The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems c...The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems containing strict inequalities. With the regular decomposition of semi-algebraic systems and the partial cylindrical algebraic decomposition method, we give a method to compute the supremum of the number of torsion-free real zeros of a given zero-dimensional parametric piecewise algebraic variety, and to get distributions of the number of real zeros in every n-dimensional cell when the number reaches the supremum. This method also produces corresponding necessary and sufficient conditions for reaching the supremum and its distributions. We also present an algorithm to produce a necessary and sufficient condition for a given zero-dimensional parametric piecewise algebraic variety to have a given number of distinct torsion-free real zeros in every n-cell in the n-complex.展开更多
磁耦合无线电能传输(Magnetic coupling wireless power transfer,MC-WPT)系统的能效受原副边线圈距离的影响较大。在过耦合状态下,由于发生了频率分裂,会导致系统的能效随着传输距离的减小而下降。通过本征模态理论求取系统的实本征态...磁耦合无线电能传输(Magnetic coupling wireless power transfer,MC-WPT)系统的能效受原副边线圈距离的影响较大。在过耦合状态下,由于发生了频率分裂,会导致系统的能效随着传输距离的减小而下降。通过本征模态理论求取系统的实本征态工作条件使系统在过耦合区保证在零相角点处以最大能效工作。并从零相角点的角度出发对比该工作模式和实本征态模式的相似之处。从而实现了利用频率跟踪使系统在过耦合区保持恒功率和恒效率输出。最后,进行了仿真验证,证实了本文计算结果的正确性。展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10271022, 60373093,60533060)the Natural Science Foundation of Zhejiang Province (Grant No. Y7080068)the Foundation of Department of Education of Zhejiang Province (Grant Nos. 20070628 and Y200802999)
文摘The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems containing strict inequalities. With the regular decomposition of semi-algebraic systems and the partial cylindrical algebraic decomposition method, we give a method to compute the supremum of the number of torsion-free real zeros of a given zero-dimensional parametric piecewise algebraic variety, and to get distributions of the number of real zeros in every n-dimensional cell when the number reaches the supremum. This method also produces corresponding necessary and sufficient conditions for reaching the supremum and its distributions. We also present an algorithm to produce a necessary and sufficient condition for a given zero-dimensional parametric piecewise algebraic variety to have a given number of distinct torsion-free real zeros in every n-cell in the n-complex.
文摘磁耦合无线电能传输(Magnetic coupling wireless power transfer,MC-WPT)系统的能效受原副边线圈距离的影响较大。在过耦合状态下,由于发生了频率分裂,会导致系统的能效随着传输距离的减小而下降。通过本征模态理论求取系统的实本征态工作条件使系统在过耦合区保证在零相角点处以最大能效工作。并从零相角点的角度出发对比该工作模式和实本征态模式的相似之处。从而实现了利用频率跟踪使系统在过耦合区保持恒功率和恒效率输出。最后,进行了仿真验证,证实了本文计算结果的正确性。
