What is this white circle on this circuit?
What kind of components are black blobs on a PCB?
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$ Problem:   If $f(x)$ is continous at $x=0$, and $\lim\limits_{x\to 0} \dfrac{f(ax)-f(x)}{x}=b$, $a, b$ are constants and $|a|&gt;1$, prove that $f'(0)$ exists and $f'(0)=\dfrac{b}{a-1}$.   This approach is definitely wrong:    \begin{align} b&amp;=\lim_{x\to 0} \frac{f(ax)-f(x)}{x}\\ &amp;=\lim_{x\to 0} \frac{f(ax)-f(0)-(f(x)-f(0))}{x}\\ &amp;=af'(0)-f'(0)\\ &amp;=(a-1)f'(0) \end{align}  I will show you a case why this approach is wrong:     \[f(x)= \begin{cases} 1,&amp;x\neq0\\ 0,&amp;x=0 \end{cases}\]   $\lim_{x\to0}\dfrac{f(3x)-f(x)}{x}=\lim_{x\to0} \dfrac{1-1}{x}=0$   but $\lim_{x\to0}\dfrac{f(3x)}{x}=\infty$,$\lim_{x\to0}\dfrac{f(x)}{x}=\infty$   Does anyone know how to prove it? Thanks in advance! What exactly did mv /tmp/folder/* /* do to my filesystem? It's hard to search for special characters on google, which is why I'm posting this here.  I recently ran (as root) a mv /tmp/folder/* /* when I meant to run mv /tmp/folder/* ./ Big mistake!  Things broke! A lot of files got mixed up and placed into strange places, none of the normal unix commands worked (ls, dir, cat, etc) and once you logged off, you couldn't ssh back in -- it would give you a prompt, but not accept the old passwords.  Running ls /* shows me that it performs ls on every directory in /. If I tried to draw a parallel, then mv should have simply moved (or copied?) the files to every directory in /. Instead, really weird things happened, and I was just curious what exactly was going on.  More info: The files in /tmp/folder had been transferred from a windows machine, and had been named file (#).txt, where (#) is a number up to two digits, with a space between file and the parenthesis. There were ~40 of these text files. points out that certain key and block lengths were a requirement for the AES submissions:     The candidate algorithm shall be capable of supporting key-block combinations with sizes of 128-128, 192-128, and 256-128 bits.   My question is this; how can having a key length that is greater than the block size enhance security?  If we look at ECB mode for simplicity, when the key length is equal to the block length we have a permutation relationship between the set of all plaintexts and the set of all ciphertexts.  Once you increase the key length beyond that, you start to introduce collisions. In fact, you only introduce collisions from then on don't you? Collisions in the sense that a key will create the same ciphertext-plantext relationship as another key.  This would lead me to believe that only part of the key-space is unique, and only that part of key-space needs to be brute-forced?  I know that I am clearly incorrect, I just don't understand why. Space which is connected but not path-connected How to completely remove desktop? I wanted to switch to Xfce (I had KDE and GNOME installed), and I did this :    sudo apt-get install xubuntu-desktop sudo apt-get remove kubuntu-desktop sudo apt-get remove ubuntu-desktop sudo apt-get autoremove   but to my surprise, I could still pick gnome, kde plasma, etc during the log in.  So, how do I completely remove KDE and GNOME desktops? I have a SRD-12VDC-SL-C relay with this configuration:  And I want to trigger it with PIR Motion Sensor Detector Module HC-SR501  The problem with direct connection to PIR is, when I connect PIR with 12v DC the Relay remains always ON, i.e. trigger from PIR does not switch it off. And when I connect it via 5V supply the Relay remains always OFF. The trigger output of PIR is 3.3V how can I rectify this problem? by adding some resistor/FETs, or something else. Edit: The voltage at Relay-In(Green) is 10.5V and the relay is OFF it need to go below 9V in order to switch the Relay ON. When I connect it to PIR trigger it goes down to 2.7V (Thus Switching ON the relay, below 9V). And when the PIR trigger of 3.3V comes it goes up to 7.2V but because it is still below 9V) Relay does not switch. Can we have cross-site badges? My public website name and AD domain name are the same. How can I get to my external website from inside my network? In English, words with a 'g' followed by a front vowel (e, i, y) can be pronounced with a soft g or a hard g:   Words with Germanic roots are usually pronounced with a hard g: gear, get, gift, give Words with Latin and Greek roots are usually pronounced with a soft g: gem, general, giraffe, giant   But how should a purely English word (if such thing even exists) with a 'g' followed by a front vowel be pronounced? In other words, if an English speaker saw a new word of unknown origin (eg: a neologism) that starts with gi- or ge-, how would they pronounce it? Is it better to difference a series (assuming it needs it) before using an Arima OR better to use the d parameter within Arima?  I was surprised how different the fitted values are depending on which route is taken with the same model and data. Or am I doing something incorrectly?  install.packages("forecast") library(forecast)  wineindT&lt;-window(wineind, start=c(1987,1), end=c(1994,8)) wineindT_diff &lt;-diff(wineindT)  #coefficients and other measures are similar modA&lt;-Arima(wineindT,order=c(1,1,0)) summary(modA) modB&lt;-Arima(wineindT_diff,order=c(1,0,0)) summary(modB)  #fitted values from modA A&lt;-forecast.Arima(modA,1)$fitted  #fitted from modB, setting initial value to the first value in the original series B&lt;-diffinv(forecast.Arima(modB,1)$fitted,xi=wineindT[1])   plot(A, col="red") lines(B, col="blue")   ADD:  Please note I am differencing the series once and fitting arima (1,0,0) then I am fitting arima (1,1,0) to the original series. I am (I think) reversing the differencing on the fitted values for the arima(1,0,0) on the differenced file.   I am comparing the fitted values - not the predictions.  Here is the plot (red is arima(1,1,0) and blue is the arima (1,0,0) on the differenced series after changing back to the original scale)  :    Response to Dr. Hyndman's Answer:  1) Can you illustrate in R code what I would need to do in order to get the two fitted values (and presumably forecasts) to match (allowing for small difference due to your first point in your answer) between Arima (1,1,0) and Arima(1,0,0) on the manually differenced series? I assume this has to do with the mean not being included in modA, but I am not entirely sure how to proceed.  2) Regarding your #3. I know I am missing the obvious, but are not $\hat{X}_t = X_{t-1} + \phi(X_{t-1}-X_{t-2}) $ and $\hat{Y}_t = \phi (X_{t-1}-X_{t-2})$ the same when $\hat{Y}_t$ is defined as $\hat{X}_t - X_{t-1}$? Are you saying I am "undifferencing" incorrectly? Minor "you have already raised this type of flag" bug? I flagged something as spam, then was only 90% sure I'd done so, so I clicked the flag link again to check. It showed me this:    I had, of course, only raised the spam flag, not the offensive/abusive/hate flag, so the latter probably shouldn't be saying I did.    Ah, this may be a duplicate, I didn't search enough:        And if so, it's been around a while. Mask and inherit the same systemd unit Suppose a package provides whatever.service file so certain events (including whatever.socket) cause a daemon to start with a certain configuration.  I want to disable this completely. In particular, I want the old socket and any other unit files that might refer to this service by name to be unable to start the daemon.  Instead, I want to create my own unit files for this daemon with a different .socket unit and different environment variables. I also want my override to automatically take account of possible upstream updates to the original unit file (which my current solution of copying whatever.service as whatever-modified.service and editing it unfortunately does not provide).  If I create the following symlinks and files: /etc/systemd/system/whatever.service → /dev/null /etc/systemd/system/whatever-modified.service → /usr/lib/systemd/system/whatever.service /etc/systemd/system/whatever-modified.service.d/fix.conf  systemd considers the new service to be masked as well and refuses to start it. How to avoid this? Checkout subdirectories in Git? Is it possible to check out subdirectories of a repository in Git?  Imagine I am setting up a new WordPress installation. I will create two new directories for my plugin and theme customization:   wordpress/wp-content/plugins/myplugins/  wordpress/wp-content/themes/mytheme/   I want to maintain these directories via Git. In Subversion, I would accomplish this by having trunk/myplugins/ and trunk/mytheme/ directories and checking out subdirectories. Does Git have a way to accomplish the same task using a single repository?  I could just be missing the boat on some Git paradigm, as a long time SVN user with little exposure to Git.  Edit:  storing different content is an interesting way to handle this. Blender is rendering an older version my project Placing null at the end of the List Mouse rotated 90 degrees I don't understand philosophy very well, and so I am wondering whether you can "prove" anything in philosophy. It always seems you can go a layer down, and find another question, almost endlessly until you get to the question of "why/how/are we here?"  Can you prove, absolutely, and 100% that something is true, in the field of philosophy? My question is from Apostol's Vol. 1 One-variable calculus with introduction to linear algebra textbook.  Page 57. Exercise 12. Show that the following are polynomials by converting them to the form $\sum_{k=0}^{m}a_kx^k$ for a suitable $m$. In each case $n$ is a positive integer. $a)$ $(1+x)^{2n}.$ $b)$ $\frac{1-x^{n+1}}{1-x}, x\not=1.$ $c)$ $\prod_{k=0}^{n}(1+x^{2^k}).$  The attempt at a solution: a) part of the problem is pretty easy I guess, it is example of binomial theorem, so the answer would be $(1+x)^{2n}=\sum_{k=0}^{2n}(^{2n}_{k})x^k.$ Answer to part b) would be the following: $$\frac{1-x^{n+1}}{1-x}=\frac{(1-x)(1+x+x^2+\cdots+x^n)}{1-x}=1+x+x^2+\cdots+x^n=‌​\sum_{k=0}^{n}x^k.$$thanks to @DiegoMath's hint. As for part c), we have $$\prod_{k=0}^{n}(1+x^{2^k})=(1+x)(1+x^2)(1+x^4)(1+x^8)\cdots(1+x^{2^n})$$ and I have trouble &quot;converting&quot; this to sum which would be of a form of polynomial. Get specific GPS location somehow on windows 8 Setting "checked" for a checkbox with jQuery I'd like to do something like this to tick a checkbox using jQuery:  $(".myCheckBox").checked(true);   or  $(".myCheckBox").selected(true);   Does such a thing exist?