Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences

This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincaré, logarithmic Sobolev and critical Sobolev (Onofri in dimension two) inequalities. The connection between optimal constants and spectral properties of the Laplace-Beltrami operator on the sphere is emphasized. The authors address a series of related observations and give proofs based on symmetrization and the ultraspherical setting.     

三维微纳米半球周期结构光学表面场分布及复合散射特性

为进一步拓展微纳米周期超结构功能特性,满足光学周期超结构高精度设计需求,基于时域多分辨分析方法,从Maxwell方程出发,推导出微纳米三维半球光学周期结构表面散射耦合场,计算结果与时域有限差分方法结果吻合良好。给出微纳米三维半球光学周期结构表面场分布并数值计算微纳米三维半球光学周期结构表面微分散射截面,提炼分析填充材质、半球尺寸、半球间距等参量对光学周期结构表面散射场影响规律。结果表明:P偏振下电场分布更能突出周期结构表面结构单元轮廓;散射场值随入射角变大,在对应镜面散射角方向逐渐减小;在半径和波长值相当时,填充单元散射场峰值个数与探测范围内填充单元个数吻合;随填充半球间距增大,散射场的极大值数递增,且极大值对应的角度区间依次减小。     

Photon diffusion in a relativistically expanding sphere

A relativistically expanding sphere exists ill many explosive astrophysical systelns, including gamma ray bursts, neutron star mergers, and some supernovae. In this paper we investigate the photon diffusion process in a relativistically expanding sphere, which is important for understanding the energetic and radiative characters of the above inentioned explosive systenls. The following contents are discussed in the frame work of special relativity： random walks of photons by scattering witti electrons, photospheres, photon diffusion, and the energy flux density emerging from the surface of the expanding sphere. Some of the results are also applicable to the Universe since the Universe is also a spherical expanding system.     

变密度球体重力位的推导及其球谐展开

天体内部密度的变化,往往引起天体表面重力位的非均匀分布.在计算变密度的重力位时,普通数值积分耗时较长,效率低下,不利于大规模的重力正反演.针对该问题,提出基于广义傅里叶变换的球谐算法,发现重力位球谐展开系数能直接由密度展开系数求出,简化了变密度问题重力位繁琐的积分过程.将算法应用于具体事例,发现球谐算法估算的重力位分布与普通数值积分方法所得一致,而计算时间得到了极大的降低.将本文算法应用于月壳变密度问题,发现相应的重力位分布与密度分布规律一致,验证了算法的合理性和实用性.     

矢引力子场论中无旋转不带电球体外时空中的零测地线运动

本文研究矢引力子场论中无旋转不带电球体外时空中的零测地线运动,得到了测地线方程的解析解,并与 Schwarzchild 时空中的零测地线运动作了比较。     

EXIT DISTRIBUTION LEAVING A BALL FROM THE CENTER AND BROWNIAN MOTION

It is skowed that if the first exit distribution leaving any ball from the center is theuniform distribution on the sphere, then the Levy process is a scaled Brownian motion.The paper also gives a characterization of a continuous Hunt process by the first exitdistribution from any ball.     

A NEW FAMILY OF FILTRATION S ＋ 5 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s ＋ 5 in the stable homotopy groups of spheres πrS,which is represented by 0 ≠γ^-s＋3hnhm∈Ext^s＋5,A ^t（Zp,Zp）in the Adams spectral sequence,where r=q（p^m＋p^n＋（s＋3）p^2＋（s＋2）p＋（s＋1））-5,t=p^mq＋p^nq＋（s＋3）p^2q＋（s＋2）pq＋（s＋1）q＋s,p≥7,m≥n＋2〉5,0≤s〈p-3,q=2（p-1）.     

物理学家发现新的地幔层

位于地球表面650km与2800km之间的低层地幔占有一半以上的地球体积，主要由含有氧、镁和硅的化合物组成．约5％是蕴含在铁方镁石和钙钛硅酸盐等化合物中的铁．     

Self-consistent field theory of adsorption of flexible polyelectrolytes onto an oppositely charged sphere

The adsorption of flexible polyelectrolyte （PE） with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.