The primary goal of this paper has been the exploration of an analytical formula for the inverse of an invertible \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepacka...
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The primary goal of this paper has been the exploration of an analytical formula for the inverse of an invertible \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{\textbf{I}}-\epsilon \textbf{Q}]$$\end{document} square matrix for two and four energy groups, explicitly in terms of the elements of that matrix. Our work aims to present efficient mathematical techniques to calculate the neutron flux into multi-dimensional homogeneous reactors using the quasi-static method and different types of the Pad & eacute;approximations, which can be applied to linear and nonlinearkinetics systems. These powerful techniques, which include the analytical inversion of the generated matrix, can be beneficial for cutting down on computing time and speeding up the suggested approximations above the set benchmarks. We have examined the sensitivity of the time step size utilizing different Pad & eacute;approximations. The results of various Pad & eacute;approximations are tested and compared with traditional and benchmark techniques for different types of reactivity, including step, ramp, sinusoidal, pulse, and nonlinear reactivity for two and three-dimensional space homogeneous reactors. These practical approximations handle stiffness, are the simplest to execute, and yield results comparable to benchmark techniques.
This paper focuses on the improvement of the concentration and productivity of 1,3-propanediol from continuous fermentation of glycerol by Klebsiella pneumoniae.A nonlinear steady-state optimization model is presented...
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This paper focuses on the improvement of the concentration and productivity of 1,3-propanediol from continuous fermentation of glycerol by Klebsiella pneumoniae.A nonlinear steady-state optimization model is presented according to engineering background.A new linear approximating method has been developed in view of the feature of the optimization model. Computer simulation is used for this paper,and the numerical simulation is in accordance with experimental *** numerical results illustrate the validity and efficiency of the *** results presented in this work can be used as guidelines for choosing proper operating parameters to get higher concentration or productivity.
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