Search results for " Overview."
showing 10 items of 153 documents
Robert de Montessus de Ballore's 1902 theorem on algebraic continued fractions : genesis and circulation
2013
Robert de Montessus de Ballore proved in 1902 his famous theorem on the convergence of Pad\'e approximants of meromorphic functions. In this paper, we will first describe the genesis of the theorem, then investigate its circulation. A number of letters addressed to Robert de Montessus by different mathematicians will be quoted to help determining the scientific context and the steps that led to the result. In particular, excerpts of the correspondence with Henri Pad\'e in the years 1901-1902 played a leading role. The large number of authors who mentioned the theorem soon after its derivation, for instance N\"orlund and Perron among others, indicates a fast circulation due to factors that w…
"Table 25" of "Multiplicity dependence of K*(892)$^{0}$ and $\phi$(1020) production in pp collisions at $\sqrt{s}$ = 13 TeV"
2020
$\phi$ transverse momentum spectrum - V0M multiplicity class VII
Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra
2019
Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, a…
A? * algebra of pseudodifferential operators on noncompact manifolds
1988
On montre qu'une classe d'operateurs pseudodifferentiels d'ordre zero a la propriete d'invariance spectrale
Pieri’s 1900 Point-and-Motion Memoir
2021
This chapter contains an English translation of Mario Pieri’s 1900a memoir, On Elementary Geometry as a Hypothetical Deductive System: Monograph on Point and on Motion.1 By elementary geometry, Pieri meant Euclidean geometry as taught then in elementary courses, except for the theorems dependent on the Euclidean parallel axiom.
Normal forms of hyperbolic logarithmic transseries
2021
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.
Student use of resources in Calculus and Linear Algebra
2018
International audience; In this study we have investigated the resources used by first year engineering students in a technical university in the Netherlands, for their learning of Calculus and Linear Algebra. Using a case study approach we have focused on how the resources and their use (a) differed from upper secondary school as compared to university, and (b) differed between the two university courses. The results indicate that, in terms of (a) students built on secondary school experiences and emulated these into their university courses, where some subsequently experienced difficulties. In terms of (b), we argue that the course organization and the alignment of curriculum materials wi…
Systèmes hyperboliques d'équations aux dérivées partielles linéaires : régularité et matrices diagonalisables
2001
Resume La regularite des solutions d'un systeme d'equations aux derivees partielles hyperbolique, est liee aux proprietes spectrales d'un faisceaux de matrices reelles. Nous nous interessons ici a la regularite L 2 . Celle ci est obtenue si et seulement si l'exponentielle imaginaire du faisceau est bornee. Nous regardons le lien entre cette condition et les proprietes spectrales du faisceau, ici diagonalisable sur R . Nous donnons en particulier un critere d'exponentielle bornee si les valeurs propres ne sont pas de multiplicites constantes, et nous montrons que dans le cas des faisceaux engendres par deux matrices 3×3, l'exponentielle est bornee si et seulement si le faisceau est analytiqu…
Historical Notes on Star Geometry in Mathematics, Art and Nature
2018
Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”
Learning About Forces Using Multiple Representations
2017
We present two research-based interventions to measure upper secondary student learning of forces using multiple representations (MRs). The first intervention is the Representational Variant of the Force Concept Inventory (R-FCI) – a multiple-choice test for evaluating students’ representational consistency in answering triplets of isomorphic items in the context of forces. The second intervention is an interaction diagram (ID) – a visual representation that helps students to identify forces resulting from interactions between two objects. Students’ representational consistency on the R-FCI pre-test correlated with their normalised learning gain on the Force Concept Inventory (FCI) suggesti…