How can I get these two pgfplots to be exactly aligned?
Alignment of axis in tikz
Image capture opens after iPhone is connected Everytime I connect my iPhone to my laptop, Image Capture opens. How to I stop it? I just need to use iTunes, not Image Capture. Is it safe to use a voltage divider for Arduino and DC motor controller? When saving a .qgs file in QGIS, another appears. Is this a backup? When saving a project file (.qgs), which when executed is automatically loaded with qgis.bat, there's another .qgs file which appears in the same directory of the original project file, although this one is not loaded with the qgis.bat file:    This is just out of curiosity but is the latter designed to be a backup of the original .qgs file? Practice problem for exam:     Let ${A_n}$ satisfy $\sum\limits_{n=1}^\infty P(A_n \cap A^c_{n+1}) &lt; \infty$ and $\lim\limits_{n\to \infty} P(A_n) = 0$.  Show that $P(\lim \sup A_n) = 0$.    I can see that it is sufficient to show that $P\left(\sum\limits_{n=1}^\infty A_n\right) &lt; \infty$ and then apply the Borel-Cantelli lemma, but I am having trouble showing this from the information given.  I see an almost identical problem here: , however the hint there is not enough for me to make headway, and this problem is also different in which term gets the complement inside the first sum. I would like to know what is the preferred way to indicate that I took a degree in some subject while also naming the place where I obtained the degree from:   I got my master's degree from the University of Somewhere; I got my master's degree in the University of Somewhere; I took my master's degree in the University of Somewhere.   I would say that "in" is more suitable to mention the particular subject (a degree in maths, for instance) than to indicate the place, but I still have doubts.  By the way, is it a "master's degree" or a "Master's degree"? How to cleanly launch a GUI app via the Terminal? How does QGIS Zonal Statistics handle partially overlapping pixels? There are a couple Stackexchange posts asking this question, but neither of them were sufficiently answered:       I am writing Python scripts that perform essentially the same operations as Zonal Stats, and I have been using Zonal Stats to check my scripts' outputs.   I have noticed that when there are many cells in the polygon being queried, my results match perfectly, but there are discrepancies when there are only a few raster cells in the polygon. The following is an example of this. I am computing "count" for each polygon.  Exhibit 1:   The returned count is 0.45, which looks roughly correct if pixels can be treated fractionally rather than simply in/out.  Exhibit 2:   Similar result; count is 0.39.  Exhibit 3:    With a larger poylgon, now we see the count is exactly 2. Note that there are exactly 2 pixel centers contained in the polygon.  Exhibit 4:    Here, only one pixel center is within the polygon. The count is 1.008, though. If you exclude the polygon area from the pixel whose center is in the polygon, the remaining area is obviously greater than 0.008 of a pixel.   From these exhibits, it seems that Zonal Statistics treats these cases specially. It looks like to me that if there are less than 2 pixel centers within the polygon, it performs some kind of averaging such as polygon_area/raster_cell_area to return the count. I should note that I have 48 of these polygons, and all returned counts greater than or equal to 2 are integers; fractional counts are only returned for &lt;2.  How are these fractional-pixel counts incorporated into the other statistics output by Zonal Stats?    indicates strange behavior with max/min when using large raster cells, and my own testing returns mean values not congruous with simple "pixel center in/out of the polygon." To reiterate, I get exact agreement when the underlying raster contains many pixels within the polygon. I couldn't find any documentation about this, and it may be important when people have never had problems with Zonal Stats but use a coarse raster and remain unaware that there is a different behavior when there are only a few pixels within the polygon. Correct way to use include and includeonly when writing a large document like a thesis How to derive the ridge regression solution? I am having some issues with the derivation of the solution for ridge regression.  I know the regression solution without the regularization term:  $$\beta = (X^TX)^{-1}X^Ty.$$  But after adding the L2 term $\lambda\|\beta\|_2^2$ to the cost function, how come the solution becomes   $$\beta = (X^TX + \lambda I)^{-1}X^Ty.$$ How do I change the screen resolution using Ubuntu command line? I installed Ubuntu and the resolution of the desktop is so big that it only shows about 50% of the screen, but is shows up normal while using command line.   What should I type in the command line to change the desktop screen resolution? How does this JavaScript/jQuery syntax work: (function( window, undefined ) { })(window)? math behind complex numbers C||RLC I have a mathematical problem with the following formula. The goal is to transform this equation to have a seperated real and imaginary part. I have already done this with several other equasions, but for this particualar one I don't know where to start.  I dont expect you to do the complete work of transforming for me, it would already be very nice if you could give me a hind on how you would start.  Thank you in advance!  C||RLC      This is my current progress:    My question is:  How can I get rid of the imaginary part jωC2*R?  When the denominator is completely real I can just split up the formula and have an imaginary and a real part. Why does the set of all singleton sets not exist? My professor proved that the kernel is a normal subgroup under a homomorphism f by saying. Let $h\in H$  by applying f to it  $f(ghg^{-1})=f(g)f(h)f(g)^{-1}=e $  My question is how is this a proof that the kernel is normal. What is the reason we apply f to it ? By applying f dont we just prove that $f(ghg^{-1})$ is normal ? NVMe PCIe x4 SSD on M.2 PCIe x2 slot? i'm about to get a new SSD for my PC, and before spending the money i have some doubts about my decision i would like to clarify First, my mobo is a B450 Aorus Pro Wifi, it has 2 M.2 slots, one of them full length (22110) compatible with PCIe 3.0 x4 and the other one standard length (2280) and support only for PCIe 3.0 x2 About the drive, i'm aiming for a 1tb XPG SX8200 Pro , which is a PCIe 3.0x4 SSD My first M.2 slot is already taken by the main SSD, which i use for the OS and other stuff, i can't really use it. Will a PCIe x4 SSD work on a PCIe x2 slot? How much performance will be lost if it does? Will it be worth it? Determining best fitting curve fitting function out of linear, exponential, and logarithmic functions Context:  From a question on Mathematics Stack Exchange , someone has a set of $x-y$ points, and wants to fit a curve to it, linear, exponential or logarithmic.  The usual method is to start by choosing one of these (which specifies the model), and then do the statistical calculations.  But what is really wanted is to find the 'best' curve out of linear, exponential or logarithmic.  Ostensibly, one could try all three, and choose the best fitted curve of the three according to the best correlation coefficient.  But somehow I'm feeling this is not quite kosher. The generally accepted method is to pick your model first, one of those three (or some other link function), then from the data calculate the coefficients. And post facto picking the best of all is cherry picking. But to me whether you're determining a function or coefficients from the data it is still the same thing, your procedure is discovering the best...thing (let's say that which function  is -also- another coefficient o be discovered).  Questions:   Is it appropriate to choose the best fitting model out of linear, exponential, and logarithmic models, based on a comparison of fit statistics? If so, what is the most appropriate way to do this? If regression helps find parameters (coefficients) in a function, why can't there be a discrete parameter to choose which of three curve families the best would come from? Should I get the +2 bonus twice for suggesting a tag wiki? Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain I want to show that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw)\subset\mathbb{A}^4$, is not a unique factorization domain.    Morally, all we need to do is find some nonzero element that can be written in two distinct ways as a product of irreducible elements, but nothing is coming to mind immediately. Thoughts? Select organic group on the user registration form There's a post already on the post installation forum, but I'm not sure if this is a OG bug.   I am using Drupal 7 and OG 7.x-2.1 version. There is no "Group Audience" in the manage fields page and I think it is replaced with "Group membership", the field type is "Entity Reference" and the widget is "OG Reference". Also there is no input type in the field setting page and I can not find any field that has a "Always show other groups" option. I have checked the option "Show on registration form of that field, but the combo box on the registration form does not have any option. Any suggestion? How to install mysql?