Search results for " Linear"
showing 3 items of 643 documents
Fostering Heuristic Strategies in Mathematics Teacher Education
2018
International audience; The “double discontinuity” stated by Felix Klein 1908 is still relevant in the mathematics teacher education at German universities. We are developing a course approach, which is intended to bridge the double discontinuity in a didactic dimension. We offer additional learning opportunities for teacher students, which are characterized by clarifications of mathematical methods that are fundamental to the regular lecture contents. We focus especially on reflections on heuristic strategies, which are the core part of mathematical methods according to George Pólya. Feedback shows that students consider our approach as helpful in the transition from school to university.
Extensions of representable linear functionals to unitized quasi *-algebras
2013
This paper starts from noting that, under certain conditions, *-representability and extensibility to the unitized *-algebra of a positive linear functional, defined on a *-algebra without unit, are equivalent. Here some conditions for the equivalence of the same concepts for a hermitian linear functional defined on a quasi *-algebra $(\A,\Ao)$ without unit are given. The approach is twofold: on the one hand, conditions for the equivalence are exhibited by introducing a condition for the *- representability of the extension of a *-representable functional to the unitized quasi *-algebra, on the other hand a *-representable extension to the unitization of a hermitian linear functional by mea…
Stochastic seismic analysis of MDOF structures with viscous damper devices
2009
Fluid damper devices in civil structures such as buildings or bridges are commonly used as energy absorbers for seismic protection. The problem in the response analysis of structures with filled dampers mainly consists in the fact that, due to the strongly nonlinear behavior of such equipments, the response spectrum technique fails. In this paper by using the concept of power spectral density function compatible with the elastic response spectrum and the stochastic linearization technique, the equivalent damping ratio is obtained. It is shown that once the system is linearized results obtained by Monte Carlo simulation and those obtained by stochastic analysis are in good agreement. Respons…