Relative Asymptotic of Multiple Orthogonal Polynomials for Nikishin Systems

We prove relative asymptotic for the ratio of two sequences of multiple orthogonal polynomials with respect to Nikishin system of measures. The first Nikishin system ${\mathcal{N}}(\sigma_1,...,\sigma_m)$ is such that for each $k$, $\sigma_k$ has constant sign on its compact support \supp {\sigma_k} \subset \mathbb{R} consisting of an interval $\widetilde{\Delta}_k$, on which $|\sigma_k^{\prime}| > 0$ almost everywhere, and a discrete set without accumulation points in $\mathbb{R} \setminus \widetilde{\Delta}_k$. If {Co}(\supp {\sigma_k}) = \Delta_k denotes the smallest interval containing \supp {\sigma_k}, we assume that $\Delta_k \cap \Delta_{k+1} = \emptyset$, $k=1,...,m-1$. The second Nikishin system ${\mathcal{N}}(r_1\sigma_1,...,r_m\sigma_m)$ is a perturbation of the first by means of rational functions $r_k$, $k=1,...,m,$ whose zeros and poles lie in $\mathbb{C} \setminus \cup_{k=1}^m \Delta_k$.Comment: 30 page

Multipoint rational approximants with preassigned poles

20 pages, no figures.-- MSC1991 codes: 41A21, 42C05, 30E10.MR#: MR1820073 (2002i:41021)Zbl#: Zbl 1160.41305Let $\mu$ be a finite positive Borel measure whose support $S(\mu)$ is a compact regular set contained in $\Bbb R$. For a function of Markov type $\hat\mu(z)=\int_{S(\mu)}d\mu(x)/(z-x)$, z\in\Bbb C\sbs S(\mu), we consider multipoint Padé-type approximants (MPTAs), where some poles are preassigned and interpolation is carried out along a table of points contained in \overline{\Bbb C}\sbs {\rm Co}(S(\mu)) which is symmetrical with respect to the real line. The main purpose of this paper is the study of the `exact rate of convergence' of the MPTAs to the function $\hat\mu$.Research by first author (F.C.) partially carried out at the Mathematics Department of Umeå University under Guest Scholarship from the Swedish Institute. Research by second author (G.L.L.) partially supported by Dirección General de Enseñanza Superior under grant PB 96-0120-CO3-01 and by INTAS under grant 93-0219 EXT.Publicad

First report of Delphastus quinculus Gordon and Diomus seminulus (Mulsant) (Coleoptera: Coccinellidae) feeding on eggs and first-instar nymphs of Crypticerya multicicatrices Kondo and Unruh (Hemiptera: Monophlebidae)

Delphastus quinculus Gordon and Diomus seminulus (Mulsant) (Coleoptera: Coccinellidae) are reported for the first time feeding on eggs and first-instar nymphs of Crypticerya multicicatrices Kondo and Unruh (Hemiptera: Monophlebidae). Diagnosis and illustrations are provided for both species. Updated information on their biology, hosts and geographical distribution is also provided.Se reportan a Delphastus quinculus Gordon y Diomus seminulus (Mulsant) (Coleoptera: Coccinellidae) por primera vez como depredadores de huevos y ninfas del primer instar de Crypticerya multicicatrices Kondo and Unruh (Hemiptera: Monophlebidae). Las dos especies de coccinélidos se diagnostican y se ilustran en detalle. Se provee también información actualizada sobre sus biologías, hospederos y distribución geográfica

Determining radii of meromorphy via orthogonal polynomials on the unit circle

19 pages, no figures.-- MSC2000 codes: 30E10, 42C05, 41A20, 30D30.MR#: MR2016676 (2004k:30087)Zbl#: Zbl 1051.30033Using a convergence theorem for Fourier–Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard's theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szegö functions.The research of D.B.R. and G.L.L. was supported, in part, by Dirección General de Investigación, Ministerio de Ciencia y Tecnología, under grant BFM 2000-0206-C04-01 and the research of G.L.L. was also supported by Ministerio da Ciencia e do Ensino Superior, under Grant PRAXIS XXI BCC-22201/99, and by INTAS under Grant 2000-272. The research of E.B.S. was supported, in part, by V.S. National Science Foundation Grant DMS-0296026.Publicad

Asymptotics of orthogonal polynomials inside the unit circle and Szegö-Padé approximants

11 pages, no figures.-- MSC2000 codes: 42C05, 41A21.MR#: MR1858277 (2002h:42043)Zbl#: Zbl 1009.42016We study the asymptotic behavior of orthogonal polynomials inside the unit circle for a subclass of measures that satisfy Szegö's condition. We give a connection between such behavior and a Montessus de Ballore-type theorem for Szegö–Padé rational approximants of the corresponding Szegö function.The research of the second author (G.L.L.) was partially supported by Dirección General de Enseñanza Superior under Grant PB 96-0120-C03-01. The research of the third author (E.B.S.) was supported, partly by NSF research Grant DMS-9801677.Publicad

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

'New' vs 'old' leaderships: the campaign of Spanish general elections 2015 on Twitter

The focus of this research is to analyze the activity on Twitter, during the campaign for the 2015 general elections in Spain, of the leaders of the main Spanish political parties: Mariano Rajoy (PP), Pedro Sánchez (PSOE), Pablo Iglesias (Podemos) and Albert Rivera (Ciudadanos). That means: how many messages and what types of messages are published; what topics they focus on; and the main features of using Twitter: to spread political messages, reference candidate activities in the media or on the campaign trail or emphasize personal aspects. The methodological approach establishes three complementary areas: a) a quantitative analysis of the tweets published by the four candidates throughout the election campaign, focused on establishing the percentage of responses and retweets; b) a content analysis to determine the issue agenda of each candidate; and c) a qualitative analysis that allows us to provide an overview of the communication preferences and profile of each candidate. The combined results of this triple methodological approach show that candidates from emerging parties tend to send messages to mobilize their supporters to campaign and to make generic announcements regarding their future victory and the arrival of political change, while the leaders of PP and PSOE tend to publish more messages with specific policy proposals