Search results for "infinity"
showing 4 items of 74 documents
Active-passive decentralized H∞ control for adjacent buildings under seismic excitation
2011
Author's version of a chapter in the book: Proceedings of the 18th IFAC World Congress 2011. Also available from the publisher at: http://dx.doi.org/10.3182/20110828-6-IT-1002.01192 In this paper, a control strategy to reduce the vibrational response of adjacent buildings under seismic excitation is presented. The proposed strategy combines passive linking elements with an active decentralized H∞ control system. The overall active-passive control system admits decentralized design and operation, and achieves an excellent vibrational reduction when the active control system works; in case of a full or partial failure of the active control system, a remarkable reduction in the vibrational res…
On the Landis conjecture for the fractional Schrödinger equation
2023
In this paper, we study a Landis-type conjecture for the general fractional Schrödinger equation ((−P)s+q)u=0. As a byproduct, we also prove the additivity and boundedness of the linear operator (−P)s for non-smooth coefficents. For differentiable potentials q, if a solution decays at a rate exp (−∣x∣1+), then the solution vanishes identically. For non-differentiable potentials q, if a solution decays at a rate exp (−∣x∣4s−14s+), then the solution must again be trivial. The proof relies on delicate Carleman estimates. This study is an extension of the work by Rüland and Wang (2019). peerReviewed
Voisinages tubulaires épointés et homotopie stable à l'infini
2022
We initiate a study of punctured tubular neighborhoods and homotopy theory at infinity in motivic settings. We use the six functors formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational tools include cdh-descent for normal crossing divisors, Euler classes, Gysin maps, and homotopy purity. Under-adic realization, the motive at infinity recovers a formula for vanishing cycles due to Rapoport-Zink; similar results hold for Steenbrink's limiting Hodge structures and Wildeshaus' boundary motives. Under the topological Betti realization, the stable motivic homotopy type at infinity of an algebraic variety recovers…
Mathematics and Art Connections Expressed in Artworks by South African Students
2022
In this chapter, we examine a collection of drawings, and paintings from South African students between the ages of 10 to 17, that provide fresh and original perceptions to some already known topics, but also several unexpected connections between mathematics and art. These works reference classic math-art connections such as: golden ratio, spirals, infinity, and geometric figures; they also contain several personal reflections, unique discoveries and references to ethnomathematical connections within the African cultural heritage. To introduce their pieces and themselves, students shared their own interpretations of their artworks. These commentaries make possible the identification of cog…