function, 51 Riemann integral, 51 adjoint bilinear form, 65 almost separably valued, 53 Ascoli Theorem, 8 Banach space reflexive, 6 separable, 2 Banach-Steinhaus Theorem, 5 Bessel’s inequality, 9 biharmonic, 61 bilinear form, 55, 58 bounded, 58 strongly positive, 58 Bochner-Pettis Theorem Theorem, 53 Bounded Inverse Theorem, 6 Calculus in W 1,p(I;X) Theorem, 54 Campanato ’63 Theorem, 86 Campana...

In a reversible hydrodynamic approximation, closed system of second order dynamic equation with respect to the displacement vector an elastic porous body and pore pressure has been obtained. The Cauchy problem for obtained poroelasticity equations in stationary case is considered. Carleman formula under consideration constructed.

Spanning trees are a representative example of linear matroid bases that efficiently countable. Perfect matchings Pfaffian bipartite graphs countable common two matrices. Generalizing these two, Webb (2004) introduced the notion pairs as pair matrices for which counting their is tractable via Cauchy–Binet formula.

This paper presents a regularization technique for the high order efficient numerical evaluation of nearly singular, principal-value, and finite-part Cauchy-type integral operators. By relying on Cauchy formula, Cauchy-Goursat theorem, on-curve Taylor interpolations input density, proposed methodology allows to recast associated operators as smooth contour integrals. As such, they can be accura...

We consider a left-linear analogue to the classical Riemann problem: Dau = 0 in Rn\Γ u+ = H(x)u− + h(x) on Γ |u(x)| = O(|x|n2−1) as |x| → ∞. For this purpose, we state a Borel-Pompeiu formula for the disturbed Dirac operator Da = D+a with a paravector a and some functiontheoretical results. We reformulate the Riemann problem as an integral equation: Pau+ HQau = h on Γ, where Pa = 2(I + Sa) and ...

defines a holomorphic function of z on the complement of the support of μ. For simplicity, let us restrict our attention to measures with compact support in C, although one can also make sense of Cauchy integrals of measures with noncompact support and infinite mass under suitable conditions. In the classical situation where μ is supported on a nice curve, the Cauchy integral of μ has a jump di...