Rare earth elements (REEs) have been increasingly emitted into the 8 atmosphere with a worldwide increase in use of these metals. However, the research 9 on REEs in atmospheric particulates is fairly limited. In this paper, atmospheric 10 particulates including total suspended particulate (TSP) matter and particles with an 11 equivalent aerodynamic diameter less than 10 μm (PM10) were collected...

We study two classes of operator algebras associated with a unital subsemigroup $P$ discrete group $G$: one related to universal structures, and co-universal structures. First we provide connections between C*-algebras that arise variously from isometric representations reflect the space $\mathcal{J}$ constructible right ideals, Fell bundles, induced partial actions. This includes appropriate q...

Let v be a valuation of the quotient field of a noetherian local domain R. Assume that v is centered at R. This paper studies the structure of the value semigroup of v, S. Ideals defining toric varieties can be defined from the graded algebra K[T ] of cancellative commutative finitely generated semigroups such that T ∩ (−T ) = {0}. The value semigroup of a valuation S need not be finitely gener...

It has long been observed that rare earth elements (REEs) regulate multiple facets of plant growth and development. However, the underlying mechanisms remain largely unclear. Here, using electron microscopic autoradiography, we show the life cycle of a light REE (lanthanum) and a heavy REE (terbium) in horseradish leaf cells. Our data indicate that REEs were first anchored on the plasma membran...

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...

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

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...