It is known that every dimension group with order-unit of size at most א1 is isomorphic to K0(R) for some locally matricial ring R (in particular, R is von Neumann regular); similarly, every conical refinement monoid with order-unit of size at most א1 is the image of a V-measure in Dobbertin’s sense, the corresponding problems for larger cardinalities being open. We settle these problems here, ...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

In this paper, we are giving MATLAB program to find the energy and Wiener index of unit graphs. Our program demonstrates an intrinsic relationship between the elements of ring and structural properties of graphs. The unit graph G(Zn) turns out to be strongly regular when n = 2k. Several new directions for further research are also indicated by means of raising problems.

We survey scaling arguments, both asymptotic (involving regular variation) and exact (involving self-similarity), in various areas of mathematical analysis and mathematical physics. 1. Scaling and Fechner’s law There is a sizeable body of theory to the effect that, where two related physically meaningful functions f and g have no natural scale in which to measure their units, and are reasonably...

The problem of estimating the tail index from truncated data is addressed in ?. In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index. In this paper, the second order behavior of the Hill estimator with that choice of k is studied, under some additional assumptions. In the untru...

In order to propose spatially-explicit conservation strategies driven by biodiversity for Baa Atoll, habitat maps were created from LANDSAT and Quickbird satellite images. The LANDSAT derived habitat map described the atoll geomorphology following the Millennium Coral Reef Mapping Project typology, which is made of 5 different hierarchical levels. The Quickbird derived high spatial resolution h...