Stabilization of positive linear continuous-time systems by using a Brauer´s theorem

[EN] In this paper we study the stability property of positive linear continuous-time systems. This property is useful to study the asymptotic behavior of a dynamical system and specifically, in positive systems. Stabilization of linear systems using feedbacks has been deeply studied during the last decades. Motivated by some results, in this paper we find conditions on the system such that the eigenvalues of the closed loop system are in the open left half plane of the complex plane C. We do this by applying a Brauer s theorem.The authors would like to thank the referees and the editor for their comments and useful suggestions for improvement of the manuscript. This research was partially supported by Spanish Grant MTM2013-43678-P.Cantó Colomina, B.; Cantó Colomina, R.; Urbano Salvador, AM. (2016). Stabilization of positive linear continuous-time systems by using a Brauer´s theorem. International Journal of Complex Systems in Science. 6(1):23-28. http://hdl.handle.net/10251/81742S23286

Patologías musculoesqueléticas y/o dolor en los músicos profesionales de orquesta: revisión bibliográfica

INTRODUCCIÓN: La interpretación musical requiere mucho tiempo de ensayo suponiendo movimientos repetitivos y esfuerzos significativos. Los músicos son susceptibles a padecer una gran variedad de patologías, sobre todo trastornos musculoesqueléticos. El término más utilizado para describir dicha patología es “playing-related musculoskeletal disorder” (PRMD). OBJETIVOS: Conocer las lesiones musculoesqueléticas y/o dolor en músicos profesionales de orquesta más prevalentes según la literatura científica. MÉTODOS: Revisión bibliográfica de artículos publicados entre el 1 de enero de 2011 y el 1 de abril del 2022 utilizando Pubmed y Scopus como base de datos. RESULTADOS: Un total de 20 artículos observacionales fueron seleccionados. El 65% confirma que la prevalencia de los PRMD está alrededor del 62,5% y el 95%. El 40% y el 30% indica que las mujeres y los músicos de cuerda son más susceptibles respectivamente. El 50% afirma que existe una relación entre el instrumento tocado y el lugar afectado y el 60% que los lugares comunes más afectados son la columna cervical y lumbar, y las extremidades superiores. Finalmente, dos de los artículos tratan la articulación temporomandibular concluyendo que es más frecuente en los músicos de viento. CONCLUSIONES: Existe una prevalencia entre el 62,5% y el 95% de PRMD en los músicos profesionales siendo más frecuente en las mujeres y los instrumentos de cuerda. La columna cervical y lumbar y las extremidades superiores son los lugares más afectados. Sería conveniente seguir investigando y concienciar a la población de los hábitos posturales para prevenir dichas lesiones.INTRODUCTION: Music performance requires a lot of rehearsal time involving repetitive movements and significant strain. Musicians are susceptible to a wide variety of pathologies, especially musculoskeletal disorders. The term most commonly used to describe such patology is “playing-related musculoskeletal disorder” (PRMD). OBJECTIVES: To know the most prevalent musculoskeletal injuries and/or pain in professional orchestra musicians according to scientific literature. METHODS: Bibliographic review of articles published between January 1st, 2011 and April 1st, 2022 using Pubmed and Scopus as database. RESULTS: A total of 20 observational articles were selected. 65% confirm that the prevalence of PRMD is around 62.5% and 95%. 40% and 30% indicate that women and stringed musician are more susceptible respectively. 50% state that there is a relationship between the instrument played and the affected site and 60% that the most common sites affected are the cervical and lumbar spine and the upper extremities. Finally, 2 of the articles deal with the temporomandibular joint, concluding that it is more frequent in wind players. CONCLUSIONS: There is a prevalence between 62,5% and 95% of PRMD in professional musicians, being more frequent in women and stringed instruments. The cervical and lumbar spine and upper extremities are the most affected sites. It would be convenient to continue researching and to make the population aware of postural habits in order to prevent these injuries

Quasi-LDU factorization of nonsingular totally nonpositive matrices

Let A = (a(ij)) is an element of R-nxn be a nonsingular totally nonpositive matrix. In this paper we describe some properties of these matrices when a(11) = 0 and obtain a characterization in terms of the quasi-LDU factorization of A, where L is a block lower triangular matrix, D is a diagonal matrix and U is a unit upper triangular matrix. (c) 2012 Elsevier Inc. All rights reserved.The authors are very grateful to the referees for their helpful suggestions. This research was supported by the Spanish DGI Grant MTM2010-18228 and the Programa de Apoyo a la Investigacion y Desarrollo (PAID-06-10) of the Universitat Politecnica de Valencia.Cantó Colomina, R.; Ricarte Benedito, B.; Urbano Salvador, AM. (2013). Quasi-LDU factorization of nonsingular totally nonpositive matrices. Linear Algebra and its Applications. 439(4):836-851. https://doi.org/10.1016/j.laa.2012.06.010S836851439

Las competencias básicas a través del huerto escolar: una propuesta de proyecto de innovación

El huerto escolar es un recurso educativo que interrelaciona las diferentes áreas curriculares y favorece el desarrollo de las competencias básicas. En esta comunicación presentamos un proyecto de innovación educativa (L’hort 2.0) que se desarrolla en la Universidad de Valencia y que implica a profesores y alumnos del Grado de Maestro en Educación Primaria. Este proyecto es una propuesta integradora en la que se pretende crear un entorno virtual a partir de las experiencias realizadas en el huerto escolar. Los materiales se han diseñado con el objetivo de relacionar las actividades realizadas fuera y dentro del aula mediante contenidos TIC que contribuyen al desarrollo de las competencias básicas de los grados de Maestro de Primaria y de Maestro de Infantil, así como las competencias especificas de sus asignatura

Propiedades de las matrices totalmente no positivas

Una matriz real A se dice que es totalmente (negativa) no positiva si todos sus menores son (negativos) no positivos. En este trabajo veremos la factorización LDU de una matriz totalmente no positiva e invertible a partir del método de eliminación completo de Neville sin intercambio de filas y columnas. Dicha factorización nos permitirá generar de una forma sencilla matrices totalmente (negativas) no positivas del cualquier orden a partir de matrices totalmente positivas.Ministerio de Educación y Ciencia. Dirección General de InvestigaciónUniversidad Politécnica de Valenci

Full rank Cholesky factorization for rank deficient matrices

[EN] Let A be a rank deficient square matrix. We characterize the unique full rank Cholesky factorization LL^T of A where the factor L is a lower echelon matrix with positive leading entries. We compute an extended decomposition for the normal matrix B^TB where B is a rectangular rank deficient matrix. This decomposition is obtained without interchange of rows and without computing all entries of the normal matrix. Algorithms to compute both factorizations are given.This research was supported by the Spanish DGI grant MTM2010-18228 and by the Chilean program FONDECYT 1100029.Cantó Colomina, R.; Peláez, MJ.; Urbano Salvador, AM. (2015). Full rank Cholesky factorization for rank deficient matrices. Applied Mathematics Letters. 40:17-22. https://doi.org/10.1016/j.aml.2014.09.001S17224

Improving the condition number of a simple eigenvalue by a rank one matrix

In this work a technique to improve the condition number si of a simple eigenvalue lambda(i) of a matrix A is an element of C-nxn is given. This technique obtains a rank one updated matrix that is similar to A with the eigenvalue condition number of lambda(i) equal to one. More precisely, the similar updated matrix A + v(i)q*, where Av(i) = lambda(i)v(i) and q is a fixed vector, has s(i) = 1 and the remaining condition numbers are at most equal to the corresponding initial condition numbers. Moreover an expression to compute the vector q, using only the eigenvalue lambda(i) and its eigenvector v(i), is given. (C) 2016 Elsevier Ltd. All rights reserved.Supported by the Spanish DGI grant MTM2013-43678-P.Bru García, R.; Cantó Colomina, R.; Urbano Salvador, AM. (2016). Improving the condition number of a simple eigenvalue by a rank one matrix. Applied Mathematics Letters. 58:7-12. https://doi.org/10.1016/j.aml.2016.01.010S7125

Sobre las Matrices Totalmente No Positivas

[ES] En este trabajo presentamos un procedimiento para construir un tipo de matrices llamadas totalmente no positivas, estudiar sus propiedades y obtener las relaciones que tienen con otra clase de matrices llamadas totalmente no negativas.Este trabajo ha sido financiado por el proyecto MTM2017-85669-P-AR.Cantó Colomina, B.; Cantó Colomina, R.; Urbano Salvador, AM. (2021). Sobre las Matrices Totalmente No Positivas. Compobell. 49-52. http://hdl.handle.net/10251/191304495

On the characterization of totally nonpositive matrices

The final publication is available at Springer via http://dx.doi.org/10.1007/s40324-016-0073-1[EN] A nonpositive real matrix $A= (a_{ij})_{1 \leq i, j \leq n}$ is said to be totally nonpositive (negative) if all its minors are nonpositive (negative) and it is abbreviated as t.n.p. (t.n.). In this work a bidiagonal factorization of a nonsingular t.n.p. matrix $A$ is computed and it is stored in an matrix represented by $\mathcal{BD}_{(t.n.p.)}(A)$ when $a_{11}< 0$ (or $\mathcal{BD}_{(zero)}(A)$ when $a_{11}= 0$). As a converse result, an efficient algorithm to know if an matrix $\mathcal{BD}_{(t.n.p.)}(A)$ ($\mathcal{BD}_{(zero)}(A)$) is the bidiagonal factorization of a t.n.p. matrix with $a_{11}<0$ ($a_{11}= 0$) is given. Similar results are obtained for t.n. matrices using the matrix $\mathcal{BD}_{(t.n.)}(A)$, and these characterizations are extended to rectangular t.n.p. (t.n.) matrices. Finally, the bidiagonal factorization of the inverse of a nonsingular t.n.p. (t.n.) matrix $A$ is directly obtained from $\mathcal{BD}_{(t.n.p.)}(A)$ ($\mathcal{BD}_{(t.n.)}(A)$).This research was supported by the Spanish DGI grant MTM2013-43678-P and by the Chilean program FONDECYT 1100029Cantó Colomina, R.; Pelaez, MJ.; Urbano Salvador, AM. (2016). On the characterization of totally nonpositive matrices. SeMA Journal. 73(4):347-368. doi:10.1007/s40324-016-0073-1S347368734Ando, T.: Totally positive matrices. Linear Algebra Appl. 90, 165–219 (1987)Alonso, P., Peña, J.M., Serrano, M.L.: Almost strictly totally negative matrices: an algorithmic characterization. J. Comput. Appl. Math. 275, 238–246 (2015)Bapat, R.B., Raghavan, T.E.S.: Nonnegative Matrices and Applications. Cambridge University Press, New York (1997)Cantó, R., Koev, P., Ricarte, B., Urbano, A.M.: $$LDU$$ L D U -factorization of nonsingular totally nonpositive matrices. SIAM J. Matrix Anal. Appl. 30(2), 777–782 (2008)Cantó, R., Ricarte, B., Urbano, A.M.: Full rank factorization in echelon form of totally nonpositive (negative) rectangular matrices. Linear Algebra Appl. 431, 2213–2227 (2009)Cantó, R., Ricarte, B., Urbano, A.M.: Characterizations of rectangular totally and strictly totally positive matrices. Linear Algebra Appl. 432, 2623–2633 (2010)Cantó, R., Ricarte, B., Urbano, A.M.: Quasi- $$LDU$$ L D U factorization of nonsingular totally nonpositive matrices. Linear Algebra Appl. 439, 836–851 (2013)Cantó, R., Ricarte, B., Urbano, A.M.: Full rank factorization in quasi- $$LDU$$ L D U form of totally nonpositive rectangular matrices. Linear Algebra Appl. 440, 61–82 (2014)Fallat, S.M., Van Den Driessche, P.: On matrices with all minors negative. Electron. J. Linear Algebra 7, 92–99 (2000)Fallat, S.M.: Bidiagonal factorizations of totally nonnegative matrices. Am. Math. Mon. 108(8), 697–712 (2001)Fallat, S.M., Johnson, C.R.: Totally Nonnegative Matrices. Princeton University Press, New Jersey (2011)Gasca, M., Micchelli, C.A.: Total positivity and applications. Math. Appl. 359, Kluwer Academic Publishers, Dordrecht (1996)Gasca, M., Peña, J.M.: Total positivity, $$QR$$ Q R factorization and Neville elimination. SIAM J. Matrix Anal. Appl. 4, 1132–1140 (1993)Gasca, M., Peña, J.M.: A test for strict sign-regularity. Linear Algebra Appl. 197(198), 133–142 (1994)Gasca, M., Peña, J.M.: A matricial description of Neville elimination with applications to total positivity. Linear Algebra Appl. 202, 33–53 (1994)Gassó, M., Torregrosa, J.R.: A totally positive factorization of rectangular matrices by the Neville elimination. SIAM J. Matrix Anal. Appl. 25, 86–994 (2004)Huang, R., Chu, D.: Total nonpositivity of nonsingular matrices. Linear Algebra Appl. 432, 2931–2941 (2010)Huang, R., Chu, D.: Relative perturbation analysis for eigenvalues and singular values of totally nonpositive matrices. SIAM J. Matrix Anal. Appl. 36(2), 476–495 (2015)Karlin, S.: Total Nonpositivity. Stanford University Press, Stanford (1968)Koev, P.: Accurate eigenvalues and SVDs of totally nonnegative matrices. SIAM J. Matrix Anal. Appl. 27(1), 1–23 (2005)Koev, P.: Accurate computations with totally nonnegative matrices. SIAM J. Matrix Anal. Appl. 29(3), 731–751 (2007)Parthasarathy, T.: $$N$$ N -matrices. Linear Algebra Appl. 139, 89–102 (1990)Peña, J.M.: Test for recognition of total positivity. SeMA J. 62(1), 61–73 (2013)Pinkus, A.: Totally Positive Matrices. Cambridge Tracts in Mathematics, vol. 181. Cambridge University Press (2009)Saigal, R.: On the class of complementary cones and Lemke’s algorithm. SIAM J. Appl. Math. 23, 46–60 (1972

Realizaciones positivas de determinados sistemas singulares

En este trabajo se estudian los sistemas singulares lineales de control a partir de las propiedades obtenidas para los sistemas estándares. Se obtienen realizaciones positivas de ciertas matrices de trasferencia con polos reales, analizando las condiciones para que la dimensión de la realización positiva sea minimal