12.2.1 Top new questions this week

12.2.1.1 Two data sets one is displaced. How to find displacement and combine data?
12.2.1.2 Confidence interval issue of NonlinearModelFit in v14.3.0.0
12.2.1.3 How to obtain a given result for this definite integral $\int_0^\infty \frac dx  x^4+a x^2+b^2 $
12.2.1.4 FDM code to simulate 3D convection flow with electromagnetic force
12.2.1.5 Solving an equation containing a convolution integral
12.2.1.6 How to extract the image part from a PDF page?
12.2.1.7 3D plot of squares in a region
12.2.1.1 Two data sets one is displaced. How to find displacement and combine data?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=318414

Edit 
This question has received much attention and has many good responses. I have accepted one but would like to accept several. I think there is enough for this to be a starting point for answering ... 
[mathematical-optimization] [data]
 
asked by Hugh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=12558 Score of 11
answered by ydd https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=72953 Score of 12
12.2.1.2 Confidence interval issue of NonlinearModelFit in v14.3.0.0

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=318398

I am trying to obtain the confidence range of the parameter of a fit. According to the documentation of the  NonlinearModelFit , it should be the model property "... 
[fitting]
 
asked by Eisbär https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=32508 Score of 8
answered by David Keith https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=44700 Score of 2
12.2.1.3 How to obtain a given result for this definite integral $\int_0^\infty \frac dx  x^4+a x^2+b^2 $

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=318399

This youtube video  shows this result 
 
But I am not sure if assumption mentioned in this video are correct. Video says only $b>0$ is needed. 
Maple gives same answer under assumption given by ... 
[calculus-and-analysis]
 
asked by Nasser https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=70 Score of 6
answered by yarchik https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9469 Score of 11
12.2.1.4 FDM code to simulate 3D convection flow with electromagnetic force

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=318391

Happy New Year! 
In our paper Numerical simulation and nonlinear dynamics in rotating magnetoconvection: Chaos, Attractors, and Stability Transitions we used code described below to simulate 3D ... 
[finite-difference-method] [fluid-dynamics] [electromagnetics] [3d] [convection]
 
asked by Alex Trounev https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=58388 Score of 6
12.2.1.5 Solving an equation containing a convolution integral

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=318418

Context 
In the context of the so-called direct-interaction approximation (DIA)$^\color{magenta}{\dagger}$ solution to the stochastic Kubo oscillator I am interested in solving the following equation 
$$... 
[differential-equations] [numerics] [convolution]
 
asked by chris https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1089 Score of 5
answered by Mariusz Iwaniuk https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=26828 Score of 7
12.2.1.6 How to extract the image part from a PDF page?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=318390

This PDF page is a Graphics filled with text, but I only want the part with the illustrations, so I wrote a PlotRange to control the drawing area, but there are many white borders on the top, bottom, ... 
[graphics] [pdf-format]
 
asked by yode https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=21532 Score of 5
answered by azerbajdzan https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=53172 Score of 3
12.2.1.7 3D plot of squares in a region

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=318397

I'm trying to plot a set of squares on a region defined in the $xy$ plane as $x^2y8-x^2$, and I managed to do this (the code below might not be optimal): 
... 
[plotting] [regions] [syntax]
 
asked by mf67 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=55498 Score of 4
answered by yarchik https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9469 Score of 3