Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clar...Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic：liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liqUid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures.展开更多
In the article,we prove that the inequalities H_(p)(K(r);E(r))>π/2;L_(q)(K(r);E(r))>π/2 hold for all r 2(0;1)if and only if p≥3=4 and q≥3=4,where Hp(a;b)and Lq(a;b)are respectively the p-th power-type Heroni...In the article,we prove that the inequalities H_(p)(K(r);E(r))>π/2;L_(q)(K(r);E(r))>π/2 hold for all r 2(0;1)if and only if p≥3=4 and q≥3=4,where Hp(a;b)and Lq(a;b)are respectively the p-th power-type Heronian mean and q-th Lehmer mean of a and b,and K(r)and E(r)are respectively the complete elliptic integrals of the first and second kinds.展开更多
This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋o...This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋ （N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3） 〉 0. On the other hand, for co 〈 ＋∞ and α（p - 3） 〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.展开更多
该文基于大电网运行实践,聚焦于全网电力平衡资源的统一优化,研究新型电力系统的全网一体化电力平衡(integrated power balancing,IPB)机理。首先,构建IPB的数学模型,其中涉及“平衡区域”、“输电通道”和“输电路径”等关键要素。基...该文基于大电网运行实践,聚焦于全网电力平衡资源的统一优化,研究新型电力系统的全网一体化电力平衡(integrated power balancing,IPB)机理。首先,构建IPB的数学模型,其中涉及“平衡区域”、“输电通道”和“输电路径”等关键要素。基于数学模型,推导IPB的网络方程,用以描述网络结构约束;其次,将电力平衡目标如电力供应和新能源消纳等与网络方程结合,推导作为IPB基本数学原理的动态方程,方程由4种过程形式组成——自然互济供电、成本互济供电、自然互济新能源消纳和成本互济新能源消纳;再次,将实际工程条件引入动态方程,分析总结工程实践用一体化电力平衡基础模式及其衍生的8种子构型;最后,通过实例验证所提理论分析的有效性和意义。展开更多
基金supported by the National Natural Science Foundation of China(No.10272034)the Fundamental Research Funds for the Central Universities of China(No.HEUCF130205)
文摘Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic：liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liqUid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures.
基金Supported by the National Natural Science Foundation of China(11971142)the Natural Science Foundation of Zhejiang Province(LY19A010012)。
文摘In the article,we prove that the inequalities H_(p)(K(r);E(r))>π/2;L_(q)(K(r);E(r))>π/2 hold for all r 2(0;1)if and only if p≥3=4 and q≥3=4,where Hp(a;b)and Lq(a;b)are respectively the p-th power-type Heronian mean and q-th Lehmer mean of a and b,and K(r)and E(r)are respectively the complete elliptic integrals of the first and second kinds.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171241, 10801102,11071177)Sichuan Youth Science and Technology Foundation (Grant No. 07ZQ026-009)China Postdoctoral Science Foundation Funded Project
文摘This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋ （N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3） 〉 0. On the other hand, for co 〈 ＋∞ and α（p - 3） 〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.
文摘该文基于大电网运行实践,聚焦于全网电力平衡资源的统一优化,研究新型电力系统的全网一体化电力平衡(integrated power balancing,IPB)机理。首先,构建IPB的数学模型,其中涉及“平衡区域”、“输电通道”和“输电路径”等关键要素。基于数学模型,推导IPB的网络方程,用以描述网络结构约束;其次,将电力平衡目标如电力供应和新能源消纳等与网络方程结合,推导作为IPB基本数学原理的动态方程,方程由4种过程形式组成——自然互济供电、成本互济供电、自然互济新能源消纳和成本互济新能源消纳;再次,将实际工程条件引入动态方程,分析总结工程实践用一体化电力平衡基础模式及其衍生的8种子构型;最后,通过实例验证所提理论分析的有效性和意义。
