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The value does not exist!A motivation for extremal analysis

Probability, Uncertainty and Quantitative Risk 2022年第3期7卷 195-214页

作者： Jean-Pierre Aubin h.l.ne frankowska Retired 14Rue Domat75005 ParisFrance CNRS IMJ-PRGSorbonne Université4Place Jussieu75252 ParisFrance

Standard mathematical economics studies the production,exchange,and consumption of goods“provided with units of measurement,”as in physics,in order to be enumerated,quantified,added,***,“baskets of goods,”which should describe subsets of goods,are mathematically represented as commodity vectors of a vector space,linear combination of units of goods,evaluated by prices,which are linear numerical ***,in this sense,mathematical economics is a branch of ***,economics,and many other domains of life sciences,investigate also what will be called entities,defining elements deprived of units of measure,which thus cannot be enumerated.(1)Denoting by X the set of entities x∈X deprived of units of measurement,a“basket of goods”is actually a subset K■X of the set entities,i.e.,an element of the“hyperset”P(X),the family of subsets of X,and no longer a commodity vector of the vector space of commodities;(2)Entities can be“gathered”instead of being“added”;(3)Entities can still be evaluated by a family of functions A:x 2 X 7!A(x)2 Rregarded as a“valuators,”in lieu and place of linear“prices”evaluating the units of economic goods.(4)Subsets of entities can be evaluated by an“interval of values”between two extremal ones,the minimum and the maximum,instead of the sum of values of units of goods weighted by their *** sciences dealing with intertwined relations among many combinations of entities,hypersets offer metaphors of“lamarckian complexity”that keeps us away from binary relations,graphs of functions,and set-valued maps,to focus our attention on“multinary relations”between families of *** deprived of units of measurement,these“proletarian”entities still enjoy enough properties for this pauperization to be mathematically *** is the object of this extremal manifesto:in economics and other domains of life sciences,vector spaces should yield their imperial status of“state space”to hypersets and linear prices to hy

关键词： Valuators Extremal topologies Transfer of topologies Confined sets Extremal evolution Inert relation Viability kernel Regulator

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Speciation analysis of aluminium in plant parts of Betula pendula and in soil

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Journal of Environmental Sciences 2018年第3期30卷 153-161页

作者： Anetta Ziola-frankowska Marcin Frankowski Adam Mickiewicz University in Poznan Faculty of Chemistry Department of Analytical Chemistry 61-614 Poznan Poland. Adam Mickiewicz University in Poznan Faculty of Chemistry Department of Water and Soil Analysis 61-614 Poznan Poland

The research presents the first results of aluminium speciation analysis in aqueous extracts of individual plant parts of Betula pendula and soil samples, using high Performance Ion Chromatography with Diode Array Detection（hPIC-DAD）. The applied method allowed us to carry out a full speciation analysis of aluminium in the form of predominant aluminium–fluoride complexes： AlF（（x = 2,3,4））^（（3-x））（first analytical signal）, AlF^（2＋）（second analytical signal） and Al^（3＋）（third analytical signal） in samples of lateral roots, tap roots, twigs, stem, leaf and soil collected under roots of B. pendula. Concentrations of aluminium and its complexes were determined for two types of environment characterised by different degree of human impact：contaminated site of the Chemical Plant in luboń and protected area of the Wielkopolski National Park. For all the analysed samples of B. pendula and soil, AlF（（x = 2,3,4））^（（3-x））had the largest contribution, followed by Al^（3＋）and AlF^（2＋）. Significant differences in concentration and contribution of Al–F complexes and Al^（3＋）form, depending on the place of sampling（different anthropogenic pressure） and plant part of B. pendula were observed. Based on the obtained results, it was found that transport of aluminium is ＂blocked＂ by lateral roots, and is closely related to Al content of soil.

关键词： Aluminium Aluminium-fluoride complexes Soil Betula pendula Plant parts Speciation analysis

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