The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak so...The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.展开更多
We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone non...We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n＋α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system：This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate展开更多
To improve the operation situation of difficulty and low efficiency in the extraction of fermented grains(FG),a high-load and large-workspace reclaiming robot for ceramic cylinder fermentation is designed,and a reclai...To improve the operation situation of difficulty and low efficiency in the extraction of fermented grains(FG),a high-load and large-workspace reclaiming robot for ceramic cylinder fermentation is designed,and a reclaiming effector is designed according to the operating characteristics.Firstly,the kinematics and singularity of the mechanism are analyzed.A multi-domain polar coordinate search method is proposed to obtain the workspace and the volume of the mechanism.Secondly,the dynamic modeling is completed and the example simulation is carried out.Thirdly,the motion-force transmission index of the mechanism is established.And based on the global transmissibility and the good-transmission workspace,the dimensional synthesis of the driving mechanism is completed by using the performance atlas-based method.Finally,aiming at the regular workspace size,stiffness and loading capacity,the Pareto optimal solution set of the executive mechanism dimension is obtained by using the multi-objective particle swarm optimization(MOPSO)algorithm.This paper can provide a theoretical basis for the optimal design and control of FG reclaiming robot.展开更多
In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We ...In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].展开更多
We study the anti-symmetric solutions to the Lane-Emden type system involving fractional Laplacian(-△)^(s)(0<s<1).First,we obtain a Liouville type theorem in the often-used defining space L_(2s).An interesting ...We study the anti-symmetric solutions to the Lane-Emden type system involving fractional Laplacian(-△)^(s)(0<s<1).First,we obtain a Liouville type theorem in the often-used defining space L_(2s).An interesting lower bound on the solutions is derived to estimate the Lipschitz coefficient in the sub-linear cases.Considering the anti-symmetric property,one can naturally extend the defining space from L_(2s) to L_(2s+1).Surprisingly,with this extension,we show the existence of non-trivial solutions.This is very different from the previous results of the Lane-Emden system.展开更多
基金partially supported by NSFC(11831003,12031012)the Institute of Modern Analysis-A Frontier Research Center of Shanghai。
文摘The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.
基金supported by NSF Grant DMS-0604638Li partially supported by NSF Grant DMS-0401174
文摘We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n＋α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system：This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate
基金supported by the National Natural Science Foundation of China(No.51905367)。
文摘To improve the operation situation of difficulty and low efficiency in the extraction of fermented grains(FG),a high-load and large-workspace reclaiming robot for ceramic cylinder fermentation is designed,and a reclaiming effector is designed according to the operating characteristics.Firstly,the kinematics and singularity of the mechanism are analyzed.A multi-domain polar coordinate search method is proposed to obtain the workspace and the volume of the mechanism.Secondly,the dynamic modeling is completed and the example simulation is carried out.Thirdly,the motion-force transmission index of the mechanism is established.And based on the global transmissibility and the good-transmission workspace,the dimensional synthesis of the driving mechanism is completed by using the performance atlas-based method.Finally,aiming at the regular workspace size,stiffness and loading capacity,the Pareto optimal solution set of the executive mechanism dimension is obtained by using the multi-objective particle swarm optimization(MOPSO)algorithm.This paper can provide a theoretical basis for the optimal design and control of FG reclaiming robot.
基金Partially supported by NSFC(11571233)NSF DMS-1405175+1 种基金NSF of Shanghai16ZR1402100China Scholarship Council
文摘In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].
基金supported by National Natural Science Foundation of China(Grant Nos.12031012,11831003 and 11701207)Natural Science Foundation of Henan Province of China(Grant No.222300420499)。
文摘We study the anti-symmetric solutions to the Lane-Emden type system involving fractional Laplacian(-△)^(s)(0<s<1).First,we obtain a Liouville type theorem in the often-used defining space L_(2s).An interesting lower bound on the solutions is derived to estimate the Lipschitz coefficient in the sub-linear cases.Considering the anti-symmetric property,one can naturally extend the defining space from L_(2s) to L_(2s+1).Surprisingly,with this extension,we show the existence of non-trivial solutions.This is very different from the previous results of the Lane-Emden system.
