An extended enterprise (EE) can be described by a set of models each representing a specific aspect of the EE. Aspects can for example be the process flow or the value description. However, different models are done by different people, which may use different terminology, which prevents relating the models. Therefore, we propose a framework consisting of process flow and value aspects and in a...

A function f = u + iv defined in the domain D ⊂ C is harmonic in D if u, v are real harmonic. Such functions can be represented as f = h+ ḡ where h, g are analytic in D. In this paper the class of harmonic functions constructed by the Hadamard product in the unit disk, and properties of some of its subclasses are examined.

We consider the overdetermined boundary value problem for the 4-harmonic operator, Δ4 = Δ(Δ3) , and show that if the solution of the problem exists, then the domain must be an open N -ball (N 2) . As a consequence of overdetermined problems mean value results are obtained for harmonic, biharmonic, triharmonic and 4-harmonic functions. Mathematics subject classification (2010): 35J25, 35P15, 35B50.

In the circuit theory, Norton and Thevenin equivalent generators are tools that simplify solutions of networks involving passive or active components. They have been extensively used in frequency domain to describe time-harmonic sources. A time-stepped evolution is instead typically include transient As a particular case latter, extended here investigate pulsed photoconducting sources, where dc...

We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold (M, cM ) to a twodimensional conformal manifold (N, cN ) can be, locally, ‘extended’ to a unique harmonic morphism from the H(eaven)-space (H, g) of (M, cN ) to (N, cN ). Moreover, any positive harmonic morphism with two-dimensional fibres from (H, g) is obtained this way.

We introduce a Hodge operator in a framework of noncommutative geometry. The complete integrability of 2-dimensional classical harmonic maps into groups (σ-models or principal chiral models) is then extended to a class of ‘noncommutative’ harmonic maps into matrix algebras.