Discrete Sturm–Liouville problems, Jacobi matrices and Lagrange interpolation series

AbstractThe close relationship between discrete Sturm–Liouville problems belonging to the so-called limit-circle case, the indeterminate Hamburger moment problem and the search of self-adjoint extensions of the associated semi-infinite Jacobi matrix is well known. In this paper, all these important topics are also related with associated sampling expansions involving analytic Lagrange-type interpolation series

The zero-removing property in some Hilbert spaces of entire functions arising in sampling theory

In the topic of sampling in reproducing kernel Hilbert spaces, sampling in Paley–Wiener spaces is the paradigmatic example. A natural generalization of Paley–Wiener spaces is obtained by substituting the Fourier kernel with an analytic Hilbert-space-valued kernel K. Thus we obtain a reproducing kernel Hilbert space HKHK of entire functions in which the Kramer property allows to prove a sampling theorem. A necessary and sufficient condition ensuring that this sampling formula can be written as a Lagrange-type interpolation series concerns the stability under removal of a finite number of zeros of the functions belonging to the space HKHK; this is the so-called zero-removing property. This work is devoted to the study of the zero-removing property in HKHK spaces, regardless of the Kramer property, revealing its connections with other mathematical fields

A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established

Inactivation of potassium-evoked adrenomedullary catecholamine release in the presence of calcium, strontium or BAY-K-8644

AbstractThe rate of catecholamine release from cat adrenal glands perfused with Krebs solution containing 59 mM K declined exponentially during the first few minutes of depolarization. The rate of decline was considerably slower when Ca was substituted by Sr. The late addition of Ca, Sr or the Ca-channel activator BAY-K-8644 evoked a revival of secretion when catecholamine release was inactivated by prior K depolarization; the revival of secretion was independent of the depolarization time. These data demonstrate that inactivation of catecholamine release is specifically dependent on Ca; the modulatory role of Ca on secretion seems to be exerted at a step distal to the transmembraneous Ca channel

Near-field focusing with optical phase antennas

We investigate the near-field focusing properties of three- dimensional phase antennas consisting of concentric rings designed to have source and image spots separated by several microns from the lens. Tight focal spots are obtained for silicon or gold rings patterned in a silica matrix. We analyze in detail the dependence of the performance of these lenses on geometrical parameters such as the number of rings, the ring thickness, and the focal distance. Subwavelength focal spots are found to form at distances of tens of wavelengths from the lens, thus suggesting applications to remote sensing and penlight microscopy and lithography. © 2009 Optical Society of America.This work has been supported by the Spanish MICINN (MAT2007-66050 and Consolider NanoLight.es) and by the EU (NMP4-2006-016881-SPANS and NMP4-SL-2008-213669- ENSEMBLE).Peer Reviewe

Riesz bases in L2(0,1) related to sampling in shift-invariant spaces

AbstractThe Fourier duality is an elegant technique to obtain sampling formulas in Paley–Wiener spaces. In this paper it is proved that there exists an analogue of the Fourier duality technique in the setting of shift-invariant spaces. In fact, any shift-invariant space Vφ with a stable generator φ is the range space of a bounded one-to-one linear operator T between L2(0,1) and L2(R). Thus, regular and irregular sampling formulas in Vφ are obtained by transforming, via T, expansions in L2(0,1) with respect to some appropriate Riesz bases

Decay process accelerated by tunneling in its very early stage

We examine a fast decay process that arises in the transition period between the Gaussian and exponential decay processes in quantum decay systems. It is usually expected that the decay is decelerated by a confinement potential barrier. However, we find a case where the decay in the transition period is accelerated by tunneling through a confinement potential barrier. We show that the acceleration gives rise to an appreciable effect on the time evolution of the nonescape probability of the decay system.Comment: 4 pages, 6 figures; accepted for publication in Phys. Rev.

Synthesis and structural characterization of trans-bis[1,3-bis(methoxy- ethyl)-4,5-bis(2,4,6-trimethylphenyl)imidazolidin-2-ylidene]dichloro- palladium(II)

A Pd(II) complex of a new N-heterocyclic carbene (NHC) ligand with bulky substituents and functionalized methoxy-donor side arms has been synthesized and characterized by elemental analyses, 1H and 13C NMR, and IR spectroscopy. Molecular and crystal structures of the title complex have been determined by single crystal X-ray diffraction. The compound crystallizes in the monoclinic space group P21/c, with a = 15.927(2), b = 8.489(2), c = 20.309(5) Å, β = 99.213(2)°, Z = 2, Dx = 1.253 g cm-3. The palladium atom is situated on an inversion center. There are several weak intramolecular C-H⋯N/O interactions. © 2007 Verlag der Zeitschrift für Naturforschung

Definición, selección y consolidación de la Raza Caprina Florida

El grupo de investigación Pastos arbustivos, comenzó a trabajar en la definición, selección y optimización de los sistemas de explotación de la raza Florida en 1985, en el rebaño experimental que la Diputación de Sevilla creó mediante convenio con José Antonio Sánchez Romero. En 1991, y dentro de esa colaboración se publica el libro Raza Caprina Florida Sevillana en el que se define y se dan los primeros datos de esta raza, demostrando científicamente sus diferencias con otras razas andaluzas. A partir de esta fecha la Diputación de Sevilla abandona el proyecto, continuando el trabajo el grupo de investigación y D. José A. Sánchez Romero hasta 1994. En este periodo se consiguen grandes avances en la selección y optimización del sistema semiextensivo de explotación pasándose de los 432 kg de leche en 216 días de los primeros controles a más de 600 kg en lactaciones de nueve meses. En 1994, el grupo firma un convenio con la Excma. Diputación de Córdoba para el mantenimiento de un rebaño en estabulación en sus instalaciones, siguiendo desde entonces con los trabajos de selección y consolidación así como la optimización de los sistemas intensivos de producción. Las lactaciones controladas bajo este sistema superan los 750 kg en 290 días de lactación. Bajo este convenio, la Diputación de Córdoba ha facilitado más de 100 animales selectos a los ganaderos de la provincia. En 1996, el Grupo de investigación promueve la creación de la Asociación Española de Criadores de la Raza Caprina Florida, a la que pertenece desde entonces.El grupo de investigación Pastos arbustivos, comenzó a trabajar en la definición, selección y optimización de los sistemas de explotación de la raza Florida en 1985, en el rebaño experimental que la Diputación de Sevilla creó mediante convenio con José Antonio Sánchez Romero. En 1991, y dentro de esa colaboración se publica el libro Raza Caprina Florida Sevillana en el que se define y se dan los primeros datos de esta raza, demostrando científicamente sus diferencias con otras razas andaluzas. A partir de esta fecha la Diputación de Sevilla abandona el proyecto, continuando el trabajo el grupo de investigación y D. José A. Sánchez Romero hasta 1994. En este periodo se consiguen grandes avances en la selección y optimización del sistema semiextensivo de explotación pasándose de los 432 kg de leche en 216 días de los primeros controles a más de 600 kg en lactaciones de nueve meses. En 1994, el grupo firma un convenio con la Excma. Diputación de Córdoba para el mantenimiento de un rebaño en estabulación en sus instalaciones, siguiendo desde entonces con los trabajos de selección y consolidación así como la optimización de los sistemas intensivos de producción. Las lactaciones controladas bajo este sistema superan los 750 kg en 290 días de lactación. Bajo este convenio, la Diputación de Córdoba ha facilitado más de 100 animales selectos a los ganaderos de la provincia. En 1996, el Grupo de investigación promueve la creación de la Asociación Española de Criadores de la Raza Caprina Florida, a la que pertenece desde entonces

Equation of State for laboratory astrophysics applications

New improvements on the calculation of Equation of State (EOS) for laboratory astrophysics applications are presented. A new empirical multiplier for the EOS is included to the original quotidian equation of state (QEOS) model developed by More et al. (Phys. Fluids 31:3059, 1988) to adapt it to the available experimental data and ab initio molecular dynamics simulation. This model is used to obtain EOS tables suited for an adaptive mesh refinement hydrodynamic code with radiation transport for high energy density plasmas simulations called ARWEN introduced by Ogando and Velarde (J. Quant. Spectrosc. Radiat. Transf. 71(2–6):541, 2001)