Weak precompactness in spaces of vector measures and in the space of Bochner integrable functions is studied. Uniform countable additivity and uniform integrability are characterized in terms of weak precompactness. Through this, a connection between strongly bounded operators and operators having weakly precompact adjoints on abstract continuous function spaces is established. These operators are compared with weakly completely continuous operators.
No abstract
Q tb 1s.Individual-based models of animal ecology can take into account spatio-temporal details of a natural environment that are overly simplijied in models based on averaged variables. Parallelizing a model that simulates long-term populations of deer and panthers in the Everglades region of south Florida allows faster computation of complex scenarios and better exploration of hydrologic management alternatives.he Florida Everglades is one of the most threatened ecosystems in the United States, owing in part to decades of adverse impacts from intensive water management that has favored agricultural and urban development more than the natural ecology.' Resource experts are currently developing management alternatives for restoring natural water flows to the area. They need to predict and compare the effects of alternative hydrologic planning scenarios on the Everglades wildlife, and can realistically project these effects only by computer modeling.2 Individual-based modelsThis article describes an application of modern computational methods to a model based upon the actions of individual organisms, in which the assumptions about the growth, reproduction, mortality, and behavior of the individuals are closely linked to observable biology. Most of the mathematical models developed to analyze ecological problems contain highly aggregated variables, in which details of individuals (age, size, location, and so forth) are averaged, leading to a simplified set of differential or difference equations.Though useful for general theory development, these models are difficult to use for real applications as they generally ignore the spatio-temporal patterns of underlying environmental factors affecting the natural system. Moreover, the aggregated nature of the component variables makes the model parameters difficult to estimate from observations. The individual-based approach, on the other hand, readily allows one to take account of the detailed information available on behavioral and physiological responses of individuals to their environment, llnk this with detailed models for environmental variations in space and time, estimate the longer-term and largerspatial-scale response of populations and communities, and validate the results through comparisons with both individual behavioral data and population estimate^.^ Simpdel modelThe Simpdel model (spatially explicit individual-based simulation model of Florida panther and white-tailed deer in the Everglades and Big Cypress landscapes) was jointly developed by a group of modelers and biologists at the Institute for Environmental Modeling, University of Tennes~ee.~ Simpdel is a member of the ATLSS family of models (Across-Trophic-Level System Simulation for the Everglades and Big Cypress Swamp) under development at a variety of institutions with support from 60
In this paper we will be concerned with studying operators T: C(K, X) → Y defined on Banach spaces of continuous functions. We will be particularly interested in studying the classes of strictly singular and strictly cosingular operators. In the process, we obtain answers to certain questions recently raised by Bombal and Porras in [5]. Specifically, we study Banach space X and Y for which an operator T: C(K, X) → Y with representing measure m is strictly singular (strictly cosingular) whenever m is strongly bounded and m(A) is strictly singular (strictly cosingular) for each Borel subset A of K. Along the way we establish several results dealing with non-compact operators on continuous function spaces, and we consolidate numerous results concerning extension theorems for operators defined on these same spaces. Also, we join Saab and Saab [25] in demonstrating that if l1 does not embed in X* then the adjoint T* of a strongly bounded map must be weakly precompact, thereby presenting an alternative solution to a question raised in [2].
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.