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Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8

Mohamad Cheaito, Piotr Mormul (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the rank–2 distributions satisfying so-called Goursat condition (GC); that is to say, codimension–2 differential systems forming with their derived systems a flag. Firstly, we restate in a clear way the main result of[7] giving preliminary local forms of such systems. Secondly – and this is the main part of the paper – in dimension 7 and 8 we explain which constants in those local forms can be made 0, normalizing the remaining ones to 1. All constructed equivalences are explicit. ...

Rarita-Schwinger type operators on spheres and real projective space

Junxia Li, John Ryan, Carmen J. Vanegas (2012)

Archivum Mathematicum

In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger...

Rational approximation near zero sets of functions.

Peter V. Paramonov (1989)

Publicacions Matemàtiques

The paper deals with the relation between global rational approximation and local approximation off the zero set. Also connections with the problem f2 ∈ R(X) ⇒ f ∈ R(X) are studied.

Rational interpolants with preassigned poles, theoretical aspects

Amiran Ambroladze, Hans Wallin (1999)

Studia Mathematica

Let ⨍ be an analytic function on a compact subset K of the complex plane ℂ, and let r n ( z ) denote the rational function of degree n with poles at the points b n i i = 1 n and interpolating ⨍ at the points a n i i = 0 n . We investigate how these points should be chosen to guarantee the convergence of r n to ⨍ as n → ∞ for all functions ⨍ analytic on K. When K has no “holes” (see [8] and [3]), it is possible to choose the poles b n i i , n without limit points on K. In this paper we study the case of general compact sets K, when such a separation...

Real and complex pseudozero sets for polynomials with applications

Stef Graillat, Philippe Langlois (2007)

RAIRO - Theoretical Informatics and Applications

Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real pseudozero...

Real C k Koebe principle

Weixiao Shen, Michael Todd (2005)

Fundamenta Mathematicae

We prove a C k version of the real Koebe principle for interval (or circle) maps with non-flat critical points.

Real Schottky uniformizations and Jacobians of May surfaces.

Rubén A. Hidalgo, Rubí E. Rodríguez (2004)

Revista Matemática Iberoamericana

Given a closed Riemann surface R of genus p ≥ 2 together with an anticonformal involution τ : R ---> R with fixed points, we consider the group K(R, τ) consisting of the conformal and anticonformal automorphisms of R which commute with τ...

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