Judith Rivas | University of the Basque Country, Euskal Herriko Unibertsitatea (original) (raw)
Papers by Judith Rivas
Mathematics and dance may be thought as disciplines very far away one from each other and it may ... more Mathematics and dance may be thought as disciplines very far away one from each other and it may seem that finding links between them is impossible, but in this paper we will show that this is not true. Wearing mathematical glasses, we will easily find basic geometrical concepts. On one hand, we will see that dancers, when organized in groups, form circumferences, rectangles and other polygons; on the other hand, we will describe symmetries among dancers’ positions, by means of rotations, translations and reflections. We will also describe other dances making use of deeper and less obvious concepts, such as permutations and combinations from combinatorics and braid theory from topology.
Numerical Methods For Partial Differential Equations, 2012
ABSTRACT We consider the approximation by spectral and pseudo‐spectral methods of the solution of... more ABSTRACT We consider the approximation by spectral and pseudo‐spectral methods of the solution of the Cauchy problem for a scalar linear hyperbolic equation in one space dimension posed in the whole real line. To deal with the fact that the domain of the equation is unbounded, we use Hermite functions as orthogonal basis. Under certain conditions on the coefficients of the equation, we prove the spectral convergence rate of the approximate solutions for regular initial data in a weighted space related to the Hermite functions. Numerical evidence of this convergence is also presented. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012
SIAM Journal on Numerical Analysis, 2011
Journal of Mathematical Analysis and Applications, 2005
Communications in Partial Differential Equations, 2003
... DOI: 10.1081/PDE-120021181 Susana Gutiérrez a * , Judith Rivas a & Luis V... more ... DOI: 10.1081/PDE-120021181 Susana Gutiérrez a * , Judith Rivas a & Luis Vega a pages 927-968. Available online: 14 Feb 2007. ...
La tesis que se presenta analiza métodos espectrales basados en funciones de Hermite aplicados a ... more La tesis que se presenta analiza métodos espectrales basados en funciones de Hermite aplicados a ecuaciones hiperbólicas escalares en una dimensión espacial, tanto lineales como no lineales, planteadas en toda la recta real, La idea de un método espectral es aproximar ...
Numerische Mathematik, 2011
La tesis que se presenta analiza métodos espectrales basados en funciones de Hermite aplicados a ... more La tesis que se presenta analiza métodos espectrales basados en funciones de Hermite aplicados a ecuaciones hiperbólicas escalares en una dimensión espacial, tanto lineales como no lineales, planteadas en toda la recta real, La idea de un método espectral es aproximar ...
Numerical Methods for Partial Differential Equations, 2012
Numerische Mathematik, 2011
SIAM Journal on Numerical Analysis, 2011
We consider the approximation by a spectral method of the solution of the Cauchy problem for a sc... more We consider the approximation by a spectral method of the solution of the Cauchy problem for a scalar conservation law in one dimension posed in the whole real line. We analyze a
spectral viscosity method in which the orthogonal basis considered is the one of Hermite functions. We prove the convergence of the approximate solution to the unique entropy solution of the problem by using compensated compactness arguments.
We find an error bound for the pseudospectral approximation of a function in terms of Hermite fun... more We find an error bound for the pseudospectral approximation of a function in terms of Hermite functions, hn(x)=e−x2Hn(x)h_n(x) = e^{-x^2} H_n(x)hn(x)=e−x2Hn(x), in certain weighted Sobolev spaces. We use properties of Hermite polynomials, as well as an asymptotic expression for their largest zeroes to achieve the mentioned
estimate.
Mathematics and dance may be thought as disciplines very far away one from each other and it may ... more Mathematics and dance may be thought as disciplines very far away one from each other and it may seem that finding links between them is impossible, but in this paper we will show that this is not true. Wearing mathematical glasses, we will easily find basic geometrical concepts. On one hand, we will see that dancers, when organized in groups, form circumferences, rectangles and other polygons; on the other hand, we will describe symmetries among dancers’ positions, by means of rotations, translations and reflections. We will also describe other dances making use of deeper and less obvious concepts, such as permutations and combinations from combinatorics and braid theory from topology.
Numerical Methods For Partial Differential Equations, 2012
ABSTRACT We consider the approximation by spectral and pseudo‐spectral methods of the solution of... more ABSTRACT We consider the approximation by spectral and pseudo‐spectral methods of the solution of the Cauchy problem for a scalar linear hyperbolic equation in one space dimension posed in the whole real line. To deal with the fact that the domain of the equation is unbounded, we use Hermite functions as orthogonal basis. Under certain conditions on the coefficients of the equation, we prove the spectral convergence rate of the approximate solutions for regular initial data in a weighted space related to the Hermite functions. Numerical evidence of this convergence is also presented. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012
SIAM Journal on Numerical Analysis, 2011
Journal of Mathematical Analysis and Applications, 2005
Communications in Partial Differential Equations, 2003
... DOI: 10.1081/PDE-120021181 Susana Gutiérrez a * , Judith Rivas a & Luis V... more ... DOI: 10.1081/PDE-120021181 Susana Gutiérrez a * , Judith Rivas a & Luis Vega a pages 927-968. Available online: 14 Feb 2007. ...
La tesis que se presenta analiza métodos espectrales basados en funciones de Hermite aplicados a ... more La tesis que se presenta analiza métodos espectrales basados en funciones de Hermite aplicados a ecuaciones hiperbólicas escalares en una dimensión espacial, tanto lineales como no lineales, planteadas en toda la recta real, La idea de un método espectral es aproximar ...
Numerische Mathematik, 2011
La tesis que se presenta analiza métodos espectrales basados en funciones de Hermite aplicados a ... more La tesis que se presenta analiza métodos espectrales basados en funciones de Hermite aplicados a ecuaciones hiperbólicas escalares en una dimensión espacial, tanto lineales como no lineales, planteadas en toda la recta real, La idea de un método espectral es aproximar ...
Numerical Methods for Partial Differential Equations, 2012
Numerische Mathematik, 2011
SIAM Journal on Numerical Analysis, 2011
We consider the approximation by a spectral method of the solution of the Cauchy problem for a sc... more We consider the approximation by a spectral method of the solution of the Cauchy problem for a scalar conservation law in one dimension posed in the whole real line. We analyze a
spectral viscosity method in which the orthogonal basis considered is the one of Hermite functions. We prove the convergence of the approximate solution to the unique entropy solution of the problem by using compensated compactness arguments.
We find an error bound for the pseudospectral approximation of a function in terms of Hermite fun... more We find an error bound for the pseudospectral approximation of a function in terms of Hermite functions, hn(x)=e−x2Hn(x)h_n(x) = e^{-x^2} H_n(x)hn(x)=e−x2Hn(x), in certain weighted Sobolev spaces. We use properties of Hermite polynomials, as well as an asymptotic expression for their largest zeroes to achieve the mentioned
estimate.