The aim of this paper is to study integer rounding properties of various systems of linear inequalities to gain insight about the algebraic properties of Rees algebras of monomial ideals and monomial subrings. We study the normality and Gorenstein property—as well as the canonical module and the a-invariant—of Rees algebras and subrings arising from systems with the integer rounding property. W...

We compute the canonical class of certain Rees algebras. Our formula generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that the formation of the canonical module commutes with subintersections in important cases. As an application we treat the classical determinantal ideals and the corresponding algebras of minors. A considerable part of Wolmer Vasconcelos’ work has been ...

We study Rees algebras of modules within a fairly general framework. We introduce an approach through the notion of Bourbaki ideals that allow the use of deformation theory. One can talk about the (essentially unique) Bourbaki ideal I(E) of a module E which, in many situations, allows to reduce the nature of the Rees algebra of E to that of its Bourbaki ideal I(E). Properties such as Cohen–Maca...

Let (R, m) be a local ring of Krull dimension d and I ⊆ R be an ideal with analytic spread d. We show that the j-multiplicity of I is determined by the Rees valuations of I centered on m. We also discuss a multiplicity that is the limsup of a sequence of lengths that grow at an O(nd) rate.

BACKGROUND AND PURPOSE Little is known of the acute, subacute, and longer-term energy demands of stroke, information essential to appropriate clinical and nutritional management. The goals of this study were to (1) determine the resting energy expenditure (REE) of stroke patients from stroke onset to 3 months, (2) examine relations between stroke size, type, location, severity, and REE, and (3)...

Previous studies on rare earth element (REE) bioaccumulation have focused on their accumulation rate and fractionation, but the processes involved remain unclear. In this study, the accumulation and fractionation of REEs in wheat (Triticum aestivum L.) were investigated using solution culture with exogenous mixed REEs. A decrease in REE contents was observed from the roots to the tops of wheat....

Optimization of the acid leaching process for Mongolian apatite-based ore containing rare-earth elements (REEs) was studied. The ore contained approximately 10% of REEs as total rare earth oxides, and the major impurities were Ca (33% as CaO) and Fe (23% as Fe2O3). Fe bearing minerals could be removed by passing the sample through a wet high-intensity magnetic separator before leaching. After m...

With the rapidly expanding use of fluorescent lamps (FLs) and increasing interest in conservation and sustainable utilization of critical metals such as rare earth elements (REEs), the recovering of REEs from phosphors in waste FLs is becoming a critical environmental and economic issue. To effectively recycle REEs with metallurgical methods, mechanical activation by ball milling was introduced...

Phosphorus (P) is an important biogeochemical element and the environmental fate of P receives increasing attention. Through batch equilibration experiments, the adsorption and desorption of P in the absence and presence of exogeneous rare earth elements (REEs) were investigated in five types of agricultural soil samples collected from China. The results showed that the addition of different do...