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.

Comparative genome maps of the pangolin, hedgehog, sloth, anteater and human revealed by cross-species chromosome painting: further insight into the ancestral karyotype and genome evolution of eutherian mammals

To better understand the evolution of genome organization of eutherian mammals, comparative maps based on chromosome painting have been constructed between human and representative species of three eutherian orders: Xenarthra, Pholidota, and Eulipotyphla,

Phylogenetic relationships of five pika species (genus Ochotona) based on mitochondrial DNA restriction maps

Restriction site mapping of mitochondrial DNA (mtDNA) with 16 restriction endonucleases was used to examine the phylogenetic relationships of Ochotona cansus, O. huangensis, O. thibetana, O. curzoniae and O. erythrotis. A 1-kb length variation between O. erythrotis of subgenus Pika and other four species of subgenus Ochotona was observed, which may be a useful genetic marker for identifying the two subgenera. The phylogenetic tree constructed using PAUP based on 61 phylogenetically informative sites suggests that O. erythrotis diverged first, followed by O. cansus, while O. curzoniae and O. huangensis are sister taxa related to O. thibetana, The results indicate that both O. cansus and O. huangensis should be treated as independent species. If the base substitution rate of pikas mtDNA was 2% per million years, then the divergence time of the two subgenera, Pika and Ochotana, is about 8.8 Ma ago of late Miocence, middle Bao-dian of Chinese mammalian age, and the divergence of the four species in subgenus Ochotona would have occurred about 2.5 - 4.2 Ma ago, Yushean of Chinese mammalian age. This calculation appears to be substantiated by the fossil record.