Approximate Best Proximity Points of Cyclic Self-maps in Metric Spaces and Cyclic Asymptotic Regularity

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) Madrid, AUG 28-31, 2014 / editado por Vagenas, EC; Vlachos, DS; Bastos, C; Hofer, T; Kominis, Y; Kosmas, O; LeLay, G; DePadova, P; Rode, B; Suraud, E; Varga, K

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

Using ReefBase to create customized maps

One of the most popular sections of the ReefBase website is the online GIS that enables users to create an almost unlimited range of maps showing a wide variety of features. A new version of the GIS, offering an even larger array of facilities and data layers, is online as of early September. In this article, we will provide an introduction to the ReefBase GIS and also highlight some of the powerful but lesser used features of the system.

An ecological characterization of the marine resources of Vieques, Puerto Rico Part II: Field studies of habitats, nutrients, contaminants, fish, and benthic communities

Since the 1940s, portions of the Island of Vieques, Puerto Rico have been used by the United States Navy (USN) as an ammunition support detachment and bombing and maneuver training range. In April 2001, the USN began phasing out military activities on the island and transferring military property to the U.S. Department of the Interior, the Municipality of Vieques, and the Puerto Rico Conservation Trust. A small number of studies have been commissioned by the USN in the past few decades to assess selected components of the coral reef ecosystem surrounding the island; however, these studies were generally of limited geographic scope and short duration. The National Oceanic and Atmospheric Administration’s (NOAA) National Centers for Coastal Ocean Science (NCCOS), in consultation with NOAA’s Office of Response and Restoration (OR&R) and other local and regional experts, conducted a more comprehensive characterization of coral reef ecosystems, contaminants, and nutrient distribution patterns around Vieques. This work was conducted using many of the same protocols as ongoing monitoring work underway elsewhere in the U.S. Caribbean and has enabled comparisons among coral reef ecosystems in Vieques and other locations in the region. This characterization of Vieques’ marine ecosystems consists of a two part series. First, available information on reefs, fish, birds, seagrasses, turtles, mangroves, climate, geology, currents, and human uses from previous studies was gathered and integrated into a single document comprising Part I of this two part series (Bauer et al. 2008). For Part II of the series, presented in this document, new field studies were conducted to fill data gaps identified in previous studies, to provide an island-wide characterization, and to establish baseline values for the distribution of habitats, nutrients, contaminants, fish, and benthic communities. An important objective underlying this suite of studies was to quantify any differences in the marine areas adjacent to the former and current land-use zoning around Vieques. Specifically of interest was the possibility that either Naval (e.g., practice bombing, munitions storage) or civilian activities (e.g., sewage pollutants, overfishing) could have a negative impact on adjacent marine resources. Measuring conditions at this time and so recently after the land transfer was essential because present conditions are likely to be reflective of past land-use practices. In addition, the assessment will establish benchmark conditions that can be influenced by the potentially dramatic future changes in land-use practices as Vieques considers its development. This report is organized into seven chapters that represent a suite of interrelated studies. Chapter 1 provides a short introduction to the island setting, the former and current land-use zoning, and how the land zoning was used to spatially stratify much of the sampling. Chapter 2 is focused on benthic mapping and provides the methods, accuracy assessment, and results of newly created benthic maps for Vieques. Chapter 3 presents the results of new surveys of fish, marine debris, and reef communities on hardbottom habitats around the island. Chapter 4 presents results of flora and fauna surveys in selected bays and lagoons. Chapter 5 examines the distribution of nutrients in lagoons, inshore, and offshore waters around the island. Chapter 6 is focused on the distribution of chemical contaminants in sediments and corals. Chapter 7 is a brief summary discussion that highlights key findings of the entire suite of studies.