I think capillary action occurs because water molecules have a little magnetic field with poles so they can stack up on each other somewhat. When it happens though, where is the energy derived from to create this kinetic movement?
When I dip a paper towel in a cup of water the water gets drawn up due to . How is this reconciled with conservation of energy, as it would seem on the surface that the potential energy of the system has gone up with no work being done?
How to really clear the terminal? I can issue the clear command or press Ctrl + L to clear the current Ubuntu terminal, but this just shifts previous output upwards and if you use mouse scroll or PgUP and PgDown keys it's hard to distinguish where the output of previous command ends and output of current command begins.  Is there a way to really clear the terminal so I won't see previous command results? Wi-Fi not working on Lenovo ThinkPad E570 (Realtek RTL8821CE) We just bought a Lenovo  (which is supposed to have the Intel 8265 for wireless). This laptop was bought in part because it is certified to run Ubuntu and as such to me at least it would make sense for things to work out of the box... but no such luck.  First, I installed Ubuntu 17.10 and after installation realised Wi-Fi was not working. I also tried Ubuntu 16.04 from a USB drive since that is the version of Ubuntu it is certified for, but no luck there either.  The wireless chip is not detected by lshw (or even lspci by the looks of it), ip link does not show a wireless interface, and the iwlwifi kernel module is not loaded at boot (I can load this myself using modprobe iwlwifi but this does not make Wi-Fi work). I think it is a combined Wi-Fi/Bluetooth chip, and Bluetooth does appear to work (or at least Bluetooth shows up in Gnome and rfkill list).  modinfo iwlwifi | grep 8265 shows me a file ending in -34 is supposedly loaded but only a file ending in -33 (and some other lower numbers) is present in /lib/firmware, if that helps).  I have also installed the Linux 4.14.9 kernel in an attempt to get things to work, but this did not resolve the issue either.  Further information  root@ThinkPad-E570:~# modinfo iwlwifi | grep 8265 firmware:       iwlwifi-8265-34.ucode root@ThinkPad-E570:~# rfkill list all 0: tpacpi_bluetooth_sw: Bluetooth     Soft blocked: no     Hard blocked: no 1: hci0: Bluetooth     Soft blocked: no     Hard blocked: no root@ThinkPad-E570:~# dmesg | grep iwl root@ThinkPad-E570:~# lspci -nnk | grep 0280 -A3 05:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. Device [10ec:c821]     Subsystem: Lenovo Device [17aa:c024]   Update  I just noticed that the laptop does not have an Intel wireless chip at all, but in fact has a Realtek one... which means that the  of the shop I bought this laptop at were not accurate... Sigh. Same problem stands, however, just with a crappier wireless chip. Is there a way to spellcheck the word under the cursor with a keyboard shortcut? Bash script copy file to user's (wildcard) home dir What is the difference between an SLR and a DSLR? What are the differences between SLRs and DSLRs? (I know that DSLRs are Digital SLRs but are there any actual differences?)  Also, what are the advantages/disadvantages of both? Stack Overflow provides good tools in the question editor, like "Links" and "Styling".  Another thing that for me would be nice is a color selector. Although an HTML editor is available, a direct click on tool would be good, and users can select different colors, as for marking errors in their program with red, and more important data with blue. Solutions of $x^2 \equiv 1 \pmod N$ If a SHA256 hash with high entropy is then hashed with one made from low entropy, is the resulting hash higher/same/lower entropy? If one were to create a SHA256 hash using 256 coin flips converted to hex (which, as I understand it, is as "entro-phized" as one can capture in SHA256) then take that hash as a string, combine that with a hash of the word "cat" and hash the resulting 512 character string, would the resulting hash from that exercise be any less random than our "perfect" hash we began with?  My thinking is the final string would capture the same amount as the original randomness as what we started with because the "extra" entropy can not be captured and is lost. Is this the case and am I thinking about this correctly? Would hashing something with high entropy with something simpler ever cause a lower amount of randomness or does it only go up?  Thanks to anyone who can help explain this a little better. Is it a good practice to refer to countries, ships etc using the feminine form? While talking about ships and countries, is it a good practice to use the feminine form?  For example:  "Her economy" - while referring to a country's economy "Her flag (or deck etc)" - while referring to a ship  Is this practice common? Is it used today? How to learn commutative algebra? I want to learn commutative algebra from scratch. I was wondering, as you are experts in mathematics, what you think is the best way to learn commutative algebra? Is there any video course available for commutative algebra? Will there be some online course for commutative algebra on some website like Coursera, etc?  I know noncommutative algebra up to the Artin-Wedderburn Theorem. Also, I know group theory up to the Sylow theorems and Galois Theory. I also know some basic topology.  I'm new to this site so I don't know what tags I should add for this question. Please feel free to edit my question.  Edit 1: I want to learn commutative algebra for learning Algebraic Geometry. Replace \input{fileX} by the content of fileX automatically Suppose I have a document with multiple include or input statements  \input{fileA} \input{fileB}   etc.   Is there an easy way to generate a single .tex file where \input{fileA} is replaced by the actual content of fileA etc. without copying it manually? I'm using the gnome flashback session with metacity window manager, but I can't change to any metacity theme in any of the tweaking tools, as they're not even appearing in the lists. Is there anything I can do? What's the difference between using a 50mm f/1.8G and a 50mm f/1.8D with a Nikon D80? Recently, Nikon announced their , as revamp of the old 50mm f/1.8D. :     The main difference between this new   "nifty fifty" and the almost   decade-old ƒ1.8D is that it has an   autofocus motor inside. This means you   can use it with any current or recent   Nikon SLR. The older lens lacks this   motor and is instead driven by one in   the camera, which cheaper bodies don't   have.   I currently use a Nikon D80 (and I don't plan on changing that any time soon), and I've been considering getting such a lens. Is there any difference between the D and the G lenses when used on a D80? I believe that the D one works just as well, since D80's have internal autofocus motors - is that right?  Besides the autofocus motor aspect, is there any other big difference between them? Since the D is priced at around $120 and the G at $220, should I just get the D? How to get address of cell which calls a VBA Functions in a Excel sheet How to name an item using /give command in MCPE? I have got myself a dxf which is built with units in the wrong scale. How do I upscale that in QGIS?   Note it does open in QGIS, just in the wrong map units and location. Sturm-Liouville Questions In thinking about Sturm-Liouville theory a bit I see I have no actual idea what is going on.  The first issue I have is that my book began with the statement that given  $$L[y] = a(x)y'' + b(x)y' + c(x)y = f(x)$$  the problem $L[y] \ = \ f$ can be re-cast in the form $L[y] \ = \ \lambda y$.  Now it could be a typo on their part but I see no justification for the way you can just do that!  More importantly though is the motivation for Sturm-Liouville theory in the first place. The story as I know it is as follows:  Given a linear second order ode   $$F(x,y,y',y'') = L[y] = a(x)y'' + b(x)y' + c(x)y = f(x)$$  it is an exact equation if it is derivable from a differential equation of one order lower, i.e.  $$F(x,y,y',y'') = \frac{d}{dx}g(x,y,y').$$  The equation is exact iff  $$a''(x) - b'(x) + c(x) = 0. $$  If $F$ is not exact it can be made exact on multiplication by a suitable integrating factor $\alpha(x)$.  This equation is exact iff  $$(\alpha(x)a(x))'' - (\alpha(x)b(x))' + \alpha(x)c(x) = 0 $$  If you expand this out you get the Adjoint operator  $$L^*[\alpha(x)] \ = \ (\alpha(x)a(x))'' \ - \ (\alpha(x)b(x))' \ + \ \alpha(x)c(x) \ = 0 $$  If you expand $L^*$ you see that we can satisfy $L \ = \ L^*$ if $a'(x) \ = \ b(x)$ &amp; $a''(x) \ = \ b'(x)$ which then turns $L[y]$ into something of the form  $$L[y] \ = \ \frac{d}{dx}[a(x)y'] \ + \ c(x)y \ = \ f(x).$$  Thus we seek an integratiing factor $\alpha(x)$ so that we can satisfy this &amp; the condition this will hold is that $\alpha(x) \ = \ \frac{1}{a(x)}e^{\int\frac{b(x)}{a(x)}dx}$  Then we're dealing with:  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ \alpha(x)c(x)y \ = \ \alpha(x)f(x)$$  But again, by what my book said they magically re-cast this problem as  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ \alpha(x)c(x)y \ = \ \lambda \alpha(x) y(x)$$  Then calling  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ ( \alpha(x)c(x)y \ - \ \lambda \alpha(x) )y(x) \ = \ 0$$  a Sturm-Liouville problem.  My question is, how can I make sense of everything I wrote above? How can I clean it up &amp; interpret it, like at one stage I thought we were turning our 2nd order ode into something so that it reduces to the derivative of a first order ode so we can easily find first integrals then the next moment we're pulling out eigenvalues &amp; finding full solutions - what's going on? I want to be able to look at $a(x)y'' \ + \ b(x)y' \ + \ c(x)y \ = \ f(x)$ &amp; know how &amp; why we're turning this into a Sturm-Liouville problem in a way that makes sense of exactness &amp; integrating factors, thanks for reading! How to justify the definition of summation $s_n=\sum_{i=1}^n a_i=a_1+\cdots+a_n$? I read  and found that they define summation via recursion, so I decided to formalize the proof that that this definition is actually valid. I've two questions:   Does my proof contain any error? Are there other simple ways to define summation?   Thank you so much!     Suppose that $(a_1,\cdots,a_n)$ is a finite sequence in $\mathbb N$. Show that there is a sequence $(s_1,\cdots,s_n)$ such that $s_1=a_1$ and $s_{i+1}=s_i+a_{i+1}$ for all $1\leq i&lt;n$.   My attempt:  We define mapping $f$ as follows: $f: \mathbb N\times\mathbb N\to\mathbb N\times\mathbb N: (i,a)\mapsto\begin{cases} (i+1,a+a_{i+1})&amp;\text{if }i&lt;n\\ (i+1,a)&amp;\text{if }i\geq n \end{cases}$  By recursion theorem, there is a unique sequence $(p_i\mid i\in\mathbb N)$ such that $p_0=(1,a_1)$ and $p_{i+1}=f(p_i)$. Let $\pi:\mathbb N\times\mathbb N\to\mathbb N$ be the projection to the second co-ordinate i.e. $\pi(i,a)=a$. Let $s_i=\pi(p_i)$ for all $1\leq i\leq n$, then $(s_i\mid 1\leq i\leq n)$ is the required sequence. It's clear from the definition of $s_i$ that $s_{i+1}=s_i+a_{i+1}$ for all $1\leq i&lt;n$. This is a  about File Permission and Why 777 is "destructive".   I'm not asking how to fix this problem, as there are a ton of references of that already on Server Fault (reinstall OS). Why does it do anything destructive at all?  If you've ever ran this command you pretty much immediately destroy your operating system. I'm not clear why removing restrictions has any impact on existing processes. For example, if I don't have read access to something and after a quick mistype in the terminal suddenly I now have access well... why does that cause Linux to break? Word to describe someone who goes to all the events in town! I'm looking for a short word that could describe people who are always going to every event in town. It doesn't need to be an existing word, feel free to create one of your own. It can also be made of words related to events and parties. (ex: club, event, guest list, etc.)  Edit  The word will serve as a new term to describ these people in a favorable way. It will probably be used for an app name so it need to be catchy and fun. ( Preferably )