How to check if two samples come from the same population?
Test of whole distribution for two samples
How to prove that a left-invariant metric on a Lie group is smooth? How does delete[] "know" the size of the operand array? Foo* set = new Foo[100]; // ... delete [] set;   You don't pass the array's boundaries to delete[]. But where is that information stored? Is it standardised? If a factor variable (e.g. gender with levels M and F) is used in the glm formula, dummy variable(s) are created, and can be found in the glm model summary along with their associated coefficients (e.g. genderM)  If, instead of relying on R to split up the factor in this way, the factor is encoded in a series of numeric 0/1 variables (e.g. genderM (1 for M, 0 for F), genderF (1 for F, 0 for M) and these variables are then used as numeric variables in the glm formula, would the coefficient result be any different?  Basically the question is: does R use a different coefficient calculation when working with factor variables versus numeric variables?  Follow-up question (possibly answered by the above): besides just the efficiency of letting R create dummy variables, is there any problem with re-coding factors as a series of numeric 0,1 variables and using those in the model instead? If a function has a finite limit at infinity, does that imply its derivative goes to zero? I've been thinking about this problem: Let $f: (a, +\infty) \to \mathbb{R}$ be a differentiable function such that $\lim\limits_{x \to +\infty} f(x) = L &lt; \infty$. Then must it be the case that $\lim\limits_{x\to +\infty}f'(x) = 0$?  It looks like it's true, but I haven't managed to work out a proof. I came up with this, but it's pretty sketchy:  $$ \begin{align} \lim_{x \to +\infty} f'(x) &amp;= \lim_{x \to +\infty} \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \lim_{x \to +\infty} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \frac1{h} \lim_{x \to +\infty}[f(x+h)-f(x)] \\ &amp;= \lim_{h \to 0} \frac1{h}(L-L) \\ &amp;= \lim_{h \to 0} \frac{0}{h} \\ &amp;= 0 \end{align} $$  In particular, I don't think I can swap the order of the limits just like that. Is this correct, and if it isn't, how can we prove the statement? I know there is  already, but I think this is different in two aspects. First, that question assumes that $\lim\limits_{x \to +\infty}f'(x)$ exists, which I don't. Second, I also wanted to know if interchanging limits is a valid operation in this case. I replaced a buggy Windows Vista installation with Ubuntu. All works fine except that the main HD where I had all my files are now inaccessible. Here is the error message I get:   Error mounting: mount exited with exit code 13: ntfs_attr_pread_i: ntfs_pread failed: Input/output error Failed to read NTFS $Bitmap: Input/output error NTFS is either inconsistent, or there is a hardware fault, or it's a SoftRAID/FakeRAID hardware. In the first case run chkdsk /f on Windows then reboot into Windows twice. The usage of the /f parameter is very important! If the device is a SoftRAID/FakeRAID then first activate it and mount a different device under the /dev/mapper/ directory, (e.g. /dev/mapper/nvidia_eahaabcc1). Please see the 'dmraid' documentation for more details   Is it necessarily a hardware problem? If not, is there a way to repair the HD from Ubuntu? What invisible flicker do different types of light bulbs have? What waveform does the light coming off different types of artificial light sources have and (of course) what are the underlying physical reason for them?    I was inspired to ask this question because of several things I have been hearing lately.  Firstly, there was a recent TED talk about how .  Researchers have been working on the problem for a little while now and they've made a fairly impressive product, but it was only recently made possible by the LED technology, which has such a fast response that it can easily compare to the transfer rates of electric information condiuits that we normally use.  My understanding is that incandescent bulbs flicker because they have 60 Hz AC power being pulsed through them.  In fact, I think 60 Hz was chosen in the first place because it was a threshold that was unnoticeable to humans.  Looking at a  demonstrates that it has a very significant lag time responding to both the normal electrical phasor and being turned off.  In other words, it flickers but it doesn't go dark at any point in the AC waveform.  Looking for more information, however, I was a little disappointed, since nothing seemed to give a graph of lumens emitted over time for all different kinds of bulbs.  Of course, there isn't just one relevant time scale.  A light could flicker with 60 Hz and also flicker with 2000 Hz (I just made that up).  I'm interested in the complete picture of what lights exhibit what patterns. Apex:OutputText to Currency Format from String Wrapper is there a way to pass a string to the &lt;apex:outputText&gt; so that it can be formatted as a currency or percent value?  Here's what I have inside a column of my visual force table:  &lt;apex:outputText value="{0, number, currecny}"&gt; &lt;apex:param value="{!row.values[1]}" /&gt; &lt;/apex:outputText   this gives me an error at runtime (when the visual force page loads), which I think may be some kind of type mismatch, where &lt;apex:outputText&gt; is expecting a Decimal or number but I am passing a string.  This is the error at runtime:     The value attribute on  is not in a valid format. It must be a positive number, and of type Number, Date, Time, or Choice.   Thanks Converting Older United States Dollar Bills I received from my Dad 150 American Dollars about 12 years ago. I never have thought to change this money but a few days I tried change it in a currency exchange in Sydney and the guy didn't change it because the series are old.     What do I have to do to change this money? How to use Whatsapp mobile application on Ubuntu Touch? In my Android I have "Whatsapp" application running. But mobile freak I am not, and specially the mobile keyboards.  So how can I run my same application, same account from my Ubuntu desktop PC?   Follow up:  Just to do keyboard routing, i have used . Which allows me to takeover the Android input fields access via web link to type in my PC keyboard, and then it re-route the keys to Mobile.  Features:   Allows me to copy and paste large texts to Android input fields without using the keyboard of Android but simply using my Desktop PC, via web link http://android.ip.address.goes.here:port/ Allows me to have key submit which is similar to key press of mobile set itself   At-least works without having mobile in rooted. Hope it helps you!! How can number of subdirectories and files be determined from the output of using ls -ld command?  I realize that this command only lists the directories. How do I add new wallpapers? I have Ubuntu 11.10 installed and want to download and install additional wallpapers on my desktop.   How do I do this? I'm building a Core  system which supports dual-channel memory (up to 16&nbsp;GB in four DIMMs), my target is 8&nbsp;GB. From the performance perspective, is it better to have two times 4&nbsp;GB or four times 2&nbsp;GB? Can Windows Virtual PC run a 64-bit OS? Selecting all objects that have been specified in Modifiers Could anyone help in making a script for selecting all objects that are specified in the different modifiers that an object has stacked? For example if my object has a Boolean modifier and an Array modifier, which both refer to an empty or another object (in the Array modifier there is for example an Object offset you can specify). Would it be possible to select all those object with one click? Thanks. How do I use the chrome driver in Ubuntu 16.04? PostgreSQL check bloating of a table I am a mathematics student with a hobby interest in physics. This means that I've taken graduate courses in quantum dynamics and general relativity without the bulk of undergraduate physics courses and sheer volume of education into the physical tools and mindset that the other students who took the course had, like Noether's theorem, Lagrangian and Hamiltonian mechanics, statistical methods, and so on.  The courses themselves went well enough. My mathematical experience more or less made up for a lacking physical understanding. However, I still haven't found an elementary explanation of gauge invariance (if there is such a thing). I am aware of some examples, like how the magnetic potential is unique only up to a (time-)constant gradient. I also came across it in linearised general relativity, where there are several different perturbations to the spacetime metric that give the same observable dynamics.  However, to really understand what's going on, I like to have simpler examples. Unfortunately, I haven't been able to find any. I guess, since "gauge invariance" is such a frightening phrase, no one use that word when writing to a high school student.  So, my (very simple) question is: In many high school physics calculations, you measure or calculate time, distance, potential energy, temperature, and other quantities. These calculations very often depend only on the difference between two values, not the concrete values themselves. You are therefore free to choose a zero to your liking. Is this an example of gauge invariance in the same sense as the graduate examples above? Or are these two different concepts? Where did the brush size lock go for sculpt mode in 2.8??? ConcurrentModificationException Woes How to buy plane tickets for job interviews? I am currently on the academic job market, and scheduling on-campus interviews with institutions that might want to hire me.  Suppose I am invited to an on-campus interview at the University of X, and must travel there by air.  They handle travel on a reimbursement basis: I buy the plane ticket, and then they reimburse me.  However, the interview is a few weeks away.  Since the job market sometimes moves fast, there is a chance that by the time of the scheduled interview, I may have already accepted another offer (say from the University of Y).  Of course I should then decline the interview at X, but I would have already bought the plane ticket.  How should I plan for this contingency?   I could buy a refundable ticket to X.  However, these are normally several times the price of a non-refundable ticket, and if I do end up traveling to X, they might balk at reimbursing me for such an expensive fare. I could buy a non-refundable ticket to X.  If I end up not going there, I could ask X to reimburse me for the cost of the ticket (or at least the "change fee" charged by the airline to let me use the ticket's value for a future flight).  However, I suspect they will be reluctant to reimburse me for a trip I'm not making, and might refuse to do so altogether, in which case I am out-of-pocket. I could wait until the last minute to buy a non-refundable ticket for X.  But it may still be expensive for them (or may exceed their limits), and the most convenient flights may be sold out. I could contact University of X and ask them for guidance.  I'm a bit hesitant to do this, as I am afraid that if I bring up the possibility that I might accept another position, they might think I am not seriously interested in theirs.   Is there a standard way to handle this situation?  This is in the United States, if it matters.