Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

Size and year class composition of catch, age and growth of yellowfin tuna in the Eastern Tropical Pacific Ocean for the years 1954-1958

ENGLISH: Data on the size composition of catch for the years 1954-1958 have been studied to determine year class composition, age and growth of yellowfin tuna in the Eastern Tropical Pacific Ocean. Direct age determination of tropical tunas has not yet proven reliable; however, this analysis has shown that the length-frequency distributions themselves are adequate to determine year class structure and growth rates. Absolute age has been estimated by comparing the average time of spawning with the time at which age groups initially appear in the catch. SPANISH: Los datos sobre la composición del tamaño de la pesca durante los años 1954-1958 han sido estudiados con el objeto de determinar la composición de las clases anuales, la edad y el crecimiento del atún aleta amarilla en el Océano Pacífico Oriental Tropical. Las determinaciones directas de la edad de los atunes tropicales no han probado todavía ser de confianza; sin embargo, este análisis ha demostrado que las distribuciones de la frecuencia de las longitudes son adecuadas para determinar la estructura de las clases anuales y de las tasas de crecimiento. La edad absoluta ha sido estimada mediante la comparación de la época promedio de desove con la epoca en que los grupos de edades comienzan a aparecer en la pesca.

Year class mortality, abundance and yield-per-recruit of yellowfin tuna in the eastern Pacific Ocean, 1954-1959

ENGLISH: One primary duty of the Inter-American Tropical Tuna Commission is to estimate the maximum sustainable catches of yellowfin tuna (Neothunnus macropterus) and skipjack (Katsuwonus pelamis), and to investigate and recommend proposals to maintain the stocks at levels which will permit these catches to be obtained. To do this, there is required some means of predicting yields relative to fishing intensity. . . The age composition of catch, and growth rate of yellowfin tuna for recent years have now been estimated (Hennemuth, 1961). In this paper, relative abundance at age of yellowfin tuna shall be estimated -and used, in turn, to estimate total mortality rate. Yield-per-recruit calculations, based on Beverton and Holt's (1957) simple equation, will be presented to compare present utilization with theoretical maxima under varying levels of fishing mortality and different ages at first capture. SPANISH: Uno de los principales deberes de la Comisión Interamericana del Atún Tropical es estimar las pescas máximas sostenibles de los atunes aleta amarilla (Neothunnus macropterus) y barrilete (Katsuwonus pelamis) , así como estudiar y recomendar proposiciones para mantener los stocks a niveles que permitan obtener estas pescas. Para lograr este propósito se requieren algunos medios que permitan predecir el rendimiento en relación con la intensidad de la pesca. . La composición de edades de la pesca y la tasa de crecimiento del atún aleta amarilla en años recientes han sido estimadas ahora (Hennemuth, 1961). En este trabajo, la abundancia relativa a una edad dada de esta especie será estimada y usada, a su vez, para estimar la tasa de mortalidad total. Los cálculos del rendimiento por recluta, basados en la ecuación simple de Beverton y Holt (1957), serán presentados para comparar la utilización actual con los máximos teóricos bajo valores variables de mortalidad por la pesca y a diferentes edades a la primera captura.

Size and year class composition of catch, age and growth of yellowfin tuna in the Eastern Tropical Pacific Ocean, 1951-1961

ENGLISH: Analysis of yellowfin tuna size-composition data encompassing data for purse-seiners and baitboats, and including data collected prior to the Commission's sampling program, has permitted a more careful examination of variations in growth rates of yellowfin year classes. SPANISH: El análisis de los datos de la composición de tamaños del atún aleta amarilla correspondiente a los que provienen de los barcos rederos y de carnada, e incluyendo datos recolectados previamente al programa de muestreo de la Comisión, ha permitido un examen más cuidadoso de las variaciones en las tasas de crecimiento de las clases anuales del atún aleta amarilla.

Estimation of year class abundance and mortality of yellowfin tuna in the Eastern Tropical Pacific

ENGLISH: Age composition of catch, and growth rate, of yellowfin tuna have been estimated by Hennemuth (1961a) and Davidoff (1963). The relative abundance and instantaneous total mortality rate of yellowfin tuna during 1954-1959 have been estimated by Hennenmuth (1961b). It is now possible to extend this work, because more data are available; these include data for 1951-1954, which were previously not available, and data for 1960-1962, which were collected subsequent to Hennemuth's (1961b) publication. In that publication, Hennemuth estimated the total instantaneous mortality rate (Z) during the entire time period a year class is present in the fishery following full recruitment. However, this method may lead to biased estimates of abundance, and hence mortality rates, because of both seasonal migrations into or out of specific fishing areas and possible seasonal differences in availability or vulnerability of the fish to the fishing gear. Schaefer, Chatwin and Broadhead (1961) and Joseph etl al. (1964) have indicated that seasonal migrations of yellowfin occur. A method of estimating mortality rates which is not biased by seasonal movements would be of value in computations of population dynamics. The method of analysis outlined and used in the present paper may obviate this bias by comparing the abundance of an individual yellowfin year class, following its period of maximum abundance, in an individual area during a specific quarter of the year with its abundance in the same area one year later. The method was suggested by Gulland (1955) and used by Chapman, Holt and Allen (1963) in assessing Antarctic whale stocks. This method, and the results of its use with data for yellowfin caught in the eastern tropical Pacific from 1951-1962 are described in this paper. SPANISH: La composición de edad de la captura, y la tasa de crecimiento del atún aleta amarilla, han sido estimadas por Hennemuth (1961a) y Davidoff (1963). Hennemuth (1961b), estimó la abundancia relativa y la tasa de mortalidad total instantánea del atún aleta amarilla durante 1954-1959. Se puede ampliar ahora, este trabajo, porque se dispone de más datos; éstos incluyen datos de 1951 1954, de los cuales no se disponía antes, y datos de 1960-1962 que fueron recolectados después de la publicación de Hennemuth (1961b). En esa obra, Hennemuth estimó la tasa de mortalidad total instantánea (Z) durante todo el período de tiempo en el cual una clase anual está presente en la pesquería, consecutiva al reclutamiento total. Sin embargo, este método puede conducir a estimaciones con bias (inclinación viciada) de abundancia, y de aquí las tasas de mortalidad, debidas tanto a migraciones estacionales dentro o fuera de las áreas determinadas de pesca, como a posibles diferencias estacionales en la disponibilidad y vulnerabilidad de los peces al equipo de pesca. Schaefer, Chatwin y Broadhead (1961) y Joseph et al. (1964) han indicado que ocurren migraciones estacionales de atún aleta amarilla. Un método para estimar las tasas de mortalidad el cual no tuviera bias debido a los movimientos estacionales, sería de valor en los cómputos de la dinámica de las poblaciones. El método de análisis delineado y usado en el presente estudio puede evitar este bias al comparar la abundancia de una clase anual individual de atún aleta amarilla, subsecuente a su período de abundancia máxima en un área individual, durante un trimestre específico del año, con su abundancia en la misma área un año más tarde. Este método fue sugerido por Gulland (1955) y empleado por Chapman, Holt y Allen (1963) en la declaración de los stocks de la ballena antártica. Este método y los resultados de su uso, en combinación con los datos del atún aleta amarilla capturado en el Pacífico oriental tropical desde 1951-1962, son descritos en este estudio.

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.)

Existence, uniqueness, and stability of solutions of a class of nonlinear partial differential equations

In this study we investigate the existence, uniqueness and asymptotic stability of solutions of a class of nonlinear integral equations which are representations for some time dependent non- linear partial differential equations. Sufficient conditions are established which allow one to infer the stability of the nonlinear equations from the stability of the linearized equations. Improved estimates of the domain of stability are obtained using a Liapunov Functional approach. These results are applied to some nonlinear partial differential equations governing the behavior of nonlinear continuous dynamical systems.

Computationally Guided Monomerization of Red Fluorescent Proteins of the Class Anthozoa

Red fluorescent proteins (RFPs) have attracted significant engineering focus because of the promise of near infrared fluorescent proteins, whose light penetrates biological tissue, and which would allow imaging inside of vertebrate animals. The RFP landscape, which numbers ~200 members, is mostly populated by engineered variants of four native RFPs, leaving the vast majority of native RFP biodiversity untouched. This is largely due to the fact that native RFPs are obligate tetramers, limiting their usefulness as fusion proteins. Monomerization has imposed critical costs on these evolved tetramers, however, as it has invariably led to loss of brightness, and often to many other adverse effects on the fluorescent properties of the derived monomeric variants. Here we have attempted to understand why monomerization has taken such a large toll on Anthozoa class RFPs, and to outline a clear strategy for their monomerization. We begin with a structural study of the far-red fluorescence of AQ143, one of the furthest red emitting RFPs. We then try to separate the problem of stable and bright fluorescence from the design of a soluble monomeric β-barrel surface by engineering a hybrid protein (DsRmCh) with an oligomeric parent that had been previously monomerized, DsRed, and a pre-stabilized monomeric core from mCherry. This allows us to use computational design to successfully design a stable, soluble, fluorescent monomer. Next we took HcRed, which is a previously unmonomerized RFP that has far-red fluorescence (λemission = 633 nm) and attempted to monomerize it making use of lessons learned from DsRmCh. We engineered two monomeric proteins by pre-stabilizing HcRed’s core, then monomerizing in stages, making use of computational design and directed evolution techniques such as error-prone mutagenesis and DNA shuffling. We call these proteins mGinger0.1 (λem = 637 nm / Φ = 0.02) and mGinger0.2 (λem = 631 nm Φ = 0.04). They are the furthest red first generation monomeric RFPs ever developed, are significantly thermostabilized, and add diversity to a small field of far-red monomeric FPs. We anticipate that the techniques we describe will be facilitate future RFP monomerization, and that further core optimization of the mGingers may allow significant improvements in brightness.