实Clifford分析中奇异积分方程的可解性

借助多元复分析的思想，首先研究实Ｃｌｉｆｆｏｒｄ分析中于特征流形上具有交换因子核的奇异积分的Ｐｏｉｎｃａｒｅ′Ｂｒｅｔｒａｎｄ置换公式．再利用这个公式研究特征流形上具有交换因子核的奇异积分方程．在一定条件下得到了该积分方程的可解性．

粗糙核奇异积分算子的有界性

Ｒ．Ｆｅｆｆｅｒｍａｎ型奇异积分算子Ｔ为Ｌｉｐｓｃｈｉｔｚ函数类上有界算子的充分必要条件是其核函数的粗糙因子ｂ（ｘ）满足：存在ε０＞０，及正数序列｛ａｋ｝，ａ０＝１，使得，对每一个Ｒ∈（０，１）成立．

Cortical Bone Model with a Microcrack under Tensile Loading

The fracture mechanics of cortical bone has received much attention in biomedical engineering.It is a fundamental question how the material constants and the geometric parameters of the cortical bone affect the fracture behavior of the cortical bone.In this work,the plane problem for cortical bone with a microcrack located in the interstitial tissue under tensile loading was considered.Using the solution for the continuously distributed edge dislocations as Green ’ s functions,the problem was formulated as singular integral equations with Cauchy kernels.The numerical results suggest that a soft osteon promotes microcrack propagation,while a stiff osteon repels it,but the interaction effect between the microcrack and the osteon is limited near the osteon.This study not only sheds light on the fracture mechanics behavior of cortical bone but also offers inspiration for the design of bioinspired materials in biomedical engineering.