Simple rings with a one-sided minimal ideal may be represented as Rees matrix rings, and conversely. The latter are defined as I ×Λ matrices over a division ring with only a finite number of nonzero entries with certain addition and multiplication. For Rees matrix rings we construct here their isomorphisms, their translational hulls and isomorphisms of the translational hulls, all this in terms...

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 prove one of conjectures, raised by Dorey and Tateo in the connection among the spectral determinant of anharmonic oscillator, vacuum eigenvalues of transfer matrices in field theory and statistical mechanics. The exact sequence of Uq(ŝl2) plays a fundamental role in the proof. ∗e-mail: [email protected]

Let M be a compact, connected non-orientable surface without boundary and of genus g ¥ 3. We investigate the pure braid groups PnpMq of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 ÝÑ PmpMz tx1, . . . , xnuq ãÝÑ Pn mpMq p ÝÑ PnpMq ÝÑ 1, where m, n ¥ 1, and p is the homomorphism which corresponds geometrically to forgetting the last m strings. This pr...

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...

We study the asymptotic behaviour of a finitely presented Rees quotient S = Inv〈A | ci = 0 (i = 1, . . . , k) 〉 of a free inverse semigroup over a finite alphabet A. It is shown that if the semigroup S has polynomial growth then S is monogenic (with zero) or k ≥ 3. The three relator case is fully characterised, yielding a sequence of two-generated three-relator semigroups whose Gelfand-Kirillov...