Sandra Ricardo - Academia.edu (original) (raw)

Papers by Sandra Ricardo

Springer proceedings in mathematics & statistics, 2023

Annales Mathematicae Silesianae

In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defi... more In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided. Tridiagonal matrices are considered to determine the general term of this sequence.

Communications in Information and Systems, 2002

We consider a convex optimization problem on linearly constrained cones in Euclidean Jordan algeb... more We consider a convex optimization problem on linearly constrained cones in Euclidean Jordan algebras. The problem is solved using a damped Newton algorithm. Quadratic convergence to the global minimum is shown using an explicit step-size selection. Moreover, we prove that the algorithm is a smooth discretization of a Newton flow with Lipschitz continuous derivative.

SIAM Journal on Control and Optimization, 2013

ABSTRACT In this paper we characterise geodesically accessible mechanical control systems under s... more ABSTRACT In this paper we characterise geodesically accessible mechanical control systems under state and mechanical state equivalence. To this end, we consider two families of structure functions which are equivariants for the mechanical state equivalence (and, more generally, for the state equivalence) of two mechanical control systems satisfying the geodesic accessibility property. Those structure functions, constructed with the help of symmetric product and Lie product, encode in a geometric way all invariant information about mechanical control systems.

Dans cette these de Doctorat nous etudions la geometrie des systemes mecaniques de controle. Une ... more Dans cette these de Doctorat nous etudions la geometrie des systemes mecaniques de controle. Une classe speciale se distingue : la classe des systemes mecaniques accessibles au sens geodesique, pour laquelle l'unicite de la structure mecanique est garantie (a un diffeomorphisme pres). Dans la partie 1, nous caracterisons, en utilisant l'equivalence d'etat, cette classe de systemes autour des points de vitesse nulle. Nous etudions egalement l'equivalence d'etat et l'equivalence d'etat mecanique des systemes mecaniques affines par connexion qui sont accessibles au sens geodesique. Ces equivalences sont caracterisees par l'utilisation de deux familles d'equivariants. Nous discutons aussi l'equivalence d'etat d'un systeme de controle mecanique lineaire sans forces du type dissipatif, cas pour lequel il n'y a pas d'accessibilite geodesique. Dans la partie 2, nous considerons des systemes non-holonomes d'ordre deux et nous caract...

In this paper, we consider extended nonholonomic normal forms with drift obtained by extending th... more In this paper, we consider extended nonholonomic normal forms with drift obtained by extending the Brockett nonholonomic integrator. Necessary and sufficient conditions for the state equivalence to such forms are given. Copyright CONTROLO2012

We consider a convex optimization problem on linearly constrained cones in a Euclidean Jordan alg... more We consider a convex optimization problem on linearly constrained cones in a Euclidean Jordan algebra. The cost function consists of a quadratic cost term plus a penalty function. A damped Newton algorithm is proposed for minimization. Quadratic convergence to the global minimum is shown using an explicit step-size selection.

História da Ciência e Ensino: construindo interfaces

Resumo Neste trabalho refletimos sobre o ensino da Matemática em torno da década de 60 em Portu... more Resumo Neste trabalho refletimos sobre o ensino da Matemática em torno da década de 60 em Portugal, focando aspetos que nos parecem fulcrais na reforma educativa levada a cabo nesse período. A explosão científica que ocorreu no pós-Segunda Guerra Mundial motivou uma procura crescente de resposta para as novas necessidades de ensino, considerado desajustado à nova realidade. Movimentos reformistas no ensino da Matemática despoletaram pelo mundo com encontros científicos onde se debateram as novas necessidades, e o sistema educativo foi sujeito a uma completa reestruturação. Também em Portugal, um pouco na cauda do que se passava lá fora, se viveram tempos de mudança no ensino da Matemática. Novas políticas educativas conduziram a reformas no sistema de ensino, destacando-se notavelmente as impulsionadas pela excelência pedagógica de Sebastião e Silva. Surgiu assim a dita “Matemática Moderna”. Palavras-chave: Matemática; Ensino; História; Reformas. In this work w...

História da Ciência e Ensino: construindo interfaces

Resumo Se perguntassem a um matemático quais as virtudes e os defeitos da Matemática, ouviriam ... more Resumo Se perguntassem a um matemático quais as virtudes e os defeitos da Matemática, ouviriam certamente dizer “poupança de esforço” e “satisfação” versus “ansiedade” e “medo”. Neste trabalho vamos contar algumas Estórias da História da Matemática que, em parte, ilustram as três formas de economia em que assenta a Matemática: a ordem, a generalização e a representação concisa. Palavras-chave: Matemática, Estórias, História. If one asks a mathematician about the virtues and defects of mathematics, the expressions "effort-saving" and "satisfaction" versus "anxiety" and "fear" would certainly appear. In this work, we will tell some Math History Stories, which, in part, illustrate the three forms of economics on which mathematics is based: order, generalization and concise representation. Keywords: Mathematics, Stories, History.

História da Ciência e Ensino: construindo interfaces

Resumo A análise de sinais biomédicos desempenha, atualmente, um papel fundamental no auxílio ... more Resumo A análise de sinais biomédicos desempenha, atualmente, um papel fundamental no auxílio ao diagnóstico clínico. Os avanços científicos multiplicam-se a um ritmo frenético numa sociedade cada vez mais consciente e desejosa de soluções para os problemas de saúde. Este trabalho pretende dar uma perspetiva histórica dos avanços no estudo dos sinais biomédicos e refletir a sua importância na sociedade.Palavras-chave: Sinais Biomédicos; diagnóstico clínico; avanços Currently the biomedical signal analysis plays a fundamental role in helping clinical diagnosis. Scientific advances multiply at a frenetic pace in a society that is increasingly aware of and desirous of solutions to health problems. The need for constant updating of the means of clinical diagnosis is necessary to meet the demands of the world today. This work intends to give a historical perspective of advances in the biomedical signal study and to reflect its importance in society. Keywords: Biomedica...

Revista de Ciência Elementar

Este artigo é de acesso livre, distribuído sob licença Creative Commons com a designação CC-BY-NC... more Este artigo é de acesso livre, distribuído sob licença Creative Commons com a designação CC-BY-NC-SA 4.0, que permite a utilização e a partilha para fins não comerciais, desde que citado o autor e a fonte original do artigo.

We consider a convex optimization problem on linearly constrained cones in a Eu-clidean Jordan al... more We consider a convex optimization problem on linearly constrained cones in a Eu-clidean Jordan algebra. The cost function consists of a quadratic cost term plus a penalty function. A damped Newton algorithm is proposed for minimization. Quadratic convergence to the global minimum is shown using an explicit step-size selection.

We study a particular class of underactuated mechanical systems, known in the literature as the s... more We study a particular class of underactuated mechanical systems, known in the literature as the second-order nonholonomic chained form. We present two sets of geometric necessary and sufficient conditions that describe the local state equivalence of a control-affine system to a system of that class.

The Journal of Geometric Mechanics, 2010

ABSTRACT We present a geometric setting for studying mechanical control systems. We distinguish a... more ABSTRACT We present a geometric setting for studying mechanical control systems. We distinguish a special class: the class of geodesically accessible mechanical systems, for which the uniqueness of the mechanical structure is guaranteed (up to an extended point transformation). We characterise nonlinear control systems that are state equivalent to a system from this class and we describe the canonical mechanical structure attached to them. Several illustrative examples are given.

8th IFAC Symposium on Nonlinear Control Systems, 2010

Springer proceedings in mathematics & statistics, 2023

Annales Mathematicae Silesianae

In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defi... more In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided. Tridiagonal matrices are considered to determine the general term of this sequence.

Communications in Information and Systems, 2002

We consider a convex optimization problem on linearly constrained cones in Euclidean Jordan algeb... more We consider a convex optimization problem on linearly constrained cones in Euclidean Jordan algebras. The problem is solved using a damped Newton algorithm. Quadratic convergence to the global minimum is shown using an explicit step-size selection. Moreover, we prove that the algorithm is a smooth discretization of a Newton flow with Lipschitz continuous derivative.

SIAM Journal on Control and Optimization, 2013

ABSTRACT In this paper we characterise geodesically accessible mechanical control systems under s... more ABSTRACT In this paper we characterise geodesically accessible mechanical control systems under state and mechanical state equivalence. To this end, we consider two families of structure functions which are equivariants for the mechanical state equivalence (and, more generally, for the state equivalence) of two mechanical control systems satisfying the geodesic accessibility property. Those structure functions, constructed with the help of symmetric product and Lie product, encode in a geometric way all invariant information about mechanical control systems.

Dans cette these de Doctorat nous etudions la geometrie des systemes mecaniques de controle. Une ... more Dans cette these de Doctorat nous etudions la geometrie des systemes mecaniques de controle. Une classe speciale se distingue : la classe des systemes mecaniques accessibles au sens geodesique, pour laquelle l'unicite de la structure mecanique est garantie (a un diffeomorphisme pres). Dans la partie 1, nous caracterisons, en utilisant l'equivalence d'etat, cette classe de systemes autour des points de vitesse nulle. Nous etudions egalement l'equivalence d'etat et l'equivalence d'etat mecanique des systemes mecaniques affines par connexion qui sont accessibles au sens geodesique. Ces equivalences sont caracterisees par l'utilisation de deux familles d'equivariants. Nous discutons aussi l'equivalence d'etat d'un systeme de controle mecanique lineaire sans forces du type dissipatif, cas pour lequel il n'y a pas d'accessibilite geodesique. Dans la partie 2, nous considerons des systemes non-holonomes d'ordre deux et nous caract...

In this paper, we consider extended nonholonomic normal forms with drift obtained by extending th... more In this paper, we consider extended nonholonomic normal forms with drift obtained by extending the Brockett nonholonomic integrator. Necessary and sufficient conditions for the state equivalence to such forms are given. Copyright CONTROLO2012

We consider a convex optimization problem on linearly constrained cones in a Euclidean Jordan alg... more We consider a convex optimization problem on linearly constrained cones in a Euclidean Jordan algebra. The cost function consists of a quadratic cost term plus a penalty function. A damped Newton algorithm is proposed for minimization. Quadratic convergence to the global minimum is shown using an explicit step-size selection.

História da Ciência e Ensino: construindo interfaces

Resumo Neste trabalho refletimos sobre o ensino da Matemática em torno da década de 60 em Portu... more Resumo Neste trabalho refletimos sobre o ensino da Matemática em torno da década de 60 em Portugal, focando aspetos que nos parecem fulcrais na reforma educativa levada a cabo nesse período. A explosão científica que ocorreu no pós-Segunda Guerra Mundial motivou uma procura crescente de resposta para as novas necessidades de ensino, considerado desajustado à nova realidade. Movimentos reformistas no ensino da Matemática despoletaram pelo mundo com encontros científicos onde se debateram as novas necessidades, e o sistema educativo foi sujeito a uma completa reestruturação. Também em Portugal, um pouco na cauda do que se passava lá fora, se viveram tempos de mudança no ensino da Matemática. Novas políticas educativas conduziram a reformas no sistema de ensino, destacando-se notavelmente as impulsionadas pela excelência pedagógica de Sebastião e Silva. Surgiu assim a dita “Matemática Moderna”. Palavras-chave: Matemática; Ensino; História; Reformas. In this work w...

História da Ciência e Ensino: construindo interfaces

Resumo Se perguntassem a um matemático quais as virtudes e os defeitos da Matemática, ouviriam ... more Resumo Se perguntassem a um matemático quais as virtudes e os defeitos da Matemática, ouviriam certamente dizer “poupança de esforço” e “satisfação” versus “ansiedade” e “medo”. Neste trabalho vamos contar algumas Estórias da História da Matemática que, em parte, ilustram as três formas de economia em que assenta a Matemática: a ordem, a generalização e a representação concisa. Palavras-chave: Matemática, Estórias, História. If one asks a mathematician about the virtues and defects of mathematics, the expressions "effort-saving" and "satisfaction" versus "anxiety" and "fear" would certainly appear. In this work, we will tell some Math History Stories, which, in part, illustrate the three forms of economics on which mathematics is based: order, generalization and concise representation. Keywords: Mathematics, Stories, History.

História da Ciência e Ensino: construindo interfaces

Resumo A análise de sinais biomédicos desempenha, atualmente, um papel fundamental no auxílio ... more Resumo A análise de sinais biomédicos desempenha, atualmente, um papel fundamental no auxílio ao diagnóstico clínico. Os avanços científicos multiplicam-se a um ritmo frenético numa sociedade cada vez mais consciente e desejosa de soluções para os problemas de saúde. Este trabalho pretende dar uma perspetiva histórica dos avanços no estudo dos sinais biomédicos e refletir a sua importância na sociedade.Palavras-chave: Sinais Biomédicos; diagnóstico clínico; avanços Currently the biomedical signal analysis plays a fundamental role in helping clinical diagnosis. Scientific advances multiply at a frenetic pace in a society that is increasingly aware of and desirous of solutions to health problems. The need for constant updating of the means of clinical diagnosis is necessary to meet the demands of the world today. This work intends to give a historical perspective of advances in the biomedical signal study and to reflect its importance in society. Keywords: Biomedica...

Revista de Ciência Elementar

Este artigo é de acesso livre, distribuído sob licença Creative Commons com a designação CC-BY-NC... more Este artigo é de acesso livre, distribuído sob licença Creative Commons com a designação CC-BY-NC-SA 4.0, que permite a utilização e a partilha para fins não comerciais, desde que citado o autor e a fonte original do artigo.

We consider a convex optimization problem on linearly constrained cones in a Eu-clidean Jordan al... more We consider a convex optimization problem on linearly constrained cones in a Eu-clidean Jordan algebra. The cost function consists of a quadratic cost term plus a penalty function. A damped Newton algorithm is proposed for minimization. Quadratic convergence to the global minimum is shown using an explicit step-size selection.

We study a particular class of underactuated mechanical systems, known in the literature as the s... more We study a particular class of underactuated mechanical systems, known in the literature as the second-order nonholonomic chained form. We present two sets of geometric necessary and sufficient conditions that describe the local state equivalence of a control-affine system to a system of that class.

The Journal of Geometric Mechanics, 2010

ABSTRACT We present a geometric setting for studying mechanical control systems. We distinguish a... more ABSTRACT We present a geometric setting for studying mechanical control systems. We distinguish a special class: the class of geodesically accessible mechanical systems, for which the uniqueness of the mechanical structure is guaranteed (up to an extended point transformation). We characterise nonlinear control systems that are state equivalent to a system from this class and we describe the canonical mechanical structure attached to them. Several illustrative examples are given.

8th IFAC Symposium on Nonlinear Control Systems, 2010