PubMed Health⌕ Search
Home/Archive/PubMed

PubMed · 2798771

Normalization and calculation of lanthanide element concentrations in environmental samples.

B Markert·H Piehler·H Lieth·A Sugimae
View original source ↗Export metadata ↓

Abstract

A mathematical model for the prediction of lanthanide element concentrations in soil and plant samples is presented. A comparison between predicted and measured lanthanide values in soil and plant samples show, that the model produces good results for the elements in the soil samples and for most elements in plant material. The accuracy of prediction worsens with decreasing concentration of the heavier lanthanide elements. The mathematical model presented is not valid on other environmental samples like aerosols, because no data for these matrices are available yet to calibrate our normalized curves.

Explore related subjects

MathematicsMetals, Rare EarthModels, TheoreticalPlantsSoilComparative StudyJournal ArticleResearch Support, Non-U.S. Gov't

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

B Markert, H Piehler, H Lieth, A Sugimae. 1989. Normalization and calculation of lanthanide element concentrations in environmental samples.. https://doi.org/10.1007/bf01211258

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2006

Content uniformity and assay requirements in current regulations.

The acceptance of a tablet batch is based both on the content uniformity test and on the assay. It is shown that these two characteristics are not independent, and the acceptance criteria for them are not even consistent. For content uniformity range three methods of calculation are compared: the present European Pharmacopoeia method, a tolerance range method with improved k tolerance factor and a one-way random effects analysis of variance model. To resolve the inconsistency several options are discussed: applying the holistic content uniformity range alone; using content uniformity standard deviation and assay mean simultaneously or applying a criterion based on Taguchi's quadratic loss function.

Mathematics↗
PubMed2006

Stable time filtering of strongly unstable spatially extended systems.

Many contemporary problems in science involve making predictions based on partial observation of extremely complicated spatially extended systems with many degrees of freedom and with physical instabilities on both large and small scale. Various new ensemble filtering strategies have been developed recently for these applications, and new mathematical issues arise. Because ensembles are extremely expensive to generate, one such issue is whether it is possible under appropriate circumstances to take long time steps in an explicit difference scheme and violate the classical Courant-Friedrichs-Lewy (CFL)-stability condition yet obtain stable accurate filtering by using the observations. These issues are explored here both through elementary mathematical theory, which provides simple guidelines, and the detailed study of a prototype model. The prototype model involves an unstable finite difference scheme for a convection-diffusion equation, and it is demonstrated below that appropriate observations can result in stable accurate filtering of this strongly unstable spatially extended system.

Mathematics↗