论文标题
求解分数高高 - 塔皮蛋白方程。绿色功能方法
Towards to solution of the fractional Takagi-Taupin equations. The Green function method
论文作者
论文摘要
通过扭曲的晶体开发X射线衍射的综合理论仍然是数学物理学的话题。到目前为止，X射线衍射理论基于X射线散射平面内两个坐标的一阶部分衍生物扎在高高 - 塔皮蛋白方程上。在工作中，已经提出了基于一阶分数的高高键蛋白方程的理论方法，其沿晶体深度的$α\ in（0,1] $的“准时间变量”已提出，并相应地制定了相应的X射线库奇问题。在不均匀的事件X射线束的情况下，已经获得了X射线射击的解决方案，并且已经获得了完美晶体的X射线衍射问题，并基于传统的Takagi-taupin方程的解决方案进行了比较。
Developing the comprehensive theory of the X-ray diffraction by distorted crystals remains to be topical of the mathematical physics. Up to now, the X-ray diffraction theory grounded on the Takagi-Taupin equations with the first-order partial derivatives over the two coordinates within the X-ray scattering plane. In the work, the theoretical approach based on the first-order fractional Takagi-Taupin equations with the 'quasi-time variable' of the order $α\in(0,1]$ along the crystal depth has been suggested and the corresponding X-ray Cauchy issue is formulated. Accordingly, using the Green function method in the scope of the Cauchy issue, the fractional Takagi-Taupin equations in the integral form have been derived. In the case of the inhomogeneous incident X-ray beam, the solution of the Cauchy issue of the X-ray diffraction by perfect crystal has been obtained and compared with the corresponding one based on the solution of the conventional Takagi-Taupin equations, $α=1.$ In turn, notice that the value of order $α$ may be adjusted from the experimental X-ray diffraction data.
