mathematical modeling of catalytic fixed bed reactors
Mathematical Modeling in Mechanics of Granular Materials potx
... Altenbach Mathematical Modeling in Mechanics of GranularMaterials123PrefaceThis monograph contains original results in the field of mathematical andnumerical modeling of mechanical behavior of granular ... with initialstrainsolution of the direct problem of description of mechanical properties of existingmaterials to the study of the inverse problem of production of materials with preas-signed ... This approach requires development of new theoretical methodsand 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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Hydraulic modeling of open channel flows over an arbitrary 3-d surface and its applications in amenity hydraulic engineering
... 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 Assessment Requirement of Ageing Fixed Offshore Structure with Joint Anomalies
... 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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Tài liệu Modeling of Data part 1 pptx
... measure of goodness -of- fit. When the third item suggests that the modelis 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: AcademicPress), 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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Tài liệu Modeling of Data part 2 doc
... assumption of a normal distribution.For a hundred years or so, mathematical statisticians have been in love withthe fact that the probability distribution of the sum of a very large number of verysmall ... time, within ±2σ 95 percent of the time, and within ±3σ 99.7 percent of the time. Extending this, one wouldexpect a measurement to be off by ±20σ only one time out of 2 × 1088.Weallknow 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 parametersgiven...
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Tài liệu Modeling of Data part 3 docx
... problem of fitting a set of N data points (xi,yi)toa straight-line modely(x)=y(x;a, b)=a+bx (15.2.1)666Chapter 15. Modeling of DataSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... variance of the linear combination yi− a − bxi of two randomvariables xiand yi,Var( yi− a − bxi)=Var( yi)+b2Var( xi)=σ2yi+b2σ2xi≡1/wi(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 unknownak. Various of the procedures described subsequently in this chapter derive from(15.1.7) and...
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Tài liệu Modeling of Data part 4 pptx
... float *xx,*yy,*sx,*sy,*ww,aa,offs;float chixy(float bang)Captive function of fitexy, returns the value of (χ2−offs) for the slopeb=tan(bang).Scaled data andoffsare communicated via the ... variance of the linear combination yi− a − bxi of two randomvariables xiand yi,Var(yi− a − bxi)=Var(yi)+b2Var(xi)=σ2yi+b2σ2xi≡1/wi(15.3.3)The sum of the square of N ... of varying b, successful numerical root-findingleads to a value of ∆a that minimizes χ2for the value of ∆b that gives ∆χ2=1.This(seeFigure 15.3.1) directly gives the tangent projection of...
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Tài liệu Modeling of Data part 5 doc
... combinations of the columns of V, with coefficients obtained by forming dot products of the columns672Chapter 15. Modeling of DataSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... certain mathematical irony in the fact that least-squaresproblems 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 EquationsThe minimum of (15.4.3) occurs...
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Tài liệu Modeling Of Data part 6 pdf
... andalamdade-creases by a factor of 10. If a step failsalamdagrows by a factor of 10. You must call this684Chapter 15. Modeling of DataSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... even when they must be offered without proof.Figure 15.6.1 shows the conceptual scheme of an experiment that “measures”a set of parameters. There is some underlying true set of parameters atruethat ... name of the game is to find some way of estimating or approximatingthe probability distributionof a(i)−atruewithout knowing atrueand withouthavingavailable to us an infinite universe of hypothetical...
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Tài liệu Modeling Of Data part 7 pptx
... even when they must be offered without proof.Figure 15.6.1 shows the conceptual scheme of an experiment that “measures”a set of parameters. There is some underlying true set of parameters atruethat ... name of the game is to find some way of estimating or approximatingthe probability distributionof a(i)−atruewithout knowing atrueand withouthavingavailable to us an infinite universe of hypothetical ... techniques, and seek to minimize the uncertainty of the result accordingto any desired criteria. Offered the choice between mastery of a five-foot shelf of analytical statistics books and middling...
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Tài liệu Modeling Of Data part 8 pptx
... formaldefinition.Someotherkindsof robusttechniques, coming from the fields ofoptimalcontroland filtering rather than fromthe field of mathematical statistics, are mentioned at theend of this section. Some ... on the following fact: The median cM of a set of numbers ciis also that value which minimizes the sum of the absolute deviationsi|ci− cM|(Proof: Differentiate the above expression ... example, the equality orinequality of two distributions can be estimated by the Wilcoxon test of computingthe mean rank of one distribution in a combined sample of both distributions.The Kolmogorov-Smirnov...
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