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The satellite era brings new challenges in the development and the implementation of potential field models. Major aspects are, therefore, the exploitation of existing space- and ground-based gravity and magnetic data for the long-term. Moreover, a continuous and near real-time global monitoring of the Earth system, allows for a consistent integration and assimilation of these data into complex models of the Earth’s gravity and magnetic fields, which have to consider the constantly increasing amount of available data. In this paper we propose how to speed up the computation of the normal equation in potential filed modeling by using local multi-polar approximations of the modeling functions. The basic idea is to take advantage of the rather smooth behavior of the internal fields at the satellite altitude and to replace the full available gravity or magnetic data by a collection of local moments. We also investigate what are the optimal values for the free parameters of our method. Results from numerical experiments with spherical harmonic models based on both scalar gravity potential and magnetic vector data are presented and discussed. The new developed method clearly shows that very large datasets can be used in potential field modeling in a fast and more economic manner.
Special p-forms are forms which have components fµ1…µp equal to +1, -1 or 0 in some orthonormal basis. A p-form ϕ ∈ pRd is called democratic if the set of nonzero components {ϕμ1...μp} is symmetric under the transitive action of a subgroup of O(d,Z) on the indices {1, . . . , d}. Knowledge of these symmetry groups allows us to define mappings of special democratic p-forms in d dimensions to special democratic P-forms in D dimensions for successively higher P = p and D = d. In particular, we display a remarkable nested structure of special forms including a U(3)-invariant 2-form in six dimensions, a G2-invariant 3-form in seven dimensions, a Spin(7)-invariant 4-form in eight dimensions and a special democratic 6-form O in ten dimensions. The latter has the remarkable property that its contraction with one of five distinct bivectors, yields, in the orthogonal eight dimensions, the Spin(7)-invariant 4-form. We discuss various properties of this ten dimensional form.
Die weltweite Forderung nach einer Zunahme der gesellschaftlichen Verantwortung der Unternehmen ist in den letzten Jahren über alle Anspruchsgruppen (Stakeholder) hinweg stetig größer geworden.1 Die Übernahme eben dieser Verantwortung findet in dem facettenreichen Begriff der Corporate Social Responsibility (CSR) ihren Ausdruck. Diesem Leitbild entsprechend verpflichten sich Unternehmen zum verantwortungsbewussten Verhalten gegenüber Eigentümern, Konsumenten, Lieferanten, Mitarbeitern und der Gesellschaft als Ganzes.2 Eine CSR-Strategie, die ein ausgewogenes Maß der ‘Triple-Bottom-Line’ bestehend aus sozialen, ökologischen und ökonomischen Aspekten berücksichtigt, wird mittlerweile als Notwendigkeit dafür angesehen, dass ein Unternehmen auch in Zukunft seine ‘license to operate’, d.h. seine gesellschaftliche Unterstützung für die Geschäftstätigkeit behält bzw. sichert.
Cause related Marketing
(2009)
Alan Duff Once Were Warriors
(2009)
Alan Duff
(2009)
Maurice Duggan
(2009)