The Grothendieck-Serre formula for the difference between the Hilbert function and Hilbert polynomial of a graded algebra is generalized for bigraded standard algebras. This is used to get a similar formula for the difference between the Bhattacharya function and Bhattacharya polynomial of two m-primary ideals I and J in a local ring (A, m) in terms of local cohomology modules of Rees algebras ...

Rare earth elements (REEs) are essential for high-techology industrial sectors. This paper presents research on material flow analysis (MFA) applied to REEs in the EU-27. Innovative aspects of this research pertain to (i) considering potential lithospheric stocks of REEs in the EU and (ii) accounting for incomplete and imprecise information in MFA data reconciliation. Results obtained to-date p...

In a previous paper, the author has introduced a number of homomorphisms of an arbitrary semigroup into the translational hull of certain Rees matrix semigroups or orthogonal sums thereof. For regular semigroups, it is proved here that all of these homomorphisms have the property that the image is a densely embedded subsemigroup, i.e., is a densely embedded ideal of its idealizer, and that the ...

These are notes for a lecture given at Ohio University on June 3, 2006. An important topic in commutative algebra is the Rees algebra of an ideal in a commutative ring. The Rees algebra encodes a lot of information about the ideal and corresponds geometrically to a blow-up. One can represent the Rees algebra as the quotient of a polynomial ring by an ideal. This ideal is generated by the defini...

we characterize function spaces of rees matrixsemigroups. then we study these spaces by using the topologicaltensor product technique.

A home made column of commercially available iminodiacetate resin, Muromac A-1 (50-100 mesh) was used to concentrate rare earth elements (REEs) (15 elements: Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu) in seawater. An automated low pressure flow analysis method with on-line column preconcentration/inductively coupled plasma mass spectrometry (ICP-MS) is described for the dete...

Introduction: The rare earth elements (REEs) are concentrated in CAIs by ~20 times the chondritic average [e.g., 1]. The REEs in CAIs are important to understand processes of CAI formation including the role of volatilization, condensation, and fractional crystallization [1,2]. REE measurements are a well-established application of ion microprobes [e.g., 3]. However the spatial resolution of RE...

Fluxes of particulate organic carbon (POC) in the East China Sea (ECS) have been reported to decrease from the inner continental shelf towards the outer continental shelf. Recent research has shown that POC fluxes in the ECS may be overestimated due to active sediment resuspension. To better characterize the effect of sediment resuspension on particle fluxes in the ECS, rare earth elements (REE...