Electrical characterization analyses are proposed in this work using the Lambert function on Schottky junctions in GaN wide band gap semiconductor devices for extraction of physical parameters.The Lambert function is ...Electrical characterization analyses are proposed in this work using the Lambert function on Schottky junctions in GaN wide band gap semiconductor devices for extraction of physical parameters.The Lambert function is used to give an explicit expression of the current in the Schottky junction.This function is applied with defined conduction phenomena,whereas other work presented arbitrary（or undefined）conduction mechanisms in such parameters＇ extractions.Based upon AlGaN/GaN HEMT structures,extractions of parameters are undergone in order to provide physical characteristics.This work highlights a new expression of current with defined conduction phenomena in order to quantify the physical properties of Schottky contacts in AlGaN/GaN HEMT transistors.展开更多
Series of exponential equations in the form of were solved graphically, numerically and analytically. The analytical solution was derived in terms of Lambert-W function. A general numerical solution for any y is found...Series of exponential equations in the form of were solved graphically, numerically and analytically. The analytical solution was derived in terms of Lambert-W function. A general numerical solution for any y is found in terms of n or in base y. A solution is close to the fine structure constant. The equation which provided the solution as the fine structure constant was derived in terms of the fundamental constants.展开更多
Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity ...Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity is a function of temperature. At a specific temperature, for the frequencies correspond to much less than the maximum intensity, an equation was derived in the form of the Lambert <em>W</em> function. Numerical calculations validate the equation. A new form of solution for the Euler’s transcendental equation was derived in the form of the Lambert <em>W</em> function with logarithmic argument. Numerical solutions to the Euler’s equation were determined iteratively and iterative convergences were investigated. Numerical coincidences with physical constants were explored.展开更多
Conventional analysis of enzyme-catalyzed reactions uses a set of initial rates of product formation or substrate decay at a variety of substrate concentrations. Alternatively to the conventional methods, attempts hav...Conventional analysis of enzyme-catalyzed reactions uses a set of initial rates of product formation or substrate decay at a variety of substrate concentrations. Alternatively to the conventional methods, attempts have been made to use an integrated Michaelis-Menten equation to assess the values of the Michaelis-Menten KM and turnover kcat constants directly from a single time course of an enzymatic reaction. However, because of weak convergence, previous fits of the integrated Michaelis-Menten equation to a single trace of the reaction have no proven records of success. Here we propose a reliable method with fast convergence based on an explicit solution of the Michaelis-Menten equation in terms of the Lambert-W function with transformed variables. Tests of the method with stopped-flow measurements of the catalytic reaction of cytochrome c oxidase, as well as with simulated data, demonstrate applicability of the approach to de termine KM and kcat constants free of any systematic errors. This study indicates that the approach could be an alternative solution for the characterization of enzymatic reactions, saving time, sample and efforts. The single trace method can greatly assist the real time monitoring of enzymatic activity, in particular when a fast control is mandatory. It may be the only alternative when conventional analysis does not apply, e.g. because of limited amount of sample.展开更多
This study proposes a new flexible family of distributions called the Lambert-G family.The Lambert family is very flexible and exhibits desirable properties.Its three-parameter special sub-models provide all significa...This study proposes a new flexible family of distributions called the Lambert-G family.The Lambert family is very flexible and exhibits desirable properties.Its three-parameter special sub-models provide all significantmonotonic and non-monotonic failure rates.A special sub-model of the Lambert family called the Lambert-Lomax(LL)distribution is investigated.General expressions for the LL statistical properties are established.Characterizations of the LL distribution are addressed mathematically based on its hazard function.The estimation of the LL parameters is discussed using six estimation methods.The performance of this estimation method is explored through simulation experiments.The usefulness and flexibility of the LL distribution are demonstrated empirically using two real-life data sets.The LL model better fits the exponentiated Lomax,inverse power Lomax,Lomax-Rayleigh,power Lomax,and Lomax distributions.展开更多
基金Project supported by the French Department of Defense(DGA)
文摘Electrical characterization analyses are proposed in this work using the Lambert function on Schottky junctions in GaN wide band gap semiconductor devices for extraction of physical parameters.The Lambert function is used to give an explicit expression of the current in the Schottky junction.This function is applied with defined conduction phenomena,whereas other work presented arbitrary（or undefined）conduction mechanisms in such parameters＇ extractions.Based upon AlGaN/GaN HEMT structures,extractions of parameters are undergone in order to provide physical characteristics.This work highlights a new expression of current with defined conduction phenomena in order to quantify the physical properties of Schottky contacts in AlGaN/GaN HEMT transistors.
文摘Series of exponential equations in the form of were solved graphically, numerically and analytically. The analytical solution was derived in terms of Lambert-W function. A general numerical solution for any y is found in terms of n or in base y. A solution is close to the fine structure constant. The equation which provided the solution as the fine structure constant was derived in terms of the fundamental constants.
文摘Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity is a function of temperature. At a specific temperature, for the frequencies correspond to much less than the maximum intensity, an equation was derived in the form of the Lambert <em>W</em> function. Numerical calculations validate the equation. A new form of solution for the Euler’s transcendental equation was derived in the form of the Lambert <em>W</em> function with logarithmic argument. Numerical solutions to the Euler’s equation were determined iteratively and iterative convergences were investigated. Numerical coincidences with physical constants were explored.
文摘Conventional analysis of enzyme-catalyzed reactions uses a set of initial rates of product formation or substrate decay at a variety of substrate concentrations. Alternatively to the conventional methods, attempts have been made to use an integrated Michaelis-Menten equation to assess the values of the Michaelis-Menten KM and turnover kcat constants directly from a single time course of an enzymatic reaction. However, because of weak convergence, previous fits of the integrated Michaelis-Menten equation to a single trace of the reaction have no proven records of success. Here we propose a reliable method with fast convergence based on an explicit solution of the Michaelis-Menten equation in terms of the Lambert-W function with transformed variables. Tests of the method with stopped-flow measurements of the catalytic reaction of cytochrome c oxidase, as well as with simulated data, demonstrate applicability of the approach to de termine KM and kcat constants free of any systematic errors. This study indicates that the approach could be an alternative solution for the characterization of enzymatic reactions, saving time, sample and efforts. The single trace method can greatly assist the real time monitoring of enzymatic activity, in particular when a fast control is mandatory. It may be the only alternative when conventional analysis does not apply, e.g. because of limited amount of sample.
文摘This study proposes a new flexible family of distributions called the Lambert-G family.The Lambert family is very flexible and exhibits desirable properties.Its three-parameter special sub-models provide all significantmonotonic and non-monotonic failure rates.A special sub-model of the Lambert family called the Lambert-Lomax(LL)distribution is investigated.General expressions for the LL statistical properties are established.Characterizations of the LL distribution are addressed mathematically based on its hazard function.The estimation of the LL parameters is discussed using six estimation methods.The performance of this estimation method is explored through simulation experiments.The usefulness and flexibility of the LL distribution are demonstrated empirically using two real-life data sets.The LL model better fits the exponentiated Lomax,inverse power Lomax,Lomax-Rayleigh,power Lomax,and Lomax distributions.
