We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical problems. 1. Witten's Conjecture 1.1. Two-Dimensional Gravity (ies). Quantum gravity, although not well-defined, looks like integration over the (infinite-dimensional) space of riemannian metrics on...

A crack of arbitrary size and orientation near bimaterial interfaces between dissimilar thermopiezoelectric materials is considered . A system of singular integral equations for the unknown thermal analog of dislocation density defined on the crack faces is derived by way of the Stroh's formulation and the thermoelectroelastic Green's fUflctions developed recently. The stress and electric displ...

In a previous work, the authors introduced a scheme for the numerical evaluation of the singular integrals which arise in the discretization of certain weakly singular integral operators of acoustic and electromagnetic scattering. That scheme is designed to achieve high-order algebraic convergence and high-accuracy when applied to operators given on smoothly parameterized surfaces. This paper g...

The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integr...