Sampling theory in shift-invariant spaces: generalizations

Roughly speaking sampling theory deals with determining whether we can or can not recover a continuous function from some discrete set of its values. The most important result and main pillar of this theory is the well-known Shannon’s sampling theorem which states that: If a signal f(t) contains no frequencies higher than 1/2 cycles per second, it is completely determined by giving its ordinates at a sequence of points spaced one second apart….A grandes rasgos la teoría de muestreo estudia el problema de recuperar una función continua a partir de un conjunto discreto de sus valores. El resultado más importante y pilar fundamental de esta teoría es el conocido teorema de muestreo de Shannon que afirma que: Si una señal f(t) no contiene frecuencias mayores que 1/2 ciclos por segundo entonces está completamente determinada por sus ordenadas en una sucesión de puntos espaciados en un segundo….Proyecto de investigación MTM2009–08345 del Ministerio de Ciencia e Innovación de España.Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Luis Alberto Ibort Latre.- Secretario: Eugenio Hernández Rodríguez.- Vocal: Ole Christense

Generalized sampling in U-invariant subspaces

In this work we carry out some results in sampling theory for U-invariant subspaces of a separable Hilbert space H, also called atomic subspaces. These spaces are a generalization of the well-known shift- invariant subspaces in L2 (R); here the space L2 (R) is replaced by H, and the shift operator by U. Having as data the samples of some related operators, we derive frame expansions allowing the recovery of the elements in Aa. Moreover, we include a frame perturbation-type result whenever the samples are affected with a jitter error

Generalized sampling: from shift-invariant to U-invariant spaces

The aim of this article is to derive a sampling theory in U-invariant subspaces of a separable Hilbert space ℋ where U denotes a unitary operator defined on ℋ. To this end, we use some special dual frames for L2(0, 1), and the fact that any U-invariant subspace with stable generator is the image of L2(0, 1) by means of a bounded invertible operator. The used mathematical technique mimics some previous sampling work for shift-invariant subspaces of L2(ℝ). Thus, sampling frame expansions in U-invariant spaces are obtained. In order to generalize convolution systems and deal with the time-jitter error in this new setting we consider a continuous group of unitary operators which includes the operator U

Finite Sampling in Multiple Generated U-Invariant Subspaces

The relevance in a sampling theory of U-invariant subspaces of a Hilbert space H, where U denotes a unitary operator on H, is nowadays a recognized fact. Indeed, shift-invariant subspaces of L-2(R) become a particular example; periodic extensions of finite signals also provide a remarkable example. As a consequence, the availability of an abstract U-sampling theory becomes a useful tool to handle these problems. In this paper, we derive a sampling theory for finite dimensional multiple generated U-invariant subspaces of a Hilbert space H. As the involved samples are identified as frame coefficients in a suitable euclidean space, the relevant mathematical technique is that of the finite frame theory. Since finite frames are nothing but spanning sets of vectors, the used technique naturally meets matrix analysis

On Some Sampling-Related Frames in U-Invariant Spaces

This paper is concerned with the characterization as frames of some sequences in -invariant spaces of a separable Hilbert space H where U denotes an unitary operator defined on H ; besides, the dual frames having the same form are also found. This general setting includes, in particular, shift-invariant or modulation-invariant subspaces in L2(R) , where these frames are intimately related to the generalized sampling problem. We also deal with some related perturbation problems. In doing so, we need the unitary operator to belong to a continuous group of unitary operators

Gestión del conocimiento: perspectiva multidisciplinaria. Volumen 12

El libro “Gestión del Conocimiento. Perspectiva Multidisciplinaria”, Volumen 12, de la Colección Unión Global, es resultado de investigaciones. Los capítulos del libro, son resultados de investigaciones desarrolladas por sus autores. El libro cuenta con el apoyo de los grupos de investigación: Universidad Sur del Lago “Jesús María Semprúm” (UNESUR), Zulia – Venezuela; Universidad Politécnica Territorial de Falcón Alonso Gamero (UPTAG), Falcón – Venezuela; Universidad Politécnica Territorial de Mérida Kleber Ramírez (UPTM), Mérida – Venezuela; Universidad Guanajuato (UG) - Campus Celaya - Salvatierra - Cuerpo Académico de Biodesarrollo y Bioeconomía en las Organizaciones y Políticas Públicas (C.A.B.B.O.P.P), Guanajuato – México; Centro de Altos Estudios de Venezuela (CEALEVE), Zulia – Venezuela, Centro Integral de Formación Educativa Especializada del Sur (CIFE - SUR) - Zulia - Venezuela, Centro de Investigaciones Internacionales SAS (CIN), Antioquia - Colombia.y diferentes grupos de investigación del ámbito nacional e internacional que hoy se unen para estrechar vínculos investigativos, para que sus aportes científicos formen parte de los libros que se publiquen en formatos digital e impreso

Gestión del conocimiento. Perspectiva multidisciplinaria. Volumen 17

El libro “Gestión del Conocimiento. Perspectiva Multidisciplinaria”, Volumen 17 de la Colección Unión Global, es resultado de investigaciones. Los capítulos del libro, son resultados de investigaciones desarrolladas por sus autores. El libro es una publicación internacional, seriada, continua, arbitrada, de acceso abierto a todas las áreas del conocimiento, orientada a contribuir con procesos de gestión del conocimiento científico, tecnológico y humanístico. Con esta colección, se aspira contribuir con el cultivo, la comprensión, la recopilación y la apropiación social del conocimiento en cuanto a patrimonio intangible de la humanidad, con el propósito de hacer aportes con la transformación de las relaciones socioculturales que sustentan la construcción social de los saberes y su reconocimiento como bien público

Mental Health Problems among COVID-19 Frontline Healthcare Workers and the Other Country-Level Epidemics: The Case of Mexico

COVID-19 frontline healthcare workers (FHCW) are struggling to cope with challenges that threaten their wellbeing. We examine the frequency and predictors of the most frequent mental health problems (MHP) among FHCW during the first COVID-19 peak in Mexico, one of the most severely affected countries in terms of FHCW’s COVID-19 mortality. A cross-sectional survey was conducted between May 8 and August 18, 2020. A total of 47.5% of the sample (n = 2218) were FHCW. The most frequent MHP were insomnia, depression, posttraumatic stress symptoms, and health anxiety/somatization (whole sample: 45.7, 37.4, 33.9, and 21.3%; FHCW: 52.4, 43.4, 40.3 and 26.1, respectively). As compared to during the initial COVID-19 phase, depression and health anxiety/somatization symptoms as well as experiences of grieving due to COVID-19, personal COVID-19 status, and having relatives and close friends with COVID-19 were more frequent during the COVID-19 peak. Obesity, domestic violence, personal COVID-19 status, and grieving because of COVID-19 were included in regression models for main FHCW’s MHP during the COVID-19 peak. In conclusion, measures to decrease other country-level epidemics contributing to the likelihood of COVID-19 complications (obesity) and MHP (domestic violence) as well as FHCW´s probability of COVID-19 infection could safeguard not only their physical but also mental health

ARIA Mexico 2014 Adaptation of the Clinical Practice Guide ARIA 2010 for Mexico. Methodology ADAPTE

Background: The global prevalence of allergic rhinitis is high. International Study of Asthma and Allergies in Childhood (ISAAC) Phase III reports a total estimated prevalence of 4.6% in Mexico. There is evidence based on allergic rhinitis Clinical Practice Guidelines (CPG), but its promotion, acceptance and application is not optimal or adequate in Mexico. Objective: To generate a guideline for the treatment of allergic rhinitis and its impact on asthma by adaptating the 2010 ARIA Guideline to Mexican reality, through a transculturation process applying the ADAPTE methodology. Material and method: Using the ADAPTE Methodology, the original 2010 ARIA CPG recommendations were evaluated by the guideline development group (GDG) into which multiple medical specialities managing patients with allergic rhinitis were incoorporated. The GDG valorated the quality of 2010 ARIA, checked and translated key clinical questions. Moreover, the GDG adjusted recommendations, patient preferences and included comments in the context of the Mexican reality (safety, costs and cultural issues). To accomplish this, we ran Delphi panels with as many rounds as necessary to reach agreement. One extra question, not included in the original 2010 ARIA, on the use of Nasal Lavages for AR was created sustained by a systematic literature review. Results: A total of 45 questions from the original 2010 ARIA were included and divided into six groups covering prevention, medical treatment, immunotherapy and alternative medicine to treat patients with allergic rhinitis with or without asthma. Most of the questions reached agreement in one or two rounds; one question required three rounds. Conclusions: An easy-to-use, adaptated, up-to-date and applicable allergic rhinitis guideline for Mexico is now available

Anuario del Centro de Estudios Martianos (Vol. 7 1984)

El Anuario del Centro de Estudios Martianos es la publicación insignia de esta institución y heredera directa del Anuario Martiano de la Biblioteca Nacional José Martí, que se publicó entre 1969 y 1977, bajo la dirección del poeta y ensayista Cintio Vitier. Desde que salió a la luz su primera entrega, en 1978, se han publicado treinta y cinco números, en los que aparecen artículos y ensayos de importantes estudiosos de la vida y obra del Apóstol, en Cuba y el resto del mundo. En sus secciones fijas (Otros textos de José Martí, Documentos, Estudios y aproximaciones, Vigencias, Publicaciones, Bibliografía, Constante) y los apartados especiales, los lectores pueden conocer disímiles temas del quehacer martiano internacional, en el año que termina además de mantenerse al tanto de las últimas contribuciones de los promotores e investigadores de la obra martiana en el orbe