AustralieFrV1, Main, Exploration, bibRecord, 00C538

Can a reaction be written between a set of minerals within error?

Identifieur interne : 00C538 ( Main/Exploration ); précédent : 00C537; suivant : 00C539

Can a reaction be written between a set of minerals within error?

Auteurs : R. Powell [France] ; M. Guiraud [France]

Source :

Journal of Metamorphic Geology [ 0263-4929 ] ; 1999-01.

RBID : ISTEX:1A451657A603D109F198E83A423DF9451EE5EF2E

Descripteurs français

Wicri :
- topic : Oxyde.

English descriptors

KwdEn :
- American mineralogist, Analytical uncertainties, Bogus, Bootstrap, Bootstrap results, Bootstrap sample, Cation, Cation basis, Column vector, Compositionally coplanar, Constraint, Coplanar, Covariance matrix, Data scatter, Data uncertainties, Diagonal matrix, Equality constraints, Error propagation, Freedom problems, Full rank, Homogeneous solution, Kernel estimator probability distribution, Least squares, Least squares problem, Matrix, Matrix analysis, Matrix form, Metamorphic, Metamorphic geology, Metamorphic mineral assemblages, Mineral, Mineral analyses, Mineral compositions, Mole proportions, Monte carlo simulation, Oxide, Reaction constraints, Real systems, Residual, Second aspect, Side vector, Singular value decomposition, Sio2, Small degree, Standard deviations, Stoichiometric, Stoichiometric constraint, Stoichiometric constraints, Stoichiometry, Stoichiometry constraints.
Teeft :
- American mineralogist, Analytical uncertainties, Bogus, Bootstrap, Bootstrap results, Bootstrap sample, Cation, Cation basis, Column vector, Compositionally coplanar, Constraint, Coplanar, Covariance matrix, Data scatter, Data uncertainties, Diagonal matrix, Equality constraints, Error propagation, Freedom problems, Full rank, Homogeneous solution, Kernel estimator probability distribution, Least squares, Least squares problem, Matrix, Matrix analysis, Matrix form, Metamorphic, Metamorphic geology, Metamorphic mineral assemblages, Mineral, Mineral analyses, Mineral compositions, Mole proportions, Monte carlo simulation, Oxide, Reaction constraints, Real systems, Residual, Second aspect, Side vector, Singular value decomposition, Sio2, Small degree, Standard deviations, Stoichiometric, Stoichiometric constraint, Stoichiometric constraints, Stoichiometry, Stoichiometry constraints.

Abstract

Determining whether a reaction can be written between a set of minerals within error is an example of the more general problem of determining whether a set of compositions are coplanar within error. Generally if the compositions are of minerals, ‘within error’ should allow the minerals to maintain stoichiometry. The problem is addressed via the addition of a ‘bogus’ composition to the set, and calculating the reaction coefficients for a reaction between the compositions in this augmented set. A reaction can be written if a confidence interval on the reaction coefficient of ‘bogus’ includes zero. The reaction coefficients can be solved for directly when the problem is posed in terms of least squares with equality constraints. The confidence interval is determined with a bootstrap method, allowing the result to depend on the scatter of the data around the solution of the least squares problem, not on the data uncertainties

Url:

https://api.istex.fr/document/1A451657A603D109F198E83A423DF9451EE5EF2E/fulltext/pdf

DOI: 10.1046/j.1525-1314.1999.00100.x

Affiliations:

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Le document en format XML

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<term>Bootstrap results</term>
<term>Bootstrap sample</term>
<term>Cation</term>
<term>Cation basis</term>
<term>Column vector</term>
<term>Compositionally coplanar</term>
<term>Constraint</term>
<term>Coplanar</term>
<term>Covariance matrix</term>
<term>Data scatter</term>
<term>Data uncertainties</term>
<term>Diagonal matrix</term>
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<term>Freedom problems</term>
<term>Full rank</term>
<term>Homogeneous solution</term>
<term>Kernel estimator probability distribution</term>
<term>Least squares</term>
<term>Least squares problem</term>
<term>Matrix</term>
<term>Matrix analysis</term>
<term>Matrix form</term>
<term>Metamorphic</term>
<term>Metamorphic geology</term>
<term>Metamorphic mineral assemblages</term>
<term>Mineral</term>
<term>Mineral analyses</term>
<term>Mineral compositions</term>
<term>Mole proportions</term>
<term>Monte carlo simulation</term>
<term>Oxide</term>
<term>Reaction constraints</term>
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<term>Side vector</term>
<term>Singular value decomposition</term>
<term>Sio2</term>
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<term>Standard deviations</term>
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<term>Covariance matrix</term>
<term>Data scatter</term>
<term>Data uncertainties</term>
<term>Diagonal matrix</term>
<term>Equality constraints</term>
<term>Error propagation</term>
<term>Freedom problems</term>
<term>Full rank</term>
<term>Homogeneous solution</term>
<term>Kernel estimator probability distribution</term>
<term>Least squares</term>
<term>Least squares problem</term>
<term>Matrix</term>
<term>Matrix analysis</term>
<term>Matrix form</term>
<term>Metamorphic</term>
<term>Metamorphic geology</term>
<term>Metamorphic mineral assemblages</term>
<term>Mineral</term>
<term>Mineral analyses</term>
<term>Mineral compositions</term>
<term>Mole proportions</term>
<term>Monte carlo simulation</term>
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<term>Standard deviations</term>
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<term>Stoichiometric constraints</term>
<term>Stoichiometry</term>
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<front><div type="abstract" xml:lang="en">Determining whether a reaction can be written between a set of minerals within error is an example of the more general problem of determining whether a set of compositions are coplanar within error. Generally if the compositions are of minerals, ‘within error’ should allow the minerals to maintain stoichiometry. The problem is addressed via the addition of a ‘bogus’ composition to the set, and calculating the reaction coefficients for a reaction between the compositions in this augmented set. A reaction can be written if a confidence interval on the reaction coefficient of ‘bogus’ includes zero. The reaction coefficients can be solved for directly when the problem is posed in terms of least squares with equality constraints. The confidence interval is determined with a bootstrap method, allowing the result to depend on the scatter of the data around the solution of the least squares problem, not on the data uncertainties</div>
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Can a reaction be written between a set of minerals within error?

Can a reaction be written between a set of minerals within error?

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri