Given two determinantal rings over a field k, we consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the secant variety. When the Rees algebra and the symmetric algebra coincide, we show that the Rees algebra is CohenMacaulay.

The ability of organic matter as well as carbonate ions to extract rare earth elements (REEs) from sandy sediments of a Coastal Plain aquifer was investigated for unpurified organic matter from different sources (i.e., Mississippi River natural organic matter, Aldrich humic acid, Nordic aquatic fulvic acid, Suwannee River fulvic acid, and Suwannee River natural organic matter) and for extractio...

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 ...