Search results for "Manipulation"
showing 10 items of 311 documents
Teaching and Learning of Algebra
2015
Topic Study Group 9 aimed to bring together researchers, developers and teachers who investigate and develop theoretical accounts of the teaching and learning of algebra. The group sought both empirically grounded contributions focussing on the learning and teaching of algebra in diverse classrooms settings, the evolution of algebraic reasoning from elementary through university schooling as well as theoretical contributions throwing light on the complexities involved in teaching and learning of algebra. Prospective contributors were requested to address one or more of the following themes: early algebra, use of ICT in algebra classrooms, proof and proving in algebra, problem solving, semio…
Chatbots by business vis-à-vis consumers: A new form of power and information asymmetry
2021
Research background: The first notable early chatbots were created in the sixties, but the growing use of artificial intelligence (AI) has powered them significantly. Studies show that basically chatbots are created and used for purposes by government and business, mostly in consumer service and marketing. The new Proposal of the Artificial intelligence act aims to promote the uptake of AI and address the risks associated with certain uses of such technology. However, the act contains only minimum transparency obligation for some specific AL systems such as chatbots. Purpose of the article: In light of this issue, the article aims to discuss how existing European Union (EU) consumer law is …
Jürgen Habermas and the risk of liberal eugenics for the ethical self-understanding of species
2016
El artículo analiza el problema de la naturaleza humana que presenta Jürgen Habermas en su obra El futuro de la naturaleza humana, ¿Hacia una eugenesia liberal? Los vertiginosos avances biotecnológicos reclaman una rigurosa reflexión bioética que el filósofo alemán afronta superponiendo a su ética del discurso una ética de la especie. Habermas esboza un modelo de naturaleza humana construido sobre preceptos como la dignidad humana y de la vida humana, la simetría de las relaciones intersubjetivas y, a resultas de estas, la autocomprensión ética de la especie. Respecto a la eugenesia liberal, el autor se posiciona criticando la eugenesia positiva y amparando la negativa, para lo que basa su …
Products of Bessel functions and associated polynomials
2013
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
Speeding up a few orders of magnitude the Jacobi method: high order Chebyshev-Jacobi over GPUs
2017
In this technical note we show how to reach a remarkable speed up when solving elliptic partial differential equations with finite differences thanks to the joint use of the Chebyshev-Jacobi method with high order discretizations and its parallel implementation over GPUs.
Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms
2017
In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to $\varepsilon$-form.
Simple differential equations for Feynman integrals associated to elliptic curves
2019
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is therefore of current interest, if these methods extend beyond the case of multiple polylogarithms. In this talk I discuss Feynman integrals, which are associated to elliptic curves and their differential equations. I show for non-trivial examples how the system of differential equations can be brought into an $\varepsilon$-form. Single-scale and multi-scale cases are discussed.
Differential equations for Feynman integrals beyond multiple polylogarithms
2017
Differential equations are a powerful tool to tackle Feynman integrals. In this talk we discuss recent progress, where the method of differential equations has been applied to Feynman integrals which are not expressible in terms of multiple polylogarithms.
On the computation of intersection numbers for twisted cocycles
2020
Intersection numbers of twisted cocycles arise in mathematics in the field of algebraic geometry. Quite recently, they appeared in physics: Intersection numbers of twisted cocycles define a scalar product on the vector space of Feynman integrals. With this application, the practical and efficient computation of intersection numbers of twisted cocycles becomes a topic of interest. An existing algorithm for the computation of intersection numbers of twisted cocycles requires in intermediate steps the introduction of algebraic extensions (for example square roots), although the final result may be expressed without algebraic extensions. In this article I present an improvement of this algorith…
A walk on sunset boulevard
2016
A walk on sunset boulevard can teach us about transcendental functions associated to Feynman diagrams. On this guided tour we will see multiple polylogarithms, differential equations and elliptic curves. A highlight of the tour will be the generalisation of the polylogarithms to the elliptic setting and the all-order solution for the sunset integral in the equal mass case.