A Polyhedral Method to Compute All Affine Solution Sets of Sparse Polynomial Systems

To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible decomposition of a variety is typically understood in affine space, including also those components with zero coordinates. We present a polyhedral method to compute all affine solution sets of a polynomial system. The method enumerates all factors contributing to a generalized permanent. Toric solution sets are recovered as a special case of this enumeration. For sparse systems as adjacent 2-by-2 minors our methods scale much better than the techniques from numerical algebraic geometry

Tropical algebraic geometry in Maple: A preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients

AbstractFinding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic–numeric computing. Taking a tropical view of this problem leads to efficient preprocessing techniques, applying polyhedral methods to the exact exponents and numerical techniques to the approximate coefficients. With Maple we will illustrate our use of tropical algebraic geometry

Innovative Lernkultur in Unternehmen aus der Perspektive der Lernenden

Zunehmende Veränderungen in der Arbeitswelt, sich verändernde Berufe und damit einhergehende neue Kompetenzanforderungen bedingen Veränderungen in der betrieblichen Ausbildung. Im Hinblick auf die Steigerung der Innovationsfähigkeit eines Unternehmens werden unter anderem die Ausprägung von hoher Selbstständigkeit, verantwortungsvollem Handeln und hoher Anpassungsfähigkeit als auch kreatives Handeln besonders relevant. Wie Unternehmen mit ihren Ausbildungskonzepten auf diese Veränderungen reagieren, war die Ausgangsfrage einer qualitativen explorativen Studie bei einem großen Schweizer Telekommunikationsunternehmen. Interviews und zahlreiche Beobachtungen vor Ort geben Aufschluss über strukturelle Maßnahmen als auch über Werte, Einstellungen und Überzeugungen, die bei allen Akteuren bzgl. der Ausbildungsgestaltung bestehen. Letztere konstituieren eine spezifische Lernkultur, die nicht nur vom Aktionsrahmen der Unternehmung, sondern auch den besonderen Erfordernissen der Branche geprägt wird

Determination of optimal parameters for rapid prototyping of the involute gears

Nowadays, rapid prototyping technologies are available at very affordable prices. This is the main reason why they are being used in almost all industry sectors. 3D printers are currently being widely used for rapid prototyping and development of the new products. However, taking into account the permanent progress of rapid prototyping materials mechanical characteristics (usually different kinds of plastics), 3D printers are sometimes used even for production of the failed parts replacements - operating at the low load and rotational speed conditions. This is the main goal of this paper - to establish optimal 3D printing parameters (printing direction, layer height and percent of infill) which will allow printed gears to replace failed steel gears, for at least some time, enough for spare steel gears to be produced and delivered on site. Taking into account previously mentioned facts, the application of the 3D printed gears can potentially provide the reduction of maintenance delays in different industrial facilities (factories, workshops, etc.) which will consequently lead to significant energy and financial savings