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Christophe Lacroix - One of the best experts on this subject based on the ideXlab platform.

  • Lactobacillus helveticus growth and lactic acid production during pH-controlled batch cultures in whey permeate/yeast extract medium. Part II: kinetic modeling and model validation
    Enzyme and Microbial Technology, 2002
    Co-Authors: Adolf Willem Schepers, Jules Thibault, Christophe Lacroix
    Abstract:

    A kinetic model was developed that describes growth and lactic acid production rates of Lactobacillus helveticus during pH-controlled batch cultures in whey permeate-yeast extract medium as a function of four variables: sugar, nitrogen substrate and lactic acid concentrations, and pH. Since available nitrogen substrate could not be measured directly, it was related to medium composition through a response surface model of maximum biomass concentration in nitrogen-limited growth cultures. The effect of pH on growth was modeled with a Gaussian equation instead of the traditional second order Polynomial Term. Product inhibition was modeled with a logistic Term for lactate and an exponential Term for undissociated lactic acid. The kinetic model accurately described the experimental data with few exceptions.

  • lactobacillus helveticus growth and lactic acid production during ph controlled batch cultures in whey permeate yeast extract medium part ii kinetic modeling and model validation
    Enzyme and Microbial Technology, 2002
    Co-Authors: Adolf Willem Schepers, Jules Thibault, Christophe Lacroix
    Abstract:

    A kinetic model was developed that describes growth and lactic acid production rates of Lactobacillus helveticus during pH-controlled batch cultures in whey permeate-yeast extract medium as a function of four variables: sugar, nitrogen substrate and lactic acid concentrations, and pH. Since available nitrogen substrate could not be measured directly, it was related to medium composition through a response surface model of maximum biomass concentration in nitrogen-limited growth cultures. The effect of pH on growth was modeled with a Gaussian equation instead of the traditional second order Polynomial Term. Product inhibition was modeled with a logistic Term for lactate and an exponential Term for undissociated lactic acid. The kinetic model accurately described the experimental data with few exceptions.

Adolf Willem Schepers - One of the best experts on this subject based on the ideXlab platform.

  • Lactobacillus helveticus growth and lactic acid production during pH-controlled batch cultures in whey permeate/yeast extract medium. Part II: kinetic modeling and model validation
    Enzyme and Microbial Technology, 2002
    Co-Authors: Adolf Willem Schepers, Jules Thibault, Christophe Lacroix
    Abstract:

    A kinetic model was developed that describes growth and lactic acid production rates of Lactobacillus helveticus during pH-controlled batch cultures in whey permeate-yeast extract medium as a function of four variables: sugar, nitrogen substrate and lactic acid concentrations, and pH. Since available nitrogen substrate could not be measured directly, it was related to medium composition through a response surface model of maximum biomass concentration in nitrogen-limited growth cultures. The effect of pH on growth was modeled with a Gaussian equation instead of the traditional second order Polynomial Term. Product inhibition was modeled with a logistic Term for lactate and an exponential Term for undissociated lactic acid. The kinetic model accurately described the experimental data with few exceptions.

  • lactobacillus helveticus growth and lactic acid production during ph controlled batch cultures in whey permeate yeast extract medium part ii kinetic modeling and model validation
    Enzyme and Microbial Technology, 2002
    Co-Authors: Adolf Willem Schepers, Jules Thibault, Christophe Lacroix
    Abstract:

    A kinetic model was developed that describes growth and lactic acid production rates of Lactobacillus helveticus during pH-controlled batch cultures in whey permeate-yeast extract medium as a function of four variables: sugar, nitrogen substrate and lactic acid concentrations, and pH. Since available nitrogen substrate could not be measured directly, it was related to medium composition through a response surface model of maximum biomass concentration in nitrogen-limited growth cultures. The effect of pH on growth was modeled with a Gaussian equation instead of the traditional second order Polynomial Term. Product inhibition was modeled with a logistic Term for lactate and an exponential Term for undissociated lactic acid. The kinetic model accurately described the experimental data with few exceptions.

Éric Gaudron - One of the best experts on this subject based on the ideXlab platform.

  • Étude du cas rationnel de la théorie des formes linéaires de logarithmes. (French) [Study of the rational case of the theory of linear forms in logarithms]
    Journal of Number Theory, 2007
    Co-Authors: Éric Gaudron
    Abstract:

    We establish new measures of linear independence of logarithms on commutative algebraic groups in the so-called \emph{rational case}. More precisely, let k be a number field and v_{0} be an arbitrary place of k. Let G be a commutative algebraic group defined over k and H be a connected algebraic subgroup of G. Denote by Lie(H) its Lie algebra at the origin. Let u\in Lie(G(C_{v_{0}})) a logarithm of a point p\in G(k). Assuming (essentially) that p is not a torsion point modulo proper connected algebraic subgroups of G, we obtain lower bounds for the distance from u to Lie(H)\otimes_{k} C_{v_{0}}. For the most part, they generalize the measures already known when G is a linear group. The main feature of these results is to provide a better dependence in the height Log a of p, removing a Polynomial Term in LogLog a. The proof relies on sharp estimates of sizes of formal subschemes associated to H (in the sense of J.-B. Bost) obtained from a lemma by M. Raynaud as well as an absolute Siegel lemma and, in the ultrametric case, a recent interpolation lemma by D. Roy.

  • Étude du cas rationnel de la théorie des formes linéaires de logarithmes
    Journal of Number Theory, 2007
    Co-Authors: Éric Gaudron
    Abstract:

    We establish new measures of linear independence of logarithms on commutative algebraic groups in the so-called rational case. More precisely, let k be a number field and v0 be an arbitrary place of k. Let G be a commutative algebraic group defined over k and H be a connected algebraic subgroup of G. Denote by Lie(H) its Lie algebra at the origin. Let u∈Lie(G(Cv0)) a logarithm of a point p∈G(k). Assuming (essentially) that p is not a torsion point modulo proper connected algebraic subgroups of G, we obtain lower bounds for the distance from u to Lie(H)⊗kCv0. For the most part, they generalize the measures already known when G is a linear group. The main feature of these results is to provide a better dependence in the height loga of p, removing a Polynomial Term in logloga. The proof relies on sharp estimates of sizes of formal subschemes associated to H (in the sense of Bost) obtained from a lemma by Raynaud as well as an absolute Siegel lemma and, in the ultrametric case, a recent interpolation lemma by Roy.

Jules Thibault - One of the best experts on this subject based on the ideXlab platform.

  • Lactobacillus helveticus growth and lactic acid production during pH-controlled batch cultures in whey permeate/yeast extract medium. Part II: kinetic modeling and model validation
    Enzyme and Microbial Technology, 2002
    Co-Authors: Adolf Willem Schepers, Jules Thibault, Christophe Lacroix
    Abstract:

    A kinetic model was developed that describes growth and lactic acid production rates of Lactobacillus helveticus during pH-controlled batch cultures in whey permeate-yeast extract medium as a function of four variables: sugar, nitrogen substrate and lactic acid concentrations, and pH. Since available nitrogen substrate could not be measured directly, it was related to medium composition through a response surface model of maximum biomass concentration in nitrogen-limited growth cultures. The effect of pH on growth was modeled with a Gaussian equation instead of the traditional second order Polynomial Term. Product inhibition was modeled with a logistic Term for lactate and an exponential Term for undissociated lactic acid. The kinetic model accurately described the experimental data with few exceptions.

  • lactobacillus helveticus growth and lactic acid production during ph controlled batch cultures in whey permeate yeast extract medium part ii kinetic modeling and model validation
    Enzyme and Microbial Technology, 2002
    Co-Authors: Adolf Willem Schepers, Jules Thibault, Christophe Lacroix
    Abstract:

    A kinetic model was developed that describes growth and lactic acid production rates of Lactobacillus helveticus during pH-controlled batch cultures in whey permeate-yeast extract medium as a function of four variables: sugar, nitrogen substrate and lactic acid concentrations, and pH. Since available nitrogen substrate could not be measured directly, it was related to medium composition through a response surface model of maximum biomass concentration in nitrogen-limited growth cultures. The effect of pH on growth was modeled with a Gaussian equation instead of the traditional second order Polynomial Term. Product inhibition was modeled with a logistic Term for lactate and an exponential Term for undissociated lactic acid. The kinetic model accurately described the experimental data with few exceptions.

Ute Seeling - One of the best experts on this subject based on the ideXlab platform.

  • Modelling of the shape of red heartwood in beech trees (Fagus sylvatica L.) based on external tree characteristics
    Annals of Forest Science, 2006
    Co-Authors: Holger Wernsdorfer, Gilles Le Moguedec, Thiéry Constant, Frédéric Mothe, Gérard Nepveu, Ute Seeling
    Abstract:

    The shape of red heartwood in beech was studied on 16 trees, based on the mean red heart radius at about every 2 m along the stem axis up to the crown base. The longitudinal red heart shape was modelled by sections of bell-shaped curves, given by an exponential function with a fourth order Polynomial Term. Using individual tree parameters for the red heart width, length and height, the observed red heart shapes were closely described by the model. An approach of a predictive model at the standing tree level was developed for estimating these parameters from the diameter at breast height, height of the crown base related to total tree height and height of a possible red heart initiation point. Remaining issues concerning the model structure should be analysed on a higher number of samples. An application of the model at the log level could be developed