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...

Canonical quantization of three dimensional gravity in the first order formalism suggests that one should allow singular solutions. This paper addresses the importance of singular solutions in the path integral approach to quantum gravity. Using a simple ansatz for the dreibein and the spin connection in the de-Sitter and the anti-de-Sitter spaces we propose that the sum over the 3D manifolds i...

A high-order accurate, explicit kernel-split, panel-based, Fourier–Nyström discretization scheme is developed for integral equations associated with the Helmholtz equation in axially symmetric domains. Extensive incorporation of analytic information about singular integral kernels and on-the-fly computation of nearly singular quadrature rules allow for very high achievable accuracy, also in the...

This paper presents an analytical solution for an orthotropic circular cross section bar with a magnetic coating weakened by multiple arbitrary oriented cracks under Saint-Venant torsion by means of the distributed dislocation technique. At first, the solution of the orthotropic bar with a magnetic coating weakened by a Volterra-type screw dislocation is achieved with the aid of the finite Four...

In a preceding paper we have introduced the t-singular homology with integral coefficient of orbifolds, which captures the orbifold structures. In this paper we introduce the s-singular homology of orbifolds, and study the s-singular homology of orbifolds and the t-singular homology with rational coefficient of orbifolds. The main theorems are the following: (i) the s-singular homology group of...

In a classical paper, E. R. Love considered a certain function defined by a singular integral which is harmonic outside a circular disk. Love's objective was to derive a simple integral equation whose solution leads to a useful formula for the capacitance of the condenser consisting of two parallel circular plates. We close a gap in Love's derivation by finding a new nonsingular representation ...

We prove results generalizing the classical Riemann Singularity Theorem to the case of integral, singular curves. The main result is a computation of the multiplicity of the theta divisor of an integral, nodal curve at an arbitrary point. We also suggest a general formula for the multiplicity of the theta divisor of a singular, integral curve at a point and present some evidence that this formu...

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted,the density function is...

In this paper we deal with a nonlinear singular integral inequality which arises in the study of partial differential equations. The integral term is non local in time and space and the kernel involved is also singular in both the time and the space variable. The estimates we prove may be used to establish (global) existence and asymptotic behavior results for solutions of the corresponding pro...

In this study, the contact problem of a layered composite which consists of two materials with different elastic constants and heights resting on two rigid flat supports with sharp edges is considered. The effect of gravity is neglected. While friction between the layers is taken into account, it is assumed that there is no friction between the supports and the layered composite so that only co...