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.

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...

INTRODUCTION Through leaching experiments and simulated rainfall experiments, characteristics of vertical leaching of exogenous rare earth elements (REEs) and phosphorus (P) and their losses with surface runoff during simulated rainfall in different types of soils (terra nera soil, cinnamon soil, red soil, loess soil, and purple soil) were investigated. RESULTS AND ANALYSES Results of the lea...

We introduce techniques to derive estimates for the degrees of the generators of the integral closure of several classes of Rees algebras of modules, and to bound the length of normalization processes. In the case of regular base rings, the bounds are expressed in terms of Buchsbaum–Rim multiplicities and a module version of Briançon–Skoda numbers. Normalization of modules is the study of the i...

Rare earth elements (REE) are widely used in advanced technology. Praseodymium (Pr), neodymium (Nd), samarium (Sm) and dysprosium (Dy) are used in high-power permanent magnets. Ytterbium (Yb), erbium (Er) and holmium (Ho) are used in lasers. Lanthanum (La), gadolinium (Gd), terbium (Tb), europium (Eu) and Yb are components of luminescent and fluorescent phosphors, used in fluorescent lamps, rad...

the dalir phosphate horizon is located ~57 km southwest of chalous, mazandaran province. the horizon developed as stratiform within upper shale of soltanieh formation (late neoproterozoic - early cambrian). according to mineralogical data, the major minerals of the phosphate horizon are calcite, fluorapatite, dolomite, quartz, pyrite, muscovite, and illite. microscopic evidence such as existenc...