Restricted Elasticity and Rings of Integer-Valued Polynomials Determined by Finite Subsets

Let D be an integral domain such that Int(D) ≠ K[X] where K is the quotient field of D. There is no known example of such a D so that Int(D) has finite elasticity. If E is a finite nonempty subset of D, then it is known that Int(E, D) = {f(X) ∈ K[X] | f(e) ∈ D for all e ∈ E} is not atomic. In this note, we restrict the notion of elasticity so that it is applicable to nonatomic domains. For each real number r ≥ 1, we produce a ring of integer-valued polynomials with restricted elasticity r. We further show that if D is a unique factorization domain and E is finite with |E| > 1, then the restricted elasticity of Int(E, D) is infinite.     

Die Bestimmung der Weins?ure

Ohne Zusammenfassung     

Problem-Solving Methodology Design on the Run

This paper discusses a risk analysis study which considered the best way to cross a river with a large diameter gas pipeline, one possibility being a bridge carrying a large diameter oil line. About 30 ‘riskateers’ were involved, over a 3-month period, most of whom were engineers or economists with no risk analysis, O.R. or systems experience. A large number of interested parties were involved, with different perspectives. The paper stresses methodology design as an organizational vehicle, and the implications of designing problem-solving methodology in the midst of a problem-solving process.     

Dipole operators in photoionization calculations

The photoionization cross section and asymmetry parameter are reported for hydrogen molecule-ion. The calculations were performed using the dipole length and dipole velocity operators in the energy range from threshold to 270 eV photon energy. The results indicate that the calculations are very sensitive to the accuracy of the bound state wavefunction, and that the velocity operator gives more accurate results.     

A controlled boundary theorem for Hilbert cube manifolds

In this paper a boundary theorem for Hilbert cube manifolds is established,where it is required that the boundary be put on the manifold with arbitrarily small control in a given compact metric parameter space.