Tài liệu Modeling of failure mechanisms for optimized mems cad pptx

Ngày tải lên: 25/01/2014, 13:20

... CRC Press LLC base for a topology A collection B of open sets of a topological space T is a base for the topology of T if each open set of T is the union of some members of B. base space Let ... for the rate of reaction of a particu- lar reaction in terms of concentrations of chem- ical species and constant parameters (normally rate coefficients and partial orders o...

Ngày tải lên: 10/12/2013, 12:15

... satisfy; examples are coefficients of rate equations in a complex network of chemical reactions, or orbital elements of a binary star. Modeling can also be used as a kind of constrained interpolation, ... email to trade@cup.cam.ac.uk (outside North America). Chapter 15. Modeling of Data 15.0 Introduction Given a set of observations, one often wants to condense and summarize the...

Ngày tải lên: 15/12/2013, 04:15

... that the standard deviations σ of these normal distributionsare the same for all points. Then the probability of the data set is the product of the probabilities of each point, P ∝ N  i=1  exp  − 1 2  y i − ... 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...

Ngày tải lên: 15/12/2013, 04:15

... considerations of the previous section more meaningful. We consider the 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) 662 Chapter 15. Modeling of ... bit of uncertainty to the parameters. Consideration of propagation of errors shows that the variance σ 2 f in the value of any function will be σ 2 f = N  i=1 σ 2 i ...

Ngày tải lên: 15/12/2013, 04:15

... 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 ... 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 p...

Ngày tải lên: 15/12/2013, 04:15

... generalization of §15.2 is to fit a set of data points (x i ,y i )to a model that is not just a linear combination of 1 and x (namely a + bx), but rather a linear combination of any M specified functions of ... build up information about the Hessian matrix. Sections 10.7 and 10.6 concerned themselves with two different techniques for buildingup this information. 672 Chapter 15. Mod...

Ngày tải lên: 15/12/2013, 04:15

... build up information about the Hessian matrix. Sections 10.7 and 10.6 concerned themselves with two different techniques for buildingup this information. 682 Chapter 15. Modeling of Data Sample ... The only reason to use (15.5.3) will be failure of (15.5.2) to improve the fit, signaling failure of (15.5.1) as a good local approximation. Calculation of the Gradient and Hessian T...

Ngày tải lên: 15/12/2013, 04:15

... one for your desired confidence level • to give the covariance matrix C ij as the “formal covariance matrix of the fit.” You are not allowed • to use formulas that we now give for the case of normal ... percent of the time (1-σ for the normal distribution), ∆χ 2 ν < 4 occurs 95.4 percent of the time (2-σ for the normal distribution), ∆χ 2 ν < 9 occurs 99.73 percent of th...

Ngày tải lên: 15/12/2013, 04:15

... guesses for a and b. Notice that the evaluation of the right-hand side of (15.7.16) occurs in the function rofunc, with communication via global (top-level) variables. 704 Chapter 15. Modeling of ... always by formal definition. Someotherkindsof robusttechniques, coming from the fields ofoptimalcontrol and filtering rather than fromthe field of mathematical statistics, are mentioned a...

Ngày tải lên: 15/12/2013, 04:15