The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points

The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0 (M + ). In addition to direct sums of regularly solvable operators defined on the separate subintervals, there are other regularly solvable restrications of the maximal operator which involve linking the various intervals together in interface like style.

INFRAWEBS Axiom Editor – A Graphical Ontology-Driven Tool for Creating Complex Logical Expressions

The current INFRAWEBS European research project aims at developing ICT framework enabling software and service providers to generate and establish open and extensible development platforms for Web Service applications. One of the concrete project objectives is developing a full-life-cycle software toolset for creating and maintaining Semantic Web Services (SWSs) supporting specific applications based on Web Service Modelling Ontology (WSMO) framework. According to WSMO, functional and behavioural descriptions of a SWS may be represented by means of complex logical expressions (axioms). The paper describes a specialized userfriendly tool for constructing and editing such axioms – INFRAWEBS Axiom Editor. After discussing the main design principles of the Editor, its functional architecture is briefly presented. The tool is implemented in Eclipse Graphical Environment Framework and Eclipse Rich Client Platform.