mathematical modeling of catalytic fixed bed reactors

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... Altenbach Mathematical Modeling in Mechanics of Granular Materials 123 Preface This monograph contains original results in the field of mathematical and numerical modeling of mechanical behavior of granular ... with initial strain solution of the direct problem of description of mechanical properties of existing materials to the study of the inverse problem of production of materials with preas- signed ... This approach requires development of new theoretical methods and improvement of known ones as well as software for mathematical modeling of the behaviour of continuous media which, at first glance,...

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... plot of water surface in 2D simulation of Exp-1 …………….95 Figure 6.35 Carpet plot of water surface in 2D simulation of Exp-2…………… 95 Figure 6.36 Carpet plot of water surface in 2D simulation of ... plot of water surface in 2D simulation of Exp-4…………… 96 Figure 6.38 Carpet plot of water surface in 2D simulation of Exp-5…………… 97 Figure 6.39 Carpet plot of water surface in 2D simulation of ... surface profile analysis of open channel flows over a circular surface. Journal of Applied Mechanics, JSCE, Vol. 8, pp 847-854, 2005. 5. Anh T. N. and Hosoda T.: Free surface profile analysis of flows...

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... Global Strength Requirement of Ageing Fixed Offshore Structure with Joint Anomalies 2 1. INTRODUCTION To date, there are increasing numbers of ageing fixed offshore structure worldwide ... of mitigation measure. Non-linear Plastic Collapse Analysis is often used to quantify the ultimate strength by introducing the Reserve Strength Ratio (RSR), which can be thought of factor of ... assessment. The purpose of this study is to demonstrate the methodology used to CAFEO28 2010 CAFEO 28 Global Strength Assessment Requirement of Ageing Fixed Offshore Structure with...

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... measure of goodness -of- fit. When the third item suggests that the model is an unlikely match to the data, then items (i) and (ii) are probably worthless. Unfortunately, many practitioners of parameter ... Academic Press). von Mises, R. 1964, Mathematical Theory of Probability and Statistics (New York: Academic Press), Chapter X. Korn, G.A., and Korn, T.M. 1968, Mathematical Handbook for Scientists ... RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission...

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... assumption of a normal distribution. For a hundred years or so, mathematical statisticians have been in love with the fact that the probability distribution of the sum of a very large number of very small ... time, within ±2σ 95 percent of the time, and within ±3σ 99.7 percent of the time. Extending this, one would expect a measurement to be off by ±20σ only one time out of 2 × 10 88 .Weall know that ... the correct choice of parameters. In other words, we identify the probability of the data given the parameters (which is a mathematically computable number), as the likelihood of the parameters given...

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... problem of fitting a set of N data points (x i ,y i )to a straight-line model y(x)=y(x;a, b)=a+bx (15.2.1) 666 Chapter 15. Modeling of Data Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... variance of the linear combination y i − a − bx i of two random variables x i and y i , Var( y i − a − bx i )=Var( y i )+b 2 Var( x i )=σ 2 yi +b 2 σ 2 xi ≡1/w i (15.3.3) The sum of the square of N ... =1, ,M (15.1.7) Equation (15.1.7) is, in general, a set of M nonlinear equations for the M unknown a k . Various of the procedures described subsequently in this chapter derive from (15.1.7) and...

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... float *xx,*yy,*sx,*sy,*ww,aa,offs; float chixy(float bang) Captive function of fitexy , returns the value of (χ 2 − offs ) for the slope b=tan(bang) . Scaled data and offs are communicated via the ... variance of the linear combination y i − a − bx i of two random variables x i and y i , Var(y i − a − bx i )=Var(y i )+b 2 Var(x i )=σ 2 yi +b 2 σ 2 xi ≡1/w i (15.3.3) The sum of the square of N ... of varying b, successful numerical root-finding leads to a value of ∆a that minimizes χ 2 for the value of ∆b that gives ∆χ 2 =1.This(see Figure 15.3.1) directly gives the tangent projection of...

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... combinations of the columns of V, with coefficients obtained by forming dot products of the columns 672 Chapter 15. Modeling of Data Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... certain mathematical irony in the fact that least-squares problems are both overdetermined (number of data points greater than number of parameters) and underdetermined (ambiguous combinations of ... thestandard deviationsof themeasureddependentvariable. The measured values of the dependent variable do not enter the design matrix. Solution by Use of the Normal Equations The minimum of (15.4.3) occurs...

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