A direct method to obtain a realization of a polynomial matrix and its applications

[EN] In this paper we present a Silverman-Ho algorithm-based method to obtain a realization of a polynomial matrix. This method provides the final formulation of a minimal realization directly from a full rank factorization of a specific given matrix. Also, some classical problems in control theory such as model reduction in singular systems or the positive realization problem in standard systems are solved with this method.Work supported by the Spanish DGI grant MTM2017-85669-P-AR.Cantó Colomina, R.; Moll López, SE.; Ricarte Benedito, B.; Urbano Salvador, AM. (2020). A direct method to obtain a realization of a polynomial matrix and its applications. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-15. https://doi.org/10.1007/s13398-020-00819-1S1151142Anderson, B.D.O., Bongpanitlerd, S.: Network Analysis and Synthesis, A Modern Systems Theory Approach. Prentice-Hall Inc., New Jersey (1968)Benvenuti, L., Farina, L.: A tutorial on the positive realization problem. IEEE Trans. Autom. Control 49(5), 651–664 (2004). https://doi.org/10.1109/TAC.2004.826715Bru, R., Coll, C., Sánchez, E.: Structural properties of positive linear time-invariant difference-algebraic equations. Linear Algebra Appl. 349, 1–10 (2002). https://doi.org/10.1016/S0024-3795(02)00277-XCantó, R., Ricarte, B., Urbano, A.M.: Positive realizations of transfer matrices with real poles. IEEE Trans. Circuits Syst. II Expr. Br. 54(6), 517–521 (2007). https://doi.org/10.1109/TCSII.2007.894408Cantó, R., Ricarte, B., Urbano, A.M.: On positivity of discrete-time singular systems and the realization problem. Lect. Notes Control Inf. Sci. 389, 251–258 (2009). https://doi.org/10.1007/978-3-642-02894-6_24Climent, J., Napp, D., Requena, V.: Block Toeplitz matrices for burst-correcting convolutional codes. RACSAM 114, 38 (2020). https://doi.org/10.1007/s13398-019-00744-yDai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences. Springer-Verlag, New York (1989)Golub, G.H., Van Loan, C.F.: Matrix Computations, Fourth edn. Johns Hopkins University Press, Baltimore (2013)Henrion, D., Šebek, M.: Polynomial and matrix fraction description. In: Control Systems, Robotics and Automation, vol. 7, pp. 211-231, (2009). http://www.eolss.net/Sample-Chapters/C18/E6-43-13-05.pdfHo, B.L., Kalman, R.E.: Effective construction of linear state-variable models from mput/output functions. Regelungstechnik 14(12), 545–548 (1966)Kaczorek, T.: Weakly positive continuous-time linear systems. Lect. Notes Control Inf. Sci. 243, 3–16 (1999)Kaczorek, T.: Positive 1D and 2D Systems, vol. 431. Springer, London (2002)Kaczorek, T.: Externally and internally positive singular discrete-time linear systems. Int. J. Appl. Math. Comput. Sci. 12(2), 197–202 (2002)MATLAB, The Math Works, Inc., Natick, Massachusetts, United States. Official website: http://www.mathworks.comMcCrory, C., Parusinski, A.: The weight filtration for real algebraic varieties II: classical homology. RACSAM 108, 63–94 (2014). https://doi.org/10.1007/s13398-012-0098-ySilverman, L.: Realization of linear dynamical systems. IEEE Trans. Autom. Control 16(6), 554–567 (1971)Virnik, E.: Stability analysis of positive descriptor systems. Linear Algebra Appl. 429(10), 2640–2659 (2008

Rapidly increasing collimation and magnetic field changes of a H2O maser outflow

W75N(B) is a massive star-forming region that contains three radio continuum sources (VLA 1, VLA 2, and VLA 3), which are thought to be three massive young stellar objects at three different evolutionary stages. VLA 1 is the most evolved and VLA 2 the least evolved source. The 22 GHz H2O masers associated with VLA 1 and VLA 2 have been mapped at several epochs over eight years. While the H2O masers in VLA 1 show a persistent linear distribution along a radio jet, those in VLA 2 are distributed around an expanding shell. Furthermore, H2O maser polarimetric measurements revealed magnetic fields aligned with the two structures. Using new polarimetric observations of H2O masers, we aim to confirm the elliptical expansion of the shell-like structure around VLA 2 and, at the same time, to determine if the magnetic fields around the two sources have changed. The NRAO Very Long Baseline Array was used to measure the linear polarization and the Zeeman-splitting of the 22 GHz H2O masers towards the massive star-forming region W75N(B). The H2O maser distribution around VLA 1 is unchanged from that previously observed. We made an elliptical fit of the H2O masers around VLA 2. We find that the shell-like structure is still expanding along the direction parallel to the thermal radio jet of VLA 1. While the magnetic field around VLA 1 has not changed in the past 7 years, the magnetic field around VLA 2 has changed its orientation according to the new direction of the major-axis of the shell-like structure and it is now aligned with the magnetic field in VLA 1.Comment: 10 pages (5 + online material), 3 figures, 4 tables, accepted by Astronomy & Astrophysics Lette

Observing the onset of outflow collimation in a massive protostar

The current paradigm of star formation through accretion disks, and magnetohydrodynamically driven gas ejections, predicts the development of collimated outflows, rather than expansion without any preferential direction. We present radio continuum observations of the massive protostar W75N(B)-VLA 2, showing that it is a thermal, collimated ionized wind and that it has evolved in 18 years from a compact source into an elongated one. This is consistent with the evolution of the associated expanding water-vapor maser shell, which changed from a nearly circular morphology, tracing an almost isotropic outflow, to an elliptical one outlining collimated motions. We model this behavior in terms of an episodic, short-lived, originally isotropic, ionized wind whose morphology evolves as it moves within a toroidal density stratification.Comment: See also Supplementary Materials (SupMat_carrasco-gonzalez_etal_astroph.pdf) within the source file

Birth and early evolution of a planetary nebula

The final expulsion of gas by a star as it forms a planetary nebula --- the ionized shell of gas often observed surrounding a young white dwarf --- is one of the most poorly understood stages of stellar evolution. Such nebulae form extremely rapidly (about 100 years for the ionization) and so the formation process is inherently difficult to observe. Particularly puzzling is how a spherical star can produce a highly asymmetric nebula with collimated outflows. Here we report optical observations of the Stingray Nebula which has become an ionized planetary nebula within the past few decades. We find that the collimated outflows are already evident, and we have identified the nebular structure that focuses the outflows. We have also found a companion star, reinforcing previous suspicions that binary companions play an important role in shaping planetary nebulae and changing the direction of successive outflows.Comment: 9 pages + 3 figures. To appear in Nature, 2 April 199

Impacts of Early Holocene environmental dynamics on open-air occupation patterns in the Western Mediterranean: insights from El Arenal de la Virgen (Alicante, Spain)

Open-air sites represent a fundamental proxy of the Early Holocene adaptive systems in the Iberian Peninsula. However, its research potential for the study of human–environmental interactions has been minimally explored. In this work, we present the results of an integrated research programme focused on open-area excavations at the Mesolithic site of Arenal de la Virgen (Alicante, Spain). Novel multi-scalar geoarchaeological and archaeo-stratigraphic studies, coupled with featured-based palaeobotanical analysis, were used to design an extensive radiocarbon dating programme and produce different Bayesian chronological models. Our results distinguish two different Mesolithic occupation phases, dating to 9.3–9.1 and 8.6–8.3k cal a bp respectively, consisting of combustion features and lithic scatters. The comparison of occupational dynamics with the nearby palaeoecological records of Salines and Villena indicated that both Mesolithic phases occurred under relatively stable environmental conditions. The second Mesolithic phase, however, ended during the onset of the 8.2k cal a bp climatic event, when sedimentation processes shifted from soil formation to accretion of aeolian sands. We demonstrate that the end of the Mesolithic occupations at Arenal de la Virgen coincides with the cessation of radiocarbon-dated activity in other open-air Postglacial sites in the central Mediterranean region of Iberia.This research is primarily part of a project that has received funding from the European Research Council (ERC) under the Horizon 2020 research and innovation programme (Grant agreement No. 683018) to JFLdP. Additional analyses on the pollen data sets have been produced in the context of the research project HAR2017-88503-P supported by the Spanish Ministry of Science and Innovation. JFLdP is additionally supported by the Plan Gen-T programme (Ref.CIDEGENT-18/040) from the Generalitat Valenciana. JRR is currently supported by a Margarita Salas fellowship (ref. MARSALAS21-22) at the University of Alicante, and AP-D is holder of a María Zambrano fellowship at the University of the Basque Country (UPV/EHU) both funded by the European Union-Next Gene and the Ministry of Universities (Government of Spain)

A Brauer's theorem and related results

Given a square matrix A, a Brauer's theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75-91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system is noncontrollable. Other applications presented are related to the Jordan form of A and Wielandt's and Hotelling's deflations. An extension of the aforementioned Brauer's result, Rado's theorem, shows how to modify r eigenvalues of A at the same time via a rank-r perturbation without changing any of the remaining eigenvalues. The same results considered by blocks can be put into the block version framework of the above theorem. © 2012 Versita Warsaw and Springer-Verlag Wien.This work is supported by Fondecyt 1085125, Chile, the Spanish grant DGI MTM2010-18228 and the Programa de Apoyo a la Investigacion y Desarrollo (PAID-06-10) of the UPV.Bru García, R.; Cantó Colomina, R.; Soto, RL.; Urbano Salvador, AM. (2012). A Brauer's theorem and related results. Central European Journal of Mathematics. 10(1):312-321. https://doi.org/10.2478/s11533-011-0113-0S312321101Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91Crouch P.E., Introduction to Mathematical Systems Theory, Mathematik-Arbeitspapiere, Bremen, 1988Delchamps D.F., State-Space and Input-Output Linear Systems, Springer, New York, 1988Hautus M.L.J., Controllability and observability condition of linear autonomous systems, Nederl. Akad. Wetensch. Indag. Math., 1969, 72, 443–448Kailath T., Linear Systems, Prentice Hall Inform. System Sci. Ser., Prentice Hall, Englewood Cliffs, 1980Langville A.N., Meyer C.D., Deeper inside PageRank, Internet Math., 2004, 1(3), 335–380Perfect H., Methods of constructing certain stochastic matrices. II, Duke Math. J., 1955, 22(2), 305–311Saad Y., Numerical Methods for Large Eigenvalue Problems, Classics Appl. Math., 66, SIAM, Philadelphia, 2011Soto R.L., Rojo O., Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem, Linear Algebra Appl., 2006, 416(2–3), 844–856Wilkinson J.H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 196

On the spherical-axial transition in supernova remnants

A new law of motion for supernova remnant (SNR) which introduces the quantity of swept matter in the thin layer approximation is introduced. This new law of motion is tested on 10 years observations of SN1993J. The introduction of an exponential gradient in the surrounding medium allows to model an aspherical expansion. A weakly asymmetric SNR, SN1006, and a strongly asymmetric SNR, SN1987a, are modeled. In the case of SN1987a the three observed rings are simulated.Comment: 19 figures and 14 pages Accepted for publication in Astrophysics & Space Science in the year 201

Photoevaporating flows from the cometary knots in the Helix nebula (NGC 7293)

We explain the Ha emission of the cometary knots in the Helix Nebula (NGC 7293) with an analytical model that describes the emission of the head of the globules as a photoevaporated flow produced by the incident ionizing radiation of the central star.We compare these models with the Ha emission obtained from the HST archival images of the Helix Nebula. From a comparison of the Ha emission with the predictions of the analytical model we obtain a rate of ionizing photons from the central star of about 5e45 s^-1, which is consistent with estimates based on the total Hb flux of the nebula. We also model the tails of the cometary knots as a photoevaporated wind from a neutral shadow region produced by the diffuse ionizing photon field of the nebula. A comparison with the HST images allows us to obtain a direct determination of the value of the diffuse ionizing flux. We compare the ratio of diffuse to direct stellar flux as a function of radius inside an HII region with those obtained from the observational data through the analytical tail and head wind model. The agreement of this model with the values determined from the observations of the knots is excellent.Comment: 9 pages, 5 figures, accepted for publication in Ap

Advances in geobotany and new tools in biogeographic and bioclimatic maps: Sierra de Guadarrama National Park

20 páginas, 14 tablas, 3 mapas

A wide-angle outflow with the simultaneous presence of a high-velocity jet in the high-mass Cepheus A HW2 system

We present five epochs of VLBI water maser observations around the massive protostar Cepheus A HW2 with 0.4 mas (0.3 AU) resolution. The main goal of these observations was to follow the evolution of the remarkable water maser linear/arcuate structures found in earlier VLBI observations. Comparing the data of our new epochs of observation with those observed five years before, we find that at "large" scales of > 1" (700 AU) the main regions of maser emission persist, implying that both the surrounding medium and the exciting sources of the masers have been relatively stable during that time span. However, at smaller scales of < 0.1" (70 AU) we see large changes in the maser structures, particularly in the expanding arcuate structures R4 and R5. R4 traces a nearly elliptical patchy ring of ~ 70 mas size (50 AU) with expanding motions of ~ 5 mas/yr (15 km/s). This structure is probably driven by the wind of a still unidentified YSO located at the centre of the ring (~ 0.18" south of HW2). On the other hand, the R5 expanding bubble structure (driven by the wind of a previously identified YSO located ~ 0.6" south of HW2) is currently dissipating in the circumstellar medium and losing its previous degree of symmetry, indicating a very short-lived event. In addition, our results reveal, at scales of ~ 1" (700 AU), the simultaneous presence of a relatively slow (~ 10-70 km/s) wide-angle outflow (opening angle of ~ 102 deg, traced by the masers, and the fast (~ 500~km/s) highly collimated radio jet associated with HW2 (opening angle of ~ 18 deg, previously observed with the VLA. This simultaneous presence of a wide-angle outflow and a highly collimated jet associated with a massive protostar is similar to what is found in some low-mass YSOs. The implications of these results in the study of the formation of high-mass stars are discussed.Comment: 28 pages, 7 figures. Animations will be included as supporting material online (MNRAS web page