On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint

This paper is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.

Variations in year-class strength and estimates of the catchability coefficient of yellowfin tuna, Thunnus albacares, in the Eastern Pacific Ocean

ENGLISH: Year-class composition of catch, virtual population size and yearclass strength were determined from serial samples of size composition of catches and catch records. Murphy's Solution to the catch equation, which is free from the effects caused by changes in fishing pressure, was used to estimate year-class strength, i.e. the total population of fish age 3/4 years. The resultant estimates indicated that the X55, X56, X57, X62 and X63 year classes were above average and the X58, X59, X60, X61 and X64 year classes were below average. The year-class designation refers to the year of actual entry or presumed year of entry into the commercial fishery (at approximately 1 year of age). The strongest and poorest year classes were the X57 and X61 classes, respectively. The ratio of the strongest to the weakest year class was 2.6. This amount of variation is small compared to that found for other species of fish. It was found that the relationship between stock size and yearclass strength is of no value in predicting year-class strength. As a by-product of the analysis, estimates of the catchability coefficients (qN) of the age groups in the fishery were obtained, These estimates were found to vary with age and time. Age-two fish apparently showed the greatest vulnerability to fishing gear, followed by ages three and one, respectively. The average estimate of the catchability coefficient in weight was calculated and found to compare favorably with Schaefer's estimate. The influence of sea-surface water temperature upon year-class strength was investigated to determine whether the latter can be predicted from a knowledge of sea-surface temperatures prevailing during and following spawning. No correlation was evident. SPANISH: La composición de la clase anual en la captura, el tamaño de la población virtual y la fuerza de clase anual, fueron determinados según una serie de muestras de la composición de tamaño de las capturas y de los registros de captura. La Solución de Murphy de la ecuación de captura, que está libre de los efectos causados por los cambios de la presión de pesca, fue usada para estimar la fuerza de la clase anual, i.e. la población total de peces de 3/4 años. Las estimaciones resultantes indican que las clases anuales X55, X56, X57, X62 y X63 fueron superiores al promedio y que las clases anuales X58, X59, X60, X61 y X64 fueron inferiores al promedio. La designación de la clase anual se refiere al año actual de entrada o al año supuesto de entrada en la pesca comercial (aproximadamente a la edad de 1 año). Las clases anuales más fuertes y más pobres fueron la X57 y X61 respectivamente. La razón de la clase anual más fuerte en relación a la más débil fue 2.6. Esta cantidad de variación es pequeña comparada con la encontrada para otras especies de peces. Se encontró que la relación entre en tamaño del stock y la fuerza de la clase anual no tiene valor en predecir la fuerza de la clase anual. Se obtuvieron estimaciones de los coeficientes de capturabilidad (qN) de los grupos de edad en la pesquería como un producto derivado del análisis. Se encontraron que estas estimaciones variaron con la edad y tiempo. Los peces de edad dos aparentemente presentaron la vulnerabilidad más grande en relación al arte pesquero, seguidos por las edades tres y una, respectivamente. La estimación promedio del coeficiente de capturabilidad en peso fue calculada y se encontró que podía compararse favorablemente con la estimación de Schaefer. La influencia de la temperatura del agua superficial del mar sobre la fuerza de la clase anual fue investigada para determinar si se podía predecir esta última según el conocimíento de las temperaturas superficiales del mar prevalecientes durante el desove y después de éste. No hubo correlación evidente. (PDF contains 44 pages.)

Energy Functions And Basic Equations For Ferroelectrics

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Procedimiento de refutación para un conjunto de restricciones sobre documentos XML

We present a prototype that implements a set of logical rules to prove the satis ability for a class of speci cations on XML documents. Speci cations are given by means of constraints built on Boolean XPath patterns. The main goal of this tool is to test if a given speci cation is satis able or not, showing the history of the execution. It can also be used to test if a given document is a model of a given speci cation and, as a subproduct, it allows to look for all the relations (monomorphisms) between two patterns or the result of doing some operations by combining patterns in di erent ways. The results of these operations are visually shown and therefore the tool makes these operations more understandable. The implementation of the algorithm has been written in Prolog but the prototype has a Java interface for an easy and friendly use.