the velocity data of seismic waves in a region has an important role in locating occurred events. information such as velocity ratio of vp/vs and velocity curves for pg, pn, sg, and sn phases directly affect the locating results. it is well known that the vp/vs ratio can be used to predict lithology, and that s-waves are sensitive to microcracks aligned by the present day stress field. also, th...

a method has been presented for finding the solution surface of the npde: u  c , bounded by a general space curve. the method is based on the geometric characteristics of the surface, and is called the “cone-slot method”. it has been shown that such a surface can be obtained by movement of a cone inside the slot formed by the boundary space curve. an algorithm has been suggested on the basis ...

We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of integral points on integral models of twists of modular curves over function fields.

We prove that there are infinitely many integral right triangle and θ-integral rhombus pairs with a common area and a common perimeter by the theory of elliptic curves.

This paper contains a theoretical formulation of multiple interface cracks in two bonded dissimilar half planes subjected to in-plane traction. The distributed dislocation technique is used to construct integral equations for a dissimilar mediums weakened by several interface cracks. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obta...