Completeness theorems for the Stokes system

The linear Stokes system is considered and the completeness (in the sense of Picone) on the boundary of a given bounded domain of polynomial solutions is proved. The completeness is obtained in both and uniform norms

On the traction problem for steady elastic oscillations equations: the double layer potential ansatz

The three-dimensional traction problem for steady elastic oscillations equations is studied. Representability of its solution by means of a double layer potential is considered instead of the more usual simple layer potential

On the double layer potential ansatz for the n-dimensional helmholtz equation with Neumann condition

In the present paper we consider the Neumann problem for the ndimensional Helmholtz equation. In particular we deal with the problem of representability of the solutions by means of double layer potentials

Compilability of Abduction

Abduction is one of the most important forms of reasoning; it has been successfully applied to several practical problems such as diagnosis. In this paper we investigate whether the computational complexity of abduction can be reduced by an appropriate use of preprocessing. This is motivated by the fact that part of the data of the problem (namely, the set of all possible assumptions and the theory relating assumptions and manifestations) are often known before the rest of the problem. In this paper, we show some complexity results about abduction when compilation is allowed

Automated Synthesis of Tableau Calculi

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page

On the Lp-theory of C0-semigroups associated with second-order elliptic operators with complex singular coefficients

A work in Perturbation Theory, with a purpose to consider well-posedness of elliptic and parabolic PDE with singular complex coefficient

Bailey, Stewart John

In the present paper we consider the Dirichlet problem for the n- dimensional Helmholtz equation. In particular we deal with the problem of rep- resentability of the solutions by means of simple layer potentials. The main result concerns the solvability of a boundary integral equation of the first kind. Such a result is here obtained by using the theories of differential forms and reducible operators

Some new applications of the theory of conjugate differential forms

In this survey we describe two applications of the concept of conjugate differential forms. Namely, after describing the concept of conjugate and selfconjugate differential forms, we consider an extension of the Brothers Riesz Theorem to higher real dimension and Riesz type inequalities for differential forms