This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an ...This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an antisymmetric constant N×N matrix,V(t,q)=-K(t,q)+W(t,q)with K,W ∈C^(1)(R,R^(N))and satisfying b1|q|^(2)≤K(t,q)≤b_(2)|q|^(2)for some positive constants b_(2)≥b_(1)>0 and external forcing term f∈C(R,R^(N))being small enough.Under some new weak superquadratic conditions for W,by using the mountain pass theorem,we obtain the existence of at least one nontrivial homoclinic solution.展开更多
In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this p...In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this paper.First,in the bounded domain,we use the moving plane method to show that the solution is radially symmetric.Second,for the unbounded domain,in view of the idea of the sliding method,we find the existence of the maximizing sequence of the bounded solution,then obtain that the solution is strictly monotone increasing in some direction.展开更多
Quantum paradoxes are essential means to reveal the incompatibility between quantum and classical theories,among which the Einstein–Podolsky–Rosen(EPR)steering paradox offers a sharper criterion for the contradictio...Quantum paradoxes are essential means to reveal the incompatibility between quantum and classical theories,among which the Einstein–Podolsky–Rosen(EPR)steering paradox offers a sharper criterion for the contradiction between localhidden-state model and quantum mechanics than the usual inequality-based method.In this work,we present a generalized EPR steering paradox,which predicts a contradictory equality“2_(Q)=(1+δ)_(C)”(0≤δ<1)given by the quantum(Q)and classical(C)theories.For any N-qubit state in which the conditional state of the steered party is pure,we test the paradox through a two-setting steering protocol,and find that the state is steerable if some specific measurement requirements are satisfied.Moreover,our construction also enlightens the building of EPR steering inequality,which may contribute to some schemes for typical quantum teleportation and quantum key distributions.展开更多
Recent advances in single-cell sequencing technologies provide significant implications for understanding cellular heterogeneity,developmental biology,and disease mechanisms.To fully exploit the potential of these dat...Recent advances in single-cell sequencing technologies provide significant implications for understanding cellular heterogeneity,developmental biology,and disease mechanisms.To fully exploit the potential of these data,numerous tools have been proposed for upstream and downstream analyses.In the the single-cell RNA sequencing(scRNA-seq)community,scRNA-tools(Zappia et al.,2018)was proposed to help researchers navigate the plethora of tools by category.Since its inception,scRNA-tools has been widely used and its updated version further reveals trends in the field with over 1000 collected tools(Zappia and Theis,2021),providing a valuable guidance in selecting tools for analyses.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12171253).
文摘This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an antisymmetric constant N×N matrix,V(t,q)=-K(t,q)+W(t,q)with K,W ∈C^(1)(R,R^(N))and satisfying b1|q|^(2)≤K(t,q)≤b_(2)|q|^(2)for some positive constants b_(2)≥b_(1)>0 and external forcing term f∈C(R,R^(N))being small enough.Under some new weak superquadratic conditions for W,by using the mountain pass theorem,we obtain the existence of at least one nontrivial homoclinic solution.
基金partially supported by the Fundamental Research Funds for the Central Universities,Nankai Universitypartially supported by NSFC(Nos.12161141006,12111540249)+2 种基金the Natural Science Foundation of Tianjin(No.20JCJQJC00090)the Fundamental Research Funds for the Central Universities,Nankai Universitypartially supported by grant DFF-7014-00037B of Independent Research Fund Denmark。
基金partially supported by the NSFC(12271269)the Fundamental Research Funds for the Central Universitiespartially supported by the Fundamental Research Funds for the Central Universities(2021YJSB006)。
文摘In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this paper.First,in the bounded domain,we use the moving plane method to show that the solution is radially symmetric.Second,for the unbounded domain,in view of the idea of the sliding method,we find the existence of the maximizing sequence of the bounded solution,then obtain that the solution is strictly monotone increasing in some direction.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12275136 and 12075001)the 111 Project(Grant No.B23045)the Nankai Zhide Foundation.
文摘Quantum paradoxes are essential means to reveal the incompatibility between quantum and classical theories,among which the Einstein–Podolsky–Rosen(EPR)steering paradox offers a sharper criterion for the contradiction between localhidden-state model and quantum mechanics than the usual inequality-based method.In this work,we present a generalized EPR steering paradox,which predicts a contradictory equality“2_(Q)=(1+δ)_(C)”(0≤δ<1)given by the quantum(Q)and classical(C)theories.For any N-qubit state in which the conditional state of the steered party is pure,we test the paradox through a two-setting steering protocol,and find that the state is steerable if some specific measurement requirements are satisfied.Moreover,our construction also enlightens the building of EPR steering inequality,which may contribute to some schemes for typical quantum teleportation and quantum key distributions.
基金partially supported by NSFC(No.12171037)the Fundamental Research Funds for the Central Universities+5 种基金partially supported by NSFC(Nos.12171037,12271040)China Postdoctoral Science Foundation(No.2022M720261)partially supported by NSFC(Nos.11931007,11871282)Nankai Zhide Foundation and Tianjin Outstanding Talents FoundationChina Postdoctoral Science Foundation(No.BX20230018)National Key R&D Program of China(No.2020YFA0712800)。
基金supported by the National Key Research and Development Program of China(2021YFF1200902,2023YFF1204802)the National Natural Science Foundation of China(62203236,62273194)the Fundamental Research Funds for the Central Universities,Nankai University(63231137).
文摘Recent advances in single-cell sequencing technologies provide significant implications for understanding cellular heterogeneity,developmental biology,and disease mechanisms.To fully exploit the potential of these data,numerous tools have been proposed for upstream and downstream analyses.In the the single-cell RNA sequencing(scRNA-seq)community,scRNA-tools(Zappia et al.,2018)was proposed to help researchers navigate the plethora of tools by category.Since its inception,scRNA-tools has been widely used and its updated version further reveals trends in the field with over 1000 collected tools(Zappia and Theis,2021),providing a valuable guidance in selecting tools for analyses.
