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LEAKINV A inverse program for transmissivities and leakances, theory and user's guideIn dit rapport wordt een theoretische uitbreiding gegeven van de inverse modelleringsmethode van S.P.Neuman zodanig dat in een gedeeltelijk afgesloten watervoerende laag schattingen met betrouwbaarheidsintervallen verkregen kunnen worden van zowel het doorlaatvermogen als het lekvermogen (respectievelijk de kD-waarde, de reciproke c-waarde) in een aantal zones (zie Neuman, Water Resourc. Res. 16 (1980) 331-346). Deze uitbreiding is geprogrammeerd (in Fortran 77) en het grootste gedeelte van dit rapport is gewijd aan een beschrijving van de wijze hoe het computerprogramma van Neuman is aangepast.
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The cation competition and electrostatic theory are equally valid in quantifying the toxicity of trivalent rare earth ions (Y and Ce) to Triticum aestivum.There is a lack of appropriate models to delineate the toxicity of rare earth elements (REEs) while taking into account the factors that affect bioavailability. Here, standardized wheat (Triticum aestivum L.) root elongation tests were conducted to examine the impact of exposure conditions (i.e., varying Ca, Mg, Na, K and pH levels) on Y and Ce toxicity. Cation competition and electrostatic theory were examined for their applicability in explaining the observed variations in toxicity. Only Ca2+ and Mg2+ significantly alleviated the toxicity of Y3+ and Ce3+, while Na+, K+ and H+ showed no significant effects. Based on the cation competition, the derived binding constants for the hypothetical biotic ligands of wheat logKCaBL, logKMgBL, logKYBL, and logKCeBL were 3.87, 3.59, 6.70, and 6.48, respectively. The biotic ligand model (BLM) succeeded in predicting toxicities of Y and Ce, with more than 93% of the variance in toxicity explained. Given the BLM requires large data sets for deriving model parameters, attempts were further made to explore a simpler electrostatic based model to quantify REEs toxicity. The results demonstrated that the predictive capacity of the electrostatic approach, which considers ion activities at the plasma membrane surface, was comparable to that of BLM with at least 87% of the variations in toxicity explained. This suggested that the electrostatic theory can serve as a surrogate to BLM in modeling Y and Ce toxicities. Therefore, we recommend the BLM and electrostatic-based model as effective approaches to incorporate bioavailability in quantifying REEs toxicity in the presence of various levels of other major cations.
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Vage verzamelingen en mogelijkheidsmaten. Een inleiding in the theorie en voorbeelden van toepassingenThe author reports on a literature search on fuzzy sets. Fuzzy sets differ from classical sets in the following sense: elements can partly belong to fuzzy sets, whereas elements do or don't belong to classical sets. Fuzzy sets can be generalized to fuzzy relations between elements ; fuzzy Markovian chains, that describe transitions between elements ; fuzzy functions ; fuzzy numbers ; fuzzy reasoning based on fuzzy relations ; fuzzy inclusion ; and fuzzy partitions. The possibility measure is a fuzzy translation of the probability measure: it quantifies the possibility of an event instead of the probability. Three applications of fuzzy sets and possibility measures have been elaborated: fuzzy linear regression, the fuzzy shortest path problem and fuzzy multi-criteria analysis. On the basis of the fuzzy shortest path problem (the interpretations of) the possibility measure and the probability measure are compared.<br>
