Classification of static spherically symmetric perfect fluid space-times via conformal vector fields in f(T) gravity

In this paper, we classify static spherically symmetric (SS) perfect fluid space-times via conformal vector fields (CVFs) in f(T) gravity. For this analysis, we first explore static SS solutions by solving the Einstein field equations in f(T) gravity. Secondly, we implement a direct integration technique to classify the resulting solutions. During the classification, there arose 20 cases. Studying each case thoroughly, we came to know that in three cases the space-times under consideration admit proper CVFs in f(T) gravity. In one case, the space-time admits proper homothetic vector fields, whereas in the remaining 16 cases either the space-times become conformally flat or they admit Killing vector fields.     

Near-field multiple super-resolution imaging from Mikaelian lens to generalized Maxwell's fish-eye lens

Super-resolution imaging is vital for optical applications, such as high capacity information transmission, real-time bio-molecular imaging, and nanolithography. In recent years, technologies and methods of super-resolution imaging have attracted much attention. Different kinds of novel lenses, from the superlens to the super-oscillatory lens, have been designed and fabricated to break through the diffraction limit. However, the effect of the super-resolution imaging in these lenses is not satisfactory due to intrinsic loss, aberration, large sidebands, and so on. Moreover, these lenses also cannot realize multiple super-resolution imaging. In this research, we introduce the solid immersion mechanism to Mikaelian lens (ML) for multiple super-resolution imaging. The effect is robust and valid for broadband frequencies. Based on conformal transformation optics as a bridge linking the solid immersion ML and generalized Maxwell's fish-eye lens (GMFEL), we also discovered the effect of multiple super-resolution imaging in the solid immersion GMFEL.     

The magnet design for the HLS storage ring upgrade project

In order to improve the performance of the Hefei Light Source (HLS), in particular to get higher brilliance synchrotron radiation and increase the number of straight section insertion devices, an upgrade project called HLSII will be launched soon. The storage ring lattice, which has a double bend achromatic structure with four periods, comprises eight dipoles, 32 quadrupoles and 32 combined function sextupoles. The design and analysis of the magnets are shown in this paper, along with the optimization of the multipurpose combined function magnet, which consists of three magnets: skew quadrupole, horizontal dipole and vertical dipole, with the main sextupole magnet. This type of magnet is the first one that has been designed and used in China. The mechanical design and fabrication procedures for the magnets are also presented.     

共形映像的Hausdorff 测度及其算法

对于Rⁿ 中满足0 < H^s(K) < ∞ 的任意紧致集K, 我们考虑其在共形映射f 作用下的像集的Hausdorff 测度H^s(f(K)). 本文给出了下面结果:
H^s(f(K)) = H^s(K) · ∫_K |D_xf|^sdμ(x),
其中概率测度μ = (H^s|K/H^s(K)) . 给定满足开集条件的自相似集K, 测度μ 恰好是自相似测度, 因此可以应用上述公式计算f(K) 的Hausdorff 测度, 例如, K 是λ-Sierpinski 地毯, f(z) = z+εz², 其中0 < λ ≤1/4,复数ε 满足|ε| ≤ 0.1. 而此刻f(K) 恰好是自共形集, 因此我们的算法能计算一类特殊的具有非线性结构的自共形集的Hausdorff 测度.     

星形裂纹的应力分析

利用复变函数的方法, 通过构造适当的保角映射研究了星形裂纹的平面弹性问题,给出了裂纹尖端I型与II型问题应力强度因子的解析解.并由此模拟出了经典的Griffith裂纹,共点均匀分布三裂纹,十字裂纹,对称八裂纹问题.      

Conformal Ricci Collineations of Static Spherically Symmetric Spacetimes

Conformal Ricei collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating eonformal Rieei eollineations is found when the Rieei tensor is non-degenerate, in which ease the number of independent eonformal Rieei eollineations is 15, the maximum number for four-dimensional manifolds. In the degenerate ease it is found that the static spherically symmetric spaeetimes always have an infinite number of eonformal Rieei eollineations. Some examples are provided which admit non-trivial eonformal Rieei eollineations, and perfect fluid source of the matter.     

Conformal Fluctuations of the Interior Schwarzschild Solution

The basic formalism for conformal fluctuations of the gravitational field is presented. After developing a master propagator for the interior Schwarzschild solution, the time development of the gravitational wave function is considered. The effect of the two classical singularities (resp. pseudo-singularities) of the Schwarzschild solution on the quantum wave function for the gravitational field is studied using a wave function initially localized on the classical solution. While the true singularity at r = 0 imparts consequences on the wave function that cannot be ignored, the pseudo-singularity at the event horizon does not seem to cause any divergences on the interior fluctuations of the Schwarzschild solution.