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
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
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
Photovoltaic(PV)systems are electrical systems designed to convert solar energy into electrical energy.As a crucial component of PV systems,harsh weather conditions,photovoltaic panel temperature and solar irradiance ...Photovoltaic(PV)systems are electrical systems designed to convert solar energy into electrical energy.As a crucial component of PV systems,harsh weather conditions,photovoltaic panel temperature and solar irradiance influence the power output of photovoltaic cells.Therefore,accurately identifying the parameters of PV models is essential for simulating,controlling and evaluating PV systems.In this study,we propose an enhanced weighted-mean-of-vectors optimisation(EINFO)for efficiently determining the unknown parameters in PV systems.EINFO introduces a Lambert W-based explicit objective function for the PV model,enhancing the computational accuracy of the algorithm's population fitness.This addresses the challenge of improving the metaheuristic algorithms'identification accuracy for unknown parameter identification in PV models.We experimentally apply EINFO to three types of PV models(single-diode,double-diode and PV-module models)to validate its accuracy and stability in parameter identification.The results demonstrate that EINFO achieves root mean square errors(RMSEs)of 7.7301E-04,6.8553E-04 and 2.0608E-03 for the single-diode model,double-diode model and PV-module model,respectively,surpassing those obtained by using INFO algorithm as well as other methods in terms of convergence speed,accuracy and stability.Furthermore,comprehensive experimental findings on three commercial PV modules(ST40,SM55 and KC200GT)indicate that EINFO consistently maintains high accuracy across varying temperatures and irradiation levels.In conclusion,EINFO emerges as a highly competitive and practical approach for parameter identification in diverse types of PV models.展开更多
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.
基金partially supported by MRC(MC_PC_17171)Royal Society(RP202G0230)+8 种基金BHF(AA/18/3/34220)Hope Foundation for Cancer Research(RM60G0680)GCRF(P202PF11)Sino-UK Industrial Fund(RP202G0289)Sino-UK Education Fund(OP202006)LIAS(P202ED10,P202RE969)Data Science Enhancement Fund(P202RE237)Fight for Sight(24NN201)BBSRC(RM32G0178B8).
文摘Photovoltaic(PV)systems are electrical systems designed to convert solar energy into electrical energy.As a crucial component of PV systems,harsh weather conditions,photovoltaic panel temperature and solar irradiance influence the power output of photovoltaic cells.Therefore,accurately identifying the parameters of PV models is essential for simulating,controlling and evaluating PV systems.In this study,we propose an enhanced weighted-mean-of-vectors optimisation(EINFO)for efficiently determining the unknown parameters in PV systems.EINFO introduces a Lambert W-based explicit objective function for the PV model,enhancing the computational accuracy of the algorithm's population fitness.This addresses the challenge of improving the metaheuristic algorithms'identification accuracy for unknown parameter identification in PV models.We experimentally apply EINFO to three types of PV models(single-diode,double-diode and PV-module models)to validate its accuracy and stability in parameter identification.The results demonstrate that EINFO achieves root mean square errors(RMSEs)of 7.7301E-04,6.8553E-04 and 2.0608E-03 for the single-diode model,double-diode model and PV-module model,respectively,surpassing those obtained by using INFO algorithm as well as other methods in terms of convergence speed,accuracy and stability.Furthermore,comprehensive experimental findings on three commercial PV modules(ST40,SM55 and KC200GT)indicate that EINFO consistently maintains high accuracy across varying temperatures and irradiation levels.In conclusion,EINFO emerges as a highly competitive and practical approach for parameter identification in diverse types of PV models.
