The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calcu...The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum p<sub>θ</sub> and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.展开更多
The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-mom...The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived . The existing related results are naturally derived as special cases from the results proposed in this paper . The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization .展开更多
High-dimensional and incomplete(HDI) matrices are primarily generated in all kinds of big-data-related practical applications. A latent factor analysis(LFA) model is capable of conducting efficient representation lear...High-dimensional and incomplete(HDI) matrices are primarily generated in all kinds of big-data-related practical applications. A latent factor analysis(LFA) model is capable of conducting efficient representation learning to an HDI matrix,whose hyper-parameter adaptation can be implemented through a particle swarm optimizer(PSO) to meet scalable requirements.However, conventional PSO is limited by its premature issues,which leads to the accuracy loss of a resultant LFA model. To address this thorny issue, this study merges the information of each particle's state migration into its evolution process following the principle of a generalized momentum method for improving its search ability, thereby building a state-migration particle swarm optimizer(SPSO), whose theoretical convergence is rigorously proved in this study. It is then incorporated into an LFA model for implementing efficient hyper-parameter adaptation without accuracy loss. Experiments on six HDI matrices indicate that an SPSO-incorporated LFA model outperforms state-of-the-art LFA models in terms of prediction accuracy for missing data of an HDI matrix with competitive computational efficiency.Hence, SPSO's use ensures efficient and reliable hyper-parameter adaptation in an LFA model, thus ensuring practicality and accurate representation learning for HDI matrices.展开更多
文摘The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum p<sub>θ</sub> and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.
基金the National Natural Science Foundation of China (10072024) the Research Foundation of Liaoning Education Committee (990111001)
文摘The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived . The existing related results are naturally derived as special cases from the results proposed in this paper . The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization .
基金supported in part by the National Natural Science Foundation of China (62372385, 62272078, 62002337)the Chongqing Natural Science Foundation (CSTB2022NSCQ-MSX1486, CSTB2023NSCQ-LZX0069)the Deanship of Scientific Research at King Abdulaziz University, Jeddah, Saudi Arabia (RG-12-135-43)。
文摘High-dimensional and incomplete(HDI) matrices are primarily generated in all kinds of big-data-related practical applications. A latent factor analysis(LFA) model is capable of conducting efficient representation learning to an HDI matrix,whose hyper-parameter adaptation can be implemented through a particle swarm optimizer(PSO) to meet scalable requirements.However, conventional PSO is limited by its premature issues,which leads to the accuracy loss of a resultant LFA model. To address this thorny issue, this study merges the information of each particle's state migration into its evolution process following the principle of a generalized momentum method for improving its search ability, thereby building a state-migration particle swarm optimizer(SPSO), whose theoretical convergence is rigorously proved in this study. It is then incorporated into an LFA model for implementing efficient hyper-parameter adaptation without accuracy loss. Experiments on six HDI matrices indicate that an SPSO-incorporated LFA model outperforms state-of-the-art LFA models in terms of prediction accuracy for missing data of an HDI matrix with competitive computational efficiency.Hence, SPSO's use ensures efficient and reliable hyper-parameter adaptation in an LFA model, thus ensuring practicality and accurate representation learning for HDI matrices.
