Analytic geometry

The paper generalizes one practical tool for analyzing the structural dynamics for the high-speed railway bridge based on Cast3M open-source. Compared with the classical approach with the analytical formulation, KD-Railway developed by the finite element method allows defining the structure with complex geometry and considering a different type of structure (truss, cable, hybrid composite) or the structure-soil interaction.

10p viengfa 28-10-2024 3 2   Download

This paper explores the application of GeoGebra software to assist teachers and students in lessons on fixed points of families of lines and circles, a relatively complex topic in secondary school geometry that requires logical reasoning and advanced proof skills. GeoGebra, as a visual modeling tool, enables the discovery and proof of fixed points in problems involving families of lines and circles.

7p viaburame 14-03-2025 5 1   Download

In this study, a simple analytical model incorporating perforation length, radius, and shot density was used to analyze oil well productivity. The results shows that the production rate can be increased by the perforation length, radius, and shot density.

10p lucastanguyen 01-06-2020 29 5   Download

A key feature of molten salt reactors is the possibility to reconfigure the fuel geometry (actively or passively driven by gravitational forces) in case of accidents. In this regard, the design of reference molten salt reactor of Generation IV International Forum, the MSFR, foresees the Emergency core Draining System (EDS).

14p christabelhuynh 29-05-2020 11 3   Download

Web geometry is devoted to the study of families of foliations which are in general position. We restrict ourselves to the local situation, in the neighborhood of the origin in C2 , with d ≥ 1 complex analytic foliations of curves in general position. We are interested in the geometry of such configurations, that is, properties of planar d-webs which are invariant with respect to analytic local isomorphisms of C2 . The initiators of the subject are W. Blaschke, G. Thomsen and G. Bol in the 1930’s (cf. [B-B], [B] and for instance [H1]). ...

22p tuanloccuoi 04-01-2013 60 7   Download

In 1991, David Gale and Raphael Robinson, building on explorations carried out by Michael Somos in the 1980s, introduced a three-parameter family of rational recurrence relations, each of which (with suitable initial conditions) appeared to give rise to a sequence of integers, even though a priori the recurrence might produce non-integral rational numbers. Throughout the '90s, proofs of integrality were known only for individual special cases. In the early '00s, Sergey Fomin and Andrei Zelevinsky proved Gale and Robinson's integrality conjecture.

37p thulanh8 19-09-2011 65 15   Download