In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is ...In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.展开更多
在试验结果的基础上,分析制冷量和能效比随干湿球温度的变化特性。用赤池信息量准则(Akaike information criterion,AIC)选取制冷量和能效比最优拟合三维曲面方程,求解制冷量和能效比随干湿球温度变化的梯度极值区间,以两者梯度极值区...在试验结果的基础上,分析制冷量和能效比随干湿球温度的变化特性。用赤池信息量准则(Akaike information criterion,AIC)选取制冷量和能效比最优拟合三维曲面方程,求解制冷量和能效比随干湿球温度变化的梯度极值区间,以两者梯度极值区间内干湿球温度允差范围的并集为A级、现行干湿球温度允差为C级,以各级最大(最小)能效比变化率相等原则,对允差进行三级非线性划分。实例表明随着允差等级的升高,能效比最大变化率由5.19%缩减至1.04%,分级允差能够更加准确地判别房间空调器的能效等级,并给国家标准的修订提供参考。展开更多
The iteration maps of Euler family for finding zeros of an operatorf in Banach spaces is defined as the partial sum of Taylor expansion of the local inversef z -1 off atz. The unified convergence theorem is establishe...The iteration maps of Euler family for finding zeros of an operatorf in Banach spaces is defined as the partial sum of Taylor expansion of the local inversef z -1 off atz. The unified convergence theorem is established for the iterations of Euler family under the assumption that $\alpha \leqslant 3 - 2\sqrt 2 $ , while the strong condition thatf is analytic in Smale’s criterion α is replaced by the weak condition thatf is of finite order derivative.展开更多
基金supported by National Natural Science Foundation of China(No.12005141)supported by National Natural Science Foundation of China(No.11805273)+2 种基金supported by the Collaborative Innovation Program of Hefei Science Center,CAS(No.2021HSCCIP019)National MC Energy R&D Program(No.2018YFE0304100)National Natural Science Foundation of China(No.11905220)。
文摘In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.
文摘在试验结果的基础上,分析制冷量和能效比随干湿球温度的变化特性。用赤池信息量准则(Akaike information criterion,AIC)选取制冷量和能效比最优拟合三维曲面方程,求解制冷量和能效比随干湿球温度变化的梯度极值区间,以两者梯度极值区间内干湿球温度允差范围的并集为A级、现行干湿球温度允差为C级,以各级最大(最小)能效比变化率相等原则,对允差进行三级非线性划分。实例表明随着允差等级的升高,能效比最大变化率由5.19%缩减至1.04%,分级允差能够更加准确地判别房间空调器的能效等级,并给国家标准的修订提供参考。
文摘The iteration maps of Euler family for finding zeros of an operatorf in Banach spaces is defined as the partial sum of Taylor expansion of the local inversef z -1 off atz. The unified convergence theorem is established for the iterations of Euler family under the assumption that $\alpha \leqslant 3 - 2\sqrt 2 $ , while the strong condition thatf is analytic in Smale’s criterion α is replaced by the weak condition thatf is of finite order derivative.
