contributes to academic burnout by exacerbating anxiety,while self-control serves as a protective factor against it.The study offers theoretical insights into the emotional mechanisms underlying burnout and provides practical implications for stress intervention and mental health promotion in higher education.展开更多
Under the constrained condition induced by the eigenfunctions and the potentials, the Laxsystems of nonlinear evolution equations in relation to a matris eigenvalue problem are nonlin-earized to be a completely integr...Under the constrained condition induced by the eigenfunctions and the potentials, the Laxsystems of nonlinear evolution equations in relation to a matris eigenvalue problem are nonlin-earized to be a completely integrable system (R^(zN),dp∧dq, H), while the time part of it isnonlinearized to be its N-involutive system {F_m}. The involutive solution of the compatiblesystem (F_0), (F_m) is transformed into the solution of the m-th nonlinear evolution equation.展开更多
We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated...We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.展开更多
The scroll expander,as the core component of the micro-compressed air energy storage and power generation system,directly affects the output efficiency of the system.Meanwhile,the scroll profile plays a central role i...The scroll expander,as the core component of the micro-compressed air energy storage and power generation system,directly affects the output efficiency of the system.Meanwhile,the scroll profile plays a central role in determining the output performance of the scroll expander.In this study,in order to investigate the output characteristics of a variable cross-section scroll expander,numerical simulation and experimental studies were con-ducted by using Computational Fluid Dynamics(CFD)methods and dynamic mesh techniques.The impact of critical parameters on the output performance of the scroll expander was analyzed through the utilization of the control variable method.It is found that increasing the inlet pressure and temperature within a certain range can improve the output power of the scroll expander.However,the increase in temperature and meshing clearance leads to a decline in the overall output performance of the scroll expander,leading to a decrease in volumetric efficiency by 8.43%and 12.79%,respectively.The experiments demonstrate that under equal inlet pressure conditions,increasing the inlet temperature elevates both the rotational speed and torque output of the scroll expander.Specifically,compared to operating at normal temperatures,the output torque increases by 21.8%under high-temperature conditions.However,the rate of speed and torque variation decreases as a consequence of enlarged meshing clearance,resulting in increased internal leakage and reduction in isentropic efficiency.展开更多
Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R2N,dp^dq, H0=1/2F0)(F0= (^q,p) + (^p,p) + (p,q)2)....Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R2N,dp^dq, H0=1/2F0)(F0= (^q,p) + (^p,p) + (p,q)2). While the nonlinearization of the time part leads to its N-involutive system (Fm).展开更多
文摘The Dirac hierarchy of isospectral evolution equations associated with the Dirac spectral problem are studied in this paper. The commutator representations of Dirac hierarchy are first presented, and then through the nonlinearization of Lax pair the involutive solutions of Dirac hierarchy are obtained.
文摘In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.
文摘Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.
文摘The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system and showed that the time evolution equations for n≤3 obtained by nonlinearizing the time parts of Lax systems for AKNS hierarchy are Liouville integrable under the constraint of the spatial part.
文摘Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and their uniqueness is proven. In previous works, the main research method for the study scalar singular integral operators and Riemann boundary value problems with Carlemann shift were operator identities, which allowed to eliminate shift and to reduce scalar problems to matrix problems without shift. In this study, the operator identities were used for the opposite purpose: to transform operators of multiplication by matrix-functions into scalar operators with Carlemann linear-fractional shift.
基金This work was supported in part by a National Key Basic Research Project of China(No.G19980306)the National Natural Science Foundation of China(Grant No.69725002).
文摘This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations.
文摘It is well known that, making use of isospectral technique of Lax, we can obtain involutive integrals of motion for some classical integrable systems. Flaschka first applied this Lax trick to the Toda lattice. Afterwards, Moser gave the Lax pairs corresponding
基金The research was supported by Key Project of Educational Department of Sichuan Province under Grant No.2006A141.
文摘In this paper, the behaviors of involutive bases under composition operation are studied. For two kinds of involutive bases, i.e., Pommaret bases, Janet bases, we study their behavior problems under composition. Some further problems are also proposed.
文摘In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.
基金funded by the Fundamental Research Funds for the Central Universities,Zhongnan University of Economics and Law(Grant 2722022DS002)Projects of Hubei Provincial Education Science Planning(Grant 2023GA020).
文摘Background:The concept of“involution”has garnered significant attention within China’s education system,encapsulating students’perceptions of intense and often fruitless academic competition.However,the impact of perceived involution on students’psychological outcomes,particularly academic burnout,remains underexplored.This study examines the relationship between perceived involution and academic burnout among university students.Specifically,it examines whether anxiety mediates this relationship and whether self-control moderates the effect of perceived involution on anxiety.Methods:A cross-sectional survey was administered to 673 university students in China.Standardized scales were employed to measure perceived involution,anxiety,self-control,and academic burnout.Data analysis was performed using SPSS 26.0 and the PROCESS macro(version 4.2),incorporating mediation(Model 4)and moderation(Model 7)analyses with bootstrapping procedures.Results:Perceived involution was positively associated with academic burnout(β=0.25,p<0.01),accounting for approximately 6%of the variance,which indicates a small-to-moderate effect.Anxiety partially mediated this relationship,with a significant indirect effect(B=0.0013,95%CI[0.0003,0.0029]).Furthermore,self-control significantly moderated the association between perceived involution and anxiety(interactionβ=0.19,p=0.03),such that the positive effect of perceived involution on anxiety was attenuated among students with higher self-control.Although the effect sizes were modest,these findings suggest meaningful psychological and practical implications at the population level in highly competitive academic environments.Conclusion:These findings suggest that perceived involution contributes to academic burnout by exacerbating anxiety,while self-control serves as a protective factor against it.The study offers theoretical insights into the emotional mechanisms underlying burnout and provides practical implications for stress intervention and mental health promotion in higher education.
文摘Under the constrained condition induced by the eigenfunctions and the potentials, the Laxsystems of nonlinear evolution equations in relation to a matris eigenvalue problem are nonlin-earized to be a completely integrable system (R^(zN),dp∧dq, H), while the time part of it isnonlinearized to be its N-involutive system {F_m}. The involutive solution of the compatiblesystem (F_0), (F_m) is transformed into the solution of the m-th nonlinear evolution equation.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11371178） and the National Science Foundation of US （Grant No. DMS 1001855）.
文摘We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.
基金funded by the National Key Research and Development Program of China(No.2024YFE0208100).
文摘The scroll expander,as the core component of the micro-compressed air energy storage and power generation system,directly affects the output efficiency of the system.Meanwhile,the scroll profile plays a central role in determining the output performance of the scroll expander.In this study,in order to investigate the output characteristics of a variable cross-section scroll expander,numerical simulation and experimental studies were con-ducted by using Computational Fluid Dynamics(CFD)methods and dynamic mesh techniques.The impact of critical parameters on the output performance of the scroll expander was analyzed through the utilization of the control variable method.It is found that increasing the inlet pressure and temperature within a certain range can improve the output power of the scroll expander.However,the increase in temperature and meshing clearance leads to a decline in the overall output performance of the scroll expander,leading to a decrease in volumetric efficiency by 8.43%and 12.79%,respectively.The experiments demonstrate that under equal inlet pressure conditions,increasing the inlet temperature elevates both the rotational speed and torque output of the scroll expander.Specifically,compared to operating at normal temperatures,the output torque increases by 21.8%under high-temperature conditions.However,the rate of speed and torque variation decreases as a consequence of enlarged meshing clearance,resulting in increased internal leakage and reduction in isentropic efficiency.
文摘Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R2N,dp^dq, H0=1/2F0)(F0= (^q,p) + (^p,p) + (p,q)2). While the nonlinearization of the time part leads to its N-involutive system (Fm).
