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, by means of the dual Brunn-Minkowski theories and methods as well as the integral transform, we have established a stability version of nonsymmetric convex bodies from intersection bodies. In addition, ...In this paper, by means of the dual Brunn-Minkowski theories and methods as well as the integral transform, we have established a stability version of nonsymmetric convex bodies from intersection bodies. In addition, a stability results of symmetric convex bodies from L_p-counterparts is established.展开更多
In this paper,we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width.Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant widt...In this paper,we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width.Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant width,and the completion of the spherical regular simplexes are the most asymmetric bodies.展开更多
Because of various error factors,the detecting errors in the real-time experimental data of the wear depth affect the accuracy of the detecting data.The self-made spherical plain bearing tester was studied,and its tes...Because of various error factors,the detecting errors in the real-time experimental data of the wear depth affect the accuracy of the detecting data.The self-made spherical plain bearing tester was studied,and its testing principle of the wear depth of the spherical plain bearing was introduced.Meanwhile,the error factors affecting the wear-depth detecting precision were analyzed.Then,the comprehensive error model of the wear-depth detecting system of the spherical plain bearing was built by the multi-body system theory(MBS).In addition,the thermal deformation of the wear-depth detecting system caused by varying the environmental temperature was detected.Finally,according to the above experimental parameters,the thermal errors of the related parts of the comprehensive error model were calculated by FEM.The results show that the difference between the simulation value and the experimental value is less than 0.005 mm,and the two values are close.The correctness of the comprehensive error model is verified under the thermal error experimental conditions.展开更多
A host of authors have proposed some theoretical and experimental formulas in hydromechanics concerning the calculation of the drag coefficient Cd of spherical bodies. But all of the existing Cd formulas hold true onl...A host of authors have proposed some theoretical and experimental formulas in hydromechanics concerning the calculation of the drag coefficient Cd of spherical bodies. But all of the existing Cd formulas hold true only at small Reynolds numbers and are restricted within certain flowing range.As regards the fall velocity ω of spherical bodies, there is yet no formula applicable to each flowing range and to a direct expression and calculation of the fall velocity ω.In view of these, from N-S equations, and meanwhile based on measured data and complicated calculations, the author has developed and proposed the following results:(1) The drag coefficient (2) The dimensionless fall velocity where Es, Ω* and constants etc. are indicated in detail in this paper.Through laborious calculation in lgRe<5 larger range, the verification proves that our results well agree with the measured data. And the leading features of formulas of this paper are: (1) simple in form, (2) convenient for general use, (3) preferable on the part of the precision and applicability.Finally, to introduce this process and to illustrate the temperature effects on the fall velocity ω, some examples are discussed in this paper.展开更多
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（11561020, 11371224）
文摘In this paper, by means of the dual Brunn-Minkowski theories and methods as well as the integral transform, we have established a stability version of nonsymmetric convex bodies from intersection bodies. In addition, a stability results of symmetric convex bodies from L_p-counterparts is established.
基金Supported by the National Natural Science Foundation of China(12071334,12071277)。
文摘In this paper,we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width.Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant width,and the completion of the spherical regular simplexes are the most asymmetric bodies.
基金Project(2014E00468R)supported by Technological Innovation Fund of Aviation Industry Corporation of China
文摘Because of various error factors,the detecting errors in the real-time experimental data of the wear depth affect the accuracy of the detecting data.The self-made spherical plain bearing tester was studied,and its testing principle of the wear depth of the spherical plain bearing was introduced.Meanwhile,the error factors affecting the wear-depth detecting precision were analyzed.Then,the comprehensive error model of the wear-depth detecting system of the spherical plain bearing was built by the multi-body system theory(MBS).In addition,the thermal deformation of the wear-depth detecting system caused by varying the environmental temperature was detected.Finally,according to the above experimental parameters,the thermal errors of the related parts of the comprehensive error model were calculated by FEM.The results show that the difference between the simulation value and the experimental value is less than 0.005 mm,and the two values are close.The correctness of the comprehensive error model is verified under the thermal error experimental conditions.
文摘A host of authors have proposed some theoretical and experimental formulas in hydromechanics concerning the calculation of the drag coefficient Cd of spherical bodies. But all of the existing Cd formulas hold true only at small Reynolds numbers and are restricted within certain flowing range.As regards the fall velocity ω of spherical bodies, there is yet no formula applicable to each flowing range and to a direct expression and calculation of the fall velocity ω.In view of these, from N-S equations, and meanwhile based on measured data and complicated calculations, the author has developed and proposed the following results:(1) The drag coefficient (2) The dimensionless fall velocity where Es, Ω* and constants etc. are indicated in detail in this paper.Through laborious calculation in lgRe<5 larger range, the verification proves that our results well agree with the measured data. And the leading features of formulas of this paper are: (1) simple in form, (2) convenient for general use, (3) preferable on the part of the precision and applicability.Finally, to introduce this process and to illustrate the temperature effects on the fall velocity ω, some examples are discussed in this paper.
