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See detailGeneral constitutive equations of heat transport at small length scales and high frequencies with extension to mass and electrical charge transport
Machrafi, Hatim ULiege; Lebon, Georgy ULiege

in Applied Mathematics Letters (2016), 52

A generalized heat transport equation applicable at small length and short time scales is proposed. It is based on extended irreversible thermodynamics with an infinite number of high-order heat fluxes ... [more ▼]

A generalized heat transport equation applicable at small length and short time scales is proposed. It is based on extended irreversible thermodynamics with an infinite number of high-order heat fluxes selected as state variables. Extensions of Fick's and Ohm's laws are also formulated. As a numerical illustration, heat conduction in a rigid body subject to fixed and oscillatory temperature boundary conditions is discussed. © 2015 Elsevier Ltd. [less ▲]

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See detailSymmetric approximations of pseudo-Boolean functions with applications to influence indexes
Marichal, Jean-Luc; Mathonet, Pierre ULiege

in Applied Mathematics Letters (2012), 25(8), 1121-1126

We introduce an index for measuring the influence of the $k$th smallest variable on a pseudo-Boolean function. This index is defined from a weighted least squares approximation of the function by linear ... [more ▼]

We introduce an index for measuring the influence of the $k$th smallest variable on a pseudo-Boolean function. This index is defined from a weighted least squares approximation of the function by linear combinations of order statistic functions. We give explicit expressions for both the index and the approximation and discuss some properties of the index. Finally, we show that this index subsumes the concept of system signature in engineering reliability and that of cardinality index in decision making. [less ▲]

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See detailA spline interpolation technique that preserves mass budgets
Delhez, Eric ULiege

in Applied Mathematics Letters (2003), 16(1), 17-26

The usual practice of forcing budget models by linear interpolations of mean data does not produce a forcing whose mean is the data value required. The usual third-order spline is modified into a fourth ... [more ▼]

The usual practice of forcing budget models by linear interpolations of mean data does not produce a forcing whose mean is the data value required. The usual third-order spline is modified into a fourth-order spline, called mc-spline, to cope with this issue. The technique provides a smooth and faithful continuous interpolation of the original data that is well suited for its graphical representations or for the forcing of numerical models. (C) 2002 Elsevier Science Ltd. All rights reserved. [less ▲]

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See detailAccuracy and stability of the discretised isopycnal mixing equation
Mathieu, P. P.; Deleersnijder, E.; Beckers, Jean-Marie ULiege

in Applied Mathematics Letters (1999), 12(4), 81-88

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See detailMICROSCOPIC RHEOLOGICAL MODELS AND EXTENDED IRREVERSIBLE THERMODYNAMICS
Dauby, Pierre ULiege; Lebon, Georgy ULiege

in Applied Mathematics Letters (1991), 4(6), 39-43

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See detailConstitutive Equations of Rheological Materials : Towards a Thermodynamic Unified Approach
Dauby, Pierre ULiege; Lebon, Georgy ULiege

in Applied Mathematics Letters (1990), 3(4), 45-48

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