Search results for " Mathematica"

Tripled Fixed Point Results for T-Contractions on Abstract Metric Spaces

2014

In this paper we introduce the notion of T-contraction for tripled fi xed points in abstract metric spaces and obtain some tripled fi xed point theorems which extend and generalize well-known comparable results in the literature. To support our results, we present an example and an application to integral equations.

Quasiconformal mappings and global integrability of the derivative

1991

Alcune riflessioni storico-critiche sul cosiddetto “paradosso di Duval”

2013

In 1993 a famous article by Raymond Duval highlighted a simple fact: students confuse the mathematical object O, that they are trying to build cognitively, with one of its semiotic representations R(O); he explained that this confusion was due to a sort of inevitable paradox: only someone who has already built O, can recognize R(O) as a representation of O and not as an object in itself. This idea has been extremely influential for researchers in the following years. However, many scholars of semiotics have emphasized the same phenomenon, even if in not quite the same words; in this paper we are going to mention some of them.

Fields of values of odd-degree irreducible characters

2019

Abstract In this paper we clarify the quadratic irrationalities that can be admitted by an odd-degree complex irreducible character χ of an arbitrary finite group. Write Q ( χ ) to denote the field generated over the rational numbers by the values of χ, and let d > 1 be a square-free integer. We prove that if Q ( χ ) = Q ( d ) then d ≡ 1 (mod 4) and if Q ( χ ) = Q ( − d ) , then d ≡ 3 (mod 4). This follows from the main result of this paper: either i ∈ Q ( χ ) or Q ( χ ) ⊆ Q ( exp ⁡ ( 2 π i / m ) ) for some odd integer m ≥ 1 .

A Realist Philosophy of Mathematics

2007

The realism/anti-realism debate is one of the traditional central themes in the philosophy of mathematics. The controversies about the existence of the irrational numbers, the complex numbers, the infinitesimals, etc. will be familiar to all who are acquainted with the history of mathematics. This book aims mainly at presenting and defending a non-Platonist form of mathematical structural realism which, in the respect of the history of mathematics, harmonizes with a plausible epistemology that naturally arises from it.

2020

Abstract We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees.

A relation between the curvature ellipse and the curvature parabola

2019

Abstract At each point in an immersed surface in ℝ4 there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. Recently, at the singular point of a corank 1 singular surface in ℝ3, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in ℝ4 to ℝ3 in a tangent direction, corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where more degenerate singularities can appear. In this paper we relate the geometry of an immersed surface in ℝ4 at a certain point to the geome…

Adiabatic evolution for systems with infinitely many eigenvalue crossings

1998

International audience; We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered projector, and some geometric hypothesis on the local behavior of the eigenvalues at the crossings.

Locally nilpotent derivations of rings graded by an abelian group

2019

International audience

Tuning the Pseudospin Polarization of Graphene by a Pseudomagnetic Field.

2016

One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudo-magnetic field as a result of mechanical deformation. In the case of graphene, the Landau quantization resulting from this pseudo-magnetic field has been measured using scanning tunneling microscopy. Here we show that a signature of the pseudo-magnetic field is a local sublattice symmetry breaking observable as a redistribution of the local density of states. This can be interpreted as a polarization of graphene's pseudospin due to a strain induced pseudo-magnetic field, in analogy to the alignment of a real spin in a magnetic field. We reveal this sublattice symmetry breaking by tunably straining grap…