(M, N) - Coherent pairs of linear functionals and Jacobi matrices

A pair of regular linear functionals (U,V) in the linear space of polynomials with complex coefficients is said to be an (M,N) -coherent pair of order m if their corresponding sequences of monic orthogonal polynomials {Pn(x)}n⩾0 and {Qn(x)}n⩾0 satisfy a structure relation ∑i=0Mai,nP(m)n+m−i(x)=∑i=0Nbi,nQn−i(x),n⩾0, Turn MathJax off where M,N , and m are non-negative integers, {ai,n}n⩾0,0⩽i⩽M , and {bi,n}n⩾0,0⩽i⩽N , are sequences of complex numbers such that aM,n≠0 if n⩾M,bN,n≠0 if n⩾N , and ai,n=bi,n=0 if i>n . When m=1,(U,V) is called an (M,N) -coherent pair. In this work, we give a matrix interpretation of (M,N) -coherent pairs of linear functionals. Indeed, an algebraic relation between the corresponding monic tridiagonal (Jacobi) matrices associated with such linear functionals is stated. As a particular situation, we analyze the case when one of the linear functionals is classical. Finally, the relation between the Jacobi matrices associated with (M,N) -coherent pairs of linear functionals of order m and the Hessenberg matrix associated with the multiplication operator in terms of the basis of monic polynomials orthogonal with respect to the Sobolev inner product defined by the pair (U,V) is deduced.The work of F. Marcellán and N. C. Pinzón-Cortés has been supported by Dirección General de Investigación, Desarrollo e Innovación, Ministerio de Economía y Competitividad of Spain, Grant MTM2012-36732-C03-01

(1,1) - Coherent pairs on the unit circle

A pair (U,V) of Hermitian regular linear functionals on the unit circle is said to be a (1, 1)-coherent pair if their corresponding sequences of monic orthogonal polynomials {()}≥0 and {()}≥0 satisfy [1] () + [1] −1() = () + −1(), ≠ 0, ≥ 1, where [1] () = +1()/( + 1). In this contribution, we consider the cases when U is the linear functional associated with the Lebesgue and Bernstein-Szeg˝o measures, respectively, and we obtain a classification of the situations where V is associated with either a positive nontrivial measure or its rational spectral transformation.The authors thank the referee the valuable comments. They greatly contributed to improve the contents of the paper. The work of Luis Garza was supported by Conacyt Grant no. 156668 and Beca Santander Iberoam´erica para J´ovenes Profesores e Investigadores (Mexico). The work of Francisco Marcell´an and Natalia C. Pinz´on-Cort´es has been supported by Direcci´on General de Investigaci´on, Desarrollo e Innovaci ´on, Ministerio de Econom´ıa y Competitividad of Spain, Grant MTM2012-36732-C03-01

On linearly related sequences of difference derivatives of discrete orthogonal polynomials

Proceedings of: OrthoQuad 2014. Puerto de la Cruz, Tenerife, Spain. January 20–24, 2014Let ν be either ω∈C∖{0} or q∈C∖{0,1} , and let Dν be the corresponding difference operator defined in the usual way either by Dωp(x)=p(x+ω)−p(x)ω or Dqp(x)=p(qx)−p(x)(q−1)x . Let U and V be two moment regular linear functionals and let {Pn(x)}n≥0 and {Qn(x)}n≥0 be their corresponding orthogonal polynomial sequences (OPS). We discuss an inverse problem in the theory of discrete orthogonal polynomials involving the two OPS {Pn(x)}n≥0 and {Qn(x)}n≥0 assuming that their difference derivatives Dν of higher orders m and k (resp.) are connected by a linear algebraic structure relation such as ∑Mi=0ai,nDmνPn+m−i(x)=∑Ni=0bi,nDkνQn+k−i(x),n≥0, Turn MathJax off where M,N,m,k∈N∪{0} , aM,n≠0 for n≥M , bN,n≠0 for n≥N , and ai,n=bi,n=0 for i>n . Under certain conditions, we prove that U and V are related by a rational factor (in the ν− distributional sense). Moreover, when m≠k then both U and V are Dν -semiclassical functionals. This leads us to the concept of (M,N) - Dν -coherent pair of order (m,k) extending to the discrete case several previous works. As an application we consider the OPS with respect to the following Sobolev-type inner product ⟨p(x),r(x)⟩λ,ν=⟨U,p(x)r(x)⟩+λ⟨V,(Dmνp)(x)(Dmνr)(x)⟩,λ>0, Turn MathJax off assuming that U and V (which, eventually, may be represented by discrete measures supported either on a uniform lattice if ν=ω , or on a q -lattice if ν=q ) constitute a (M,N) - Dν -coherent pair of order m (that is, an (M,N) - Dν -coherent pair of order (m,0) ), m∈N being fixed.We are grateful to Prof. Francisco Marcellán for his valuable comments and remarks that helped us to improve the paper. This work was supported by Dirección General de Investigación, Desarrollo e Innovación, Ministerio de Economía y Competitividad of Spain, under grants MTM2012-36732-C03 (RAN, NCP-C, JP), Junta de Andalucía (Spain) under grants FQM262, FQM-7276, and P09-FQM-4643 (RAN), FEDER funds (RAN

(M, N)-coherent pairs of order (m, k) and Sobolev orthogonal polynomials

A pair of regular linear functionals (U,V)(U,V) is said to be a (M,N)(M,N)-coherent pair of order (m,k)(m,k) if their corresponding sequences of monic orthogonal polynomials...We thank the referees for the careful revision of the manuscript. Their comments and suggestions have contributed to improve substantially the presentation. The work of F. Marcellán, J. Petronilho, and N.C. Pinzón-Cortés has been supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain, under grants MTM2012-36732-C03-01 (FM and NCP-C) and MTM2012-36732-C03-02 (JP). The work of J. Petronilho was also supported by the Centro de Matemática da Universidade de Coimbra (CMUC), funded by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT—Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0324/2011, and the research project PTDC/MAT/098060/2008 (FCT)

A matrix characterization for the D-v-semiclassical and D-v-coherent orthogonal polynomials

We present a new structure relation for the sequence of orthogonal polynomials associated with a D-v-semiclassical linear functional of class s, and then we use it to obtain a matrix characterization of the D-v-semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials, and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials. We also provide a matrix characterization of D-v-coherent pairs of linear functionals.The work of the first author was supported by a grant of the Secretar´ıa de Educaci´on P´ublica of M´exico and the Mexican Government. The work of the second author was supported by Consejo Nacional de Ciencia y Tecnolog´ıa of M´exico, grant 156668. The work of the third author was supported by Direcci ´on General de Investigaci´on Cient´ıfica y T´ecnica, Ministerio de Econom´ıa y Competitividad of Spain, grant MTM2012-36732-C03-01. The authors thank the anonymous referee for her/his valuable comments and suggestions. They contributed to improve the presentation of the manuscript

Algebras de azumaya y el locus de azumaya de una algebra de weyl cuantizada

Magíster en MatemáticasMaestrí

(1,1)-Dw-omega-coherent pairs

In this work, we introduce the notion of (1; 1)-Dw-coherent pair of weakly quasi-de nite linear functionals (U; V) as the Dw-analogue to the generalized coherent pair studied by A. Delgado and F. Marcell an in [8]. This means that their corresponding families of monic orthogonal poly- nomials fPn(x)gM0 n=0 and fRn(x)gM1 n=0 satisfy We prove that (1; 1)-Dw-coherence is a su cient condition for the weakly quasi-de nite linear functionals to be Dw-semiclassical, one of them of class at most 1 and the another of class at most 5, and they are related by a expression of rational type. Additionally, a matrix interpretation of (1; 1)-Dw-coherence in terms of the corresponding monic Jacobi matrices is given. The particular case when μ is Dw-classical linear functional is studied.The authors thank the hard work done by the referees. Their suggestions and remarks have contributed to improve the presentation of the manuscript. The work of F. Marcell´an and N. C. Pinzo´n-Cort´es has been supported by Direcci´on General de Investigaci´on Cient´ıfica y T´ecnica, Ministerio de Econom´ıa y Competitividad of Spain, grant MTM2012-36732-C03-01

Carta de Psicología No. 54

El capital psicológico y el engagement en el trabajo: revisión teórica / Angie Lorena Escobar Giraldo, Carol Valentina Londoño Pantoja y Laura Valentina Rojas Montealegre. Relación entre clima organizacional y engagement desde una mirada del modelo de Avalores en competencia / Karol Sunev Encinales y Angie Julieth Riaño. Relación de los estilos de liderazgo transformacional y transaccional en el clima organizacional: una revisión de la literatura / Leidy Tatiana Javela Avila y Angie Johana Maldonado Bejarano. El bienestar organizacional: una revisión teórica desde lo hedónico y lo eudaimónico / Astrid Carolina Rodríguez Prieto, Daniela Sthefania Pérez Arango y Laura Jimena Mondragón. Estudio comparativo de la normatividad en torno al acoso laboral / Magda Cardozo y Paola Andrea Rubiano. Análisis del estilo lingüístico prosocial y altruista / Luis Fernando Benedetti, Luisa Fernanda Martínez y Juan Camilo Carvajal-Builes. Violencia intrafamiliar como una problemática juvenil en Colombia / María José Saavedra Vargas y Daniela Barbosa Ardila. Análisis psicológico de la trata de personas con fines / María José Saavedra Vargas y Daniela Barbosa Ardila. Sobre el reciclaje: su debida ejecución y su importancia para el medio ambiente / María Camila Londoño Fernández y Camilo Jesús Alejandro Vivas Becerra. Estrategias de aprendizaje espacial con apoyo virtual en hombres y mujeres desde una visión evolutiva / Natalia Pareja Henao, J. Jacobo Pinto Galindo, Esteban Ayala Vargas, Ivonne Edith Alejo Castañeda y Tatiana Manrique Zuluaga. La música favorece la atención en niños / Manuela María del Rocío Pinzón, Laura Geraldine Cortés, Tatiana Manrique Zuluaga e Ivonne Edith Alejo Castañeda. La autorregulación y la autonomía, un abordaje desde la psicología del desarrollo infantil / Diana Paola Pardo Galvis, Lizeth Tatiana Herrera Toro y Julieth María Ospina Osorio. Importancia e incidencia de la vocación y la profesión en el sector social LGBTIQ / Lieen D. Guevara G. Sistema de Responsabilidad Penal para Niños o Adolescentes (SRPA) en Colombia / Diana Paola Pardo Galvis, Lizeth Tatiana Herrera Toro y Erika Natalia Algarra Martínez. Breve revisión de la importancia del desarrollo de los niños, niñas y adolescentes (NNA) y sus derechos de participación dentro del contexto sociopolítico / Daniela Barbosa Ardila y María José Saavedra Vargas. “Verdad y mentira”: conceptos relacionados con el ejercicio de la psicología del testimonio / María Paula Castro y Juan Camilo Carvajal-Builes. Comportamientos de violencia conyugal naturalizados por jóvenes universitarios de Bogotá / Daniela Alejandra Martínez Sarmiento, María Fernanda Nieto Ramírez, Laura Andrea Torres Pulido, María Emily Triana Jiménez y Darío León Rincó

ENGIU: Encuentro Nacional de Grupos de Investigación de UNIMINUTO.

El desarrollo del prototipo para el sistema de detección de Mina Antipersona (MAP), inicia desde el semillero ADSSOF perteneciente al programa de Administración en Seguridad y Salud en el trabajo de la UNIMINUTO, se realiza a partir de un detector de metales que emite una señal audible, que el usuario puede interpretar como aviso de presencia de un objeto metálico, en este caso una MAP. La señal audible se interpreta como un dato, como ese dato no es perceptible a 5 metros de distancia, se implementa el transmisor de Frecuencia Modulada FM por la facilidad de modulación y la escogencia de frecuencia de transmisión de acuerdo con las normas y resolución del Ministerio de Comunicaciones; de manera que esta sea la plataforma base para enviar los datos obtenidos a una frecuencia establecida. La idea es que el ser humano no explore zonas peligrosas y buscar la forma de crear un sistema que permita eliminar ese riesgo, por otro lado, buscar la facilidad de uso de elementos ya disponibles en el mercado