Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triax...Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.展开更多
The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are sol...The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.展开更多
Let K be a 1-unconditional convex bodies in Euclidean spaces.We study the asymptotic properties of two affine invariants m2（K） and S2（K） for a random simplex inside K.As an application,we discuss the asymptotic pr...Let K be a 1-unconditional convex bodies in Euclidean spaces.We study the asymptotic properties of two affine invariants m2（K） and S2（K） for a random simplex inside K.As an application,we discuss the asymptotic properties of two affine invariants m2（Bpn ） and S2（Bpn ）,where Bpn = {x ∈ Rn ： ‖x‖ p 1}.展开更多
Recently P.Bokulich suggests a newway to grab the first horn of Hempel’s Dilemma.His strategy is to define "the physical" with "the stuff recognized by currently well-understood parts of physics",...Recently P.Bokulich suggests a newway to grab the first horn of Hempel’s Dilemma.His strategy is to define "the physical" with "the stuff recognized by currently well-understood parts of physics",such as Quantum electrodynamics,as far as the mindbody problem is concerned.I argue that the physicalism doctrine formulated following Bokulich’s suggestion is still under the threat of being misjudged and also will not be welcomed by the physicalists.After considering some potential objections,I conclude that Bokulich’s strategy fails.展开更多
Let K (?) Rn be a convex body of volume 1 whose barycenter is at the origin, LK be the isotropic constant of K. Finding the least upper bound of LK , being called Bourgain's problem, is a well known open problem i...Let K (?) Rn be a convex body of volume 1 whose barycenter is at the origin, LK be the isotropic constant of K. Finding the least upper bound of LK , being called Bourgain's problem, is a well known open problem in the local theory of Banach space. The best estimate known today is LK < cn1/4 log n, recently shown by Bourgain, for an arbitrary convex body in any finite dimension. Utilizing the method of spherical section function, it is proven that if K is a convex body with volume 1 and r1Bn2 (?) K (?) r2Bn2,(r1≥1/2, r2≤(?)/2), then (?) ≤ (?) and find the conditions with equality. Further, the geometric characteristic of isotropic bodies is shown.展开更多
In this paper, we develop a Fourier analytic approach to study the problem in the Brunn-Minkowski-Firey theory of convex bodies. We formulate and solve a quasi-Shephard＇s problem on projections of convex bodies.
设K是Rn中体积为1,质心在原点的凸体,LK是它的迷向常数,寻找LK的上确界,是Banach空间局部理论(现代几何分析)中著名的未解决问题.目前最好的上界估计是LK<cn1/4logn,它是由Bourgain证明的.最近,何斌吾、冷岗松又证明了当r1Bn2 K r2Bn...设K是Rn中体积为1,质心在原点的凸体,LK是它的迷向常数,寻找LK的上确界,是Banach空间局部理论(现代几何分析)中著名的未解决问题.目前最好的上界估计是LK<cn1/4logn,它是由Bourgain证明的.最近,何斌吾、冷岗松又证明了当r1Bn2 K r2Bn2(r1≥1/2,r2≤n/2)时,LK≤1/(2 3),并猜测在对称几何体中以超立方体的迷向常数为最大,在非对称几何体中以单形的迷向常数为最大.给出了在三维空间中全部正多面体的迷向常数的数值,从而说明这一猜测对三维空间中的正多面体是正确的.展开更多
文摘Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.
基金Funded by the National Natural Science Foundation of China (No.40574004).
文摘The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.
基金Project supported by the National Natural Science Foundation of China (Grant No.10671119)
文摘Let K be a 1-unconditional convex bodies in Euclidean spaces.We study the asymptotic properties of two affine invariants m2（K） and S2（K） for a random simplex inside K.As an application,we discuss the asymptotic properties of two affine invariants m2（Bpn ） and S2（Bpn ）,where Bpn = {x ∈ Rn ： ‖x‖ p 1}.
文摘Recently P.Bokulich suggests a newway to grab the first horn of Hempel’s Dilemma.His strategy is to define "the physical" with "the stuff recognized by currently well-understood parts of physics",such as Quantum electrodynamics,as far as the mindbody problem is concerned.I argue that the physicalism doctrine formulated following Bokulich’s suggestion is still under the threat of being misjudged and also will not be welcomed by the physicalists.After considering some potential objections,I conclude that Bokulich’s strategy fails.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10271071).
文摘Let K (?) Rn be a convex body of volume 1 whose barycenter is at the origin, LK be the isotropic constant of K. Finding the least upper bound of LK , being called Bourgain's problem, is a well known open problem in the local theory of Banach space. The best estimate known today is LK < cn1/4 log n, recently shown by Bourgain, for an arbitrary convex body in any finite dimension. Utilizing the method of spherical section function, it is proven that if K is a convex body with volume 1 and r1Bn2 (?) K (?) r2Bn2,(r1≥1/2, r2≤(?)/2), then (?) ≤ (?) and find the conditions with equality. Further, the geometric characteristic of isotropic bodies is shown.
基金Supported by the National Natural Science Foundation of China(11161019,11371224)
文摘In this paper, we develop a Fourier analytic approach to study the problem in the Brunn-Minkowski-Firey theory of convex bodies. We formulate and solve a quasi-Shephard＇s problem on projections of convex bodies.
文摘设K是Rn中体积为1,质心在原点的凸体,LK是它的迷向常数,寻找LK的上确界,是Banach空间局部理论(现代几何分析)中著名的未解决问题.目前最好的上界估计是LK<cn1/4logn,它是由Bourgain证明的.最近,何斌吾、冷岗松又证明了当r1Bn2 K r2Bn2(r1≥1/2,r2≤n/2)时,LK≤1/(2 3),并猜测在对称几何体中以超立方体的迷向常数为最大,在非对称几何体中以单形的迷向常数为最大.给出了在三维空间中全部正多面体的迷向常数的数值,从而说明这一猜测对三维空间中的正多面体是正确的.
