The Rees algebra of an ideal is a classical object that has been studied throughout many decades. Our interest to Rees algebras comes from the fact that they provide the algebraic realizations for certain class of rational n-folds, namely those obtained from P by blowing up at a subscheme. In this paper, we study the Rees algebras of certain codimension two perfect ideals. To be more precise, w...

The determination of rare earth elements (REEs) in airborne particulate matter (APM) was conducted, and the distribution pattern of atmospheric REEs was evaluated in this study. The APM was collected in the center of Tokyo, Japan, where serious air pollution is always of concern. A cellulose acetate membrane filter was used to collect the APM because Ba and REEs contamination is lower than that...

There are many sources trough which the soil get enriched and contaminated with REEs. The determination of REEs in environmental samples has been limited because of the lack of sensitive analytical techniques. Soil samples were collected from four sites including open cast coal mine, natural coal burning, coal washery and control in the coal field located in Dhanbad, India. Total concentrations...

This paper makes a comprehensive survey of results relating to finite Rees index for semigroups. In particular, we survey of the state of knowledge on whether various finiteness properties (such as finite generation, finite presentability, automaticity, and hopficity) are inherited by finite Rees index subsemigroups and extensions. We survey other properties that are invariant under passing to ...

Let J be the ideal of vertex covers of a graph G. We give a graph theoretical characterization of the minimal generators of the symbolic Rees algebra of J . If G is perfect, it is shown that the Rees algebra of J is normal and we compute the irreducible representation of the Rees cone of J in terms of cliques. Then we prove that if G is perfect and unmixed, then the Rees algebra of J is a Goren...

Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring. We introduce the basis Rees cone of a matroid (or a polymatroid) and study their facets. Some application...

With the exploitation of rare earth ore, more and more REEs came into groundwater. This was a waste of resources and could be harmful to the organisms. This study aimed to find an efficient adsorption material to mitigate the above issue. Through doping sodium alginate (SA) with poly-γ-glutamate (PGA), an immobilized gel particle material was produced. The composite exhibited excellent capacity...