In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting p...In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.展开更多
This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solu...This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula.展开更多
The Higgs-like boson H(126) discovered in 2012 is tentatively assigned to a newly found bound state of two charged gauge bosons W<sup>+</sup>W<sup>-</sup>. Starting from the scalar strong inter...The Higgs-like boson H(126) discovered in 2012 is tentatively assigned to a newly found bound state of two charged gauge bosons W<sup>+</sup>W<sup>-</sup>. Starting from the scalar strong interaction hadron theory, a first principles’ theory, a nonlinear, soliton-like differential equation dependent upon the distance between the two W bosons is derived. This equation is solved on a computer. A new, nonlinear confinement mechanism, not yet understood, binds the both bosons and gives a bound state mass E<sub>B</sub> = 155.8 GeV. This E<sub>B</sub>, derived at the quantum mechanical level, is estimated to reduce to E<sub>B</sub> = 110 GeV when quantized field effects are included via coarse approximations and replacement of the bare constants by renormalized ones. These developments lead to a revised status of the standard model.展开更多
基金supported by the National Natural Science Foundation of China(12271344)the Natural Science Foundation of Shanghai(23ZR1425800)。
文摘In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.
基金supported by National Natural Science Foundation of China(Grant Nos.11431014,11371041,11401557 and 11271356)the Fundamental Research Funds for the Central Universities(Grant No.0010000048)+1 种基金Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)the Applied Mathematical Research for the Important Strategic Demand of China in Information Science and Related Fields(Grant No.2011CB808000)
文摘This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula.
基金The project is partially supported by the National Natural Science Foundation(No.10071005),the Specialized Research Fund for the Doctoral Program of Higher Education(No.1999002705)and the Scientific Research Foundation for the Returned Overseas Chinese S
文摘The Higgs-like boson H(126) discovered in 2012 is tentatively assigned to a newly found bound state of two charged gauge bosons W<sup>+</sup>W<sup>-</sup>. Starting from the scalar strong interaction hadron theory, a first principles’ theory, a nonlinear, soliton-like differential equation dependent upon the distance between the two W bosons is derived. This equation is solved on a computer. A new, nonlinear confinement mechanism, not yet understood, binds the both bosons and gives a bound state mass E<sub>B</sub> = 155.8 GeV. This E<sub>B</sub>, derived at the quantum mechanical level, is estimated to reduce to E<sub>B</sub> = 110 GeV when quantized field effects are included via coarse approximations and replacement of the bare constants by renormalized ones. These developments lead to a revised status of the standard model.
