The most general form of a linear continuous functional operation on a function f(x) continuous on (a, b) has been expressed by F. Rieszf as a Stieltjes integral of f(x) with respect to a function of bounded variation. By virtue of the extension theorem of Hahn,$ this result can be extended to the case where f(x) has discontinuities of the first kind on (a, b). In establishing this more general...

The effect of conservation of integral invariants by finite-element discretization schemes of the shallow-water equations as a model for long-term integrations of atmospheric models is investigated. Two finite-element models are used. The first uses rectangular elements and conserves total energy using an intrinsic method. The second model uses triangular elements and a high-accuracy two-stage ...

Denda and Marante [1] have developed the boundary element method for the mixed mode fracture analysis of multiple curvilinear cracks in the general anisotropic solids in two dimensions for which in-plane Mode I, II, and out-of-plane Mode III, of fracture are coupled. They have developed the crack tip singular element (CTSE) to model any curvilinear cracks, including center and edge cracks. The ...

Two-dimensional weakly-singular Symmetric Galerkin Boundary Elements (SGBEMs) are developed, following the work of [Han and Atluri (2003)], using non-hypersingular integral equations for tractions. Specifically, the present 2D SGBEM is used to compute the stress intensity factors for arbitrary-shaped line cracks, including embedded, edge, branching, and intersecting cracks. The computed stress ...

We obtain the Laplace transform and integrability properties of the integral over R+ of the call quantity associated with geometric Brownian motion with negative drift, thus adding a new element to the list of already studied Brownian perpetuities.

We consider mixed boundary value problems in Physical Geodesy and study possibilities in order to transform them into a system of integral equations over the boundary of the domain. The system of integral equations can be solved numerically, by, e.g. boundary element methods, provided that (a) the mixed boundary value problem is uniquely solvable, (b) the system of integral equations is equival...

Integral representations are derived from a differential-type boundary value problem using a fundamental solution. A set of integral representations is equivalent to a set of differential equations. If the boundary conditions are substituted into the integral representations, the integral equations are obtained, and the unknown variables are determined by solving the integral equations. In othe...