In reinventing itself, the Shanghai Cooperation Organization should stick to being a regional cooperative organization guided by a new concept and prioritizing security and economic cooperation. Meanwhile, brash expan...In reinventing itself, the Shanghai Cooperation Organization should stick to being a regional cooperative organization guided by a new concept and prioritizing security and economic cooperation. Meanwhile, brash expansion of the organization will cause a lot of problems.展开更多
In this paper, the Almgren＇s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group：-Cu＋V（z,t）u=Xi（aij（z,t）Xju）＋V（z,t）u=0 is introduced. The monotonicity ...In this paper, the Almgren＇s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group：-Cu＋V（z,t）u=Xi（aij（z,t）Xju）＋V（z,t）u=0 is introduced. The monotonicity property of the frequency is established and a doubling condition is obtained. Consequently, a quantitative proof of the strong unique continuation property for such equation is given.展开更多
The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a u...The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a uniqueness result and a reciprocal theorem.The proof of the reciprocal theorem avoids both using the Laplace transform and incorporating the initial conditions into the equations of motion.The uniqueness theorem is derived with no definiteness assumption on the elastic constitutive coefficients.Then the continuous dependence theorem is discussed upon two external data systems.Finally,the variational principle of Hamilton type which fully characterizes the solution of the mixed boundary-initial-value problem（mixed problem） is obtained.These theorems lay a solid foundation for further theoretical and numerical studies on microstretch thermomagnetoelectroelastic materials.展开更多
文摘In reinventing itself, the Shanghai Cooperation Organization should stick to being a regional cooperative organization guided by a new concept and prioritizing security and economic cooperation. Meanwhile, brash expansion of the organization will cause a lot of problems.
基金Project supported by the National Natural Science Foundation of China (Nos. 11071119, 11101132)
文摘In this paper, the Almgren＇s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group：-Cu＋V（z,t）u=Xi（aij（z,t）Xju）＋V（z,t）u=0 is introduced. The monotonicity property of the frequency is established and a doubling condition is obtained. Consequently, a quantitative proof of the strong unique continuation property for such equation is given.
基金Project supported by the National Natural Science Fundation of China(Nos.11572358 and 11272223)the Training Program for Leading Talent in University Innovative Research Team in Hebei Province(No.LJRC006)
文摘The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a uniqueness result and a reciprocal theorem.The proof of the reciprocal theorem avoids both using the Laplace transform and incorporating the initial conditions into the equations of motion.The uniqueness theorem is derived with no definiteness assumption on the elastic constitutive coefficients.Then the continuous dependence theorem is discussed upon two external data systems.Finally,the variational principle of Hamilton type which fully characterizes the solution of the mixed boundary-initial-value problem（mixed problem） is obtained.These theorems lay a solid foundation for further theoretical and numerical studies on microstretch thermomagnetoelectroelastic materials.
