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Is there a proof from the first principle that for the Lagrangian $L$,    $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$  in classical mechanics? Assume that Cartesian coordinates are used. Among the combinations, $L = T - nV$, only $n=1$ works. Is there a fundamental reason for it?  On the other hand, the variational principle used in deriving the equations of motion, Euler-Lagrange equation, is general enough (can be used to to find the optimum of any parametrized integral) and does not specify the form of Lagrangian. I appreciate for anyone who gives the  answer, and if possible, the primary source (who published the answer first in the literature).      Notes added on Sept 22: - Both answers are correct as far as I can find. Both answerers were not sure about what I meant by the term I used: 'first principle'. I like to elaborate what I was thinking, not meant to be condescending or anything near to that. Please have a little understanding if the words I use are not well-thought of. - We do science by collecting facts, forming empirical laws, building a theory which generalizes the laws, then we go back to the lab and find if the generalization part can stand up to the verification. Newton's laws are close to the end of empirical laws, meaning that they are easily verified in the lab. These laws are not limited to gravity, but are used mostly under the condition of gravity. When we generalize and express them in Lagrangian or Hamiltonian, they can be used where Newton's laws cannot, for example, on electromagnetism, or any other forces unknown to us. Lagrangian or Hamiltonian and the derived equations of motion are generalizations and more on the theory side, relatively speaking; at least those are a little more theoretical than Newton's laws. We still go to lab to verify these generalizations, but it's somewhat harder to do so, like we have to use Large Hadron Collider. - But here is a new problem, as @Jerry Schirmer pointed out in his comment and I agreed. Lagrangian is great tool if we know its expression. If we don't, then we are at lost. Lagrangian is almost as useless as Newton's laws for a new mysterious force. It's almost as useless but not quite, because we can try and error. We have much better luck to try and error on Lagrangian than on equations of motion. - Oh, variational principle is a 'first principle' in my mind and is used to derive Euler-Lagrange equation. But variational principle does not give a clue about the explicit expression of Lagrangian. This is the point I'm driving at. This is why I'm looking for help, say, in Physics SE. If someone knew the reason why n=1 in L=T-nV, then we could use this reasoning to find out about a mysterious force. It looks like that someone is in the future. Create an item in sharepoint calender when infopath form is submitted in sharepoint 2010 through workflow So, I understand that by using 'tee' I can redirect the output of a command such as 'ping' to stdout as well as a file.  For example:  &gt; ping google.com | tee somefile   This would display the ping statistics on terminal and write them to 'somefile'.  Now, if I wish to modify the output from 'ping', I can use 'cut' in such a way:  &gt; ping google.com | cut -d' ' -f 1   But, if I wish to use all the three commands together, I get a no output on stdout and an empty file.  &gt; ping google.com | cut -d' ' -f 1 | tee somefile   What am I doing wrong? Is there a better way to do this? Somehow I feel I am not using 'tee' properly. Any insight would be appreciated.  I'm using bash shell, if this is relevant. Preimage of codimension one subspace of the quotient $g/D^1 g$ I am trying to prove the following.  Proposition Let $g$ be a Lie algebra such that the first derived algebra $Dg$ is a proper ideal of $g$. Consider the quotient $g/D^1 g$, and show that the preimage of any codimension 1 subspace is   an ideal, and has codimension 1.   I could show that the preimage is indeed an ideal, but I need some help with the part about the dimensions:  So suppose that $\phi: x \mapsto [x]$ is the quotient projection. And write $[h] + Dg$  for a codimension 1 subspace of $g$ (here $h\subset g$). Then the preimage of this subspace is just the linear span $h+Dg\leq g$. Let $y+z \in h+Dg$ with $y\in h$ and $z\in Dg$. Let $x\in g$. We want to show that $[x, y+z]\in h$, ie that $h + Dg \lhd g$. We can write $x$ as $x_0+x_1$ for $x_0 \in Dg$, $x_1\not\in Dg$. Then  $$[x,y+z] = [x_0, y+z] + [x_1, y] + [x_1,z] \in h + Dg$$  The inclusion follows since $Dg$ is an ideal so the first and third terms belong $Dg$; and $[x_1, y] \in D_g$, as $g/Dg$ is abelian. Are there cheap GPS or other navigator devices with downloadable maps for the whole world? I don't need a recommendation or a list but my knowledge of GPS and "navi"s and the differences between them is an utter mystery to me.  But often I'm lost in backstreets in random countries where access to something like a live Google Maps would be awesome. I absolutely cannot afford a smartphone with worldwide roaming though.  Can GPS's do what I want or am I barking up the wrong tree? If they can is it only high end ones than can? How do I recover my accidentally lost Windows partitions after installing Ubuntu? I have a Toshiba satellite A-200 laptop with a Vista OS on it with 4 NTFS partitions  (C:) Vista  (D:) Entertainment  (E:) Work  (F:) Sources   and I wanted to start using Ubuntu instead. So I tried it first from the live CD and everything was OK and all the partitions were shown and working and so I decided to install Ubuntu to replace Vista on the (C:) drive. After I did that I can no longer find my folders and files on the (D:), (E:), (F:) partitions and the only file system that is shown is one 198 GB although my HDD is 320 GB.  I can't access the lost data on the remaining 120 GB which I hope is still there and not totally lost  I am now working from the live CD but I am unable to install testdisk. Can I recover the Vista partitions by the product recovery CD to get my laptop back to the factory settings? Can I recover the NTFS partitions using a recovery program for Windows or will that make the problem worse?   I need these data badly as I don't have a backup for them. Why do DNGs only show in low resolution on Google Photos? Through my NAS at home I store and backup all my photos on Google Drive. These photos also show up on Google Photos. I use Lightroom and convert all photos to DNG when copying to my NAS.  When I look at the photos in Google Photos the image is rather small. Clicking the (i) info button tells me the image has a resolution of 1024x680, file size 9.8 MB and a MP of 0.7. This is probably just a preview or thumbnail of some sort, but how do I view the image in larger resolutions in Google Photos? Whenever adding a new wireless network, android seems to forget the network after disabling then re-enabling wifi. I am forced to manually connect to the network and enter the password each time. This also happens with open networks. The problem occurs on any wireless network, at home, work, public networks, etc.  Further inspection on the /data/misc/wifi/wpa_supplicant.conf file shows "disabled=1" added to the end of each network.    click image for larger version  This has been going on for weeks. Any help would be much appreciated.  Phone: Nexus 4 Version: 4.4.4 I am trying to (partially) reproduce the algorithm displayed in Figure 4 from   My problem is with the multi-line conditions present in the "IFs". I want them to be indented, but \Indp does not seem to take effect if a new line \\ is not present in the same line.  This is what I tried:  \begin{algorithm}[htb]     \SetAlgoNoLine%     \SetNoFillComment     \SetKwIF{If}{ElseIf}{Else}{if}{:}{elif}{else:}{}%      \If{(SYNs from both hosts and \\             \Indp SYNs in earliest NFs of both hosts and \\             \Indp hosts' earliest packets differ)}{         Host with earliest NF is originator      }     \If{(SYN only from one host and \\         \Indp SYN is in connection's earliest NF)}{     Host is originator     }     \If{one host uses port 20 (ftp-data)}{     Host is originator     }     \If{only one host uses a well-known port}{     Host is responder     }     \If{start of hosts' first packets differ}{     Host with earliest NF is originator     }     Arbitrarily choose originator     \caption{Pseudo code for determining connection server side}     \label{algo:serverside2} \end{algorithm}   For instance, the line "SYNs in earliest NFs of both hosts and" is indented correctly, but "hosts' earliest packets differ" is not. Maximum and minimum distance of two points Consider six distinct points in a plane. Let $m$ and $M$ denote respectively the minimum and the maximum distance between any pair of points.  Show that $M/m \geqslant \sqrt{3}$. I want to be able to ask a question by sending an email to some special email address for Stack Overflow. I have found this convenient in other situations like Google Groups, blogging, and Facebook walls, and it seems that technically it shouldn't be too hard to do.  Does this feature exist already? I'm kind of afraid to ask for features as some of them get downvoted simply since users think they are not neccessary (and not because the post is bad). Is it feasible to convert math in a picture, say written by hand, into LaTeX?   For example, I'd deem it faster to write down (de novo)  a 10 x 10 matrix with long, complex entries, rather than typing it in LaTeX or MathType. If I then take a picture or scan my writing, how can it be rendered or transformed into LaTeX? I tried to change network interfaces name on this new Ubuntu 16.04 LTS version but doesn't have the /etc/udev/rules.d/70-persistent-net.rules.  So, I tried to use /lib/udev/write_net_rules but it not exist.  Why do I need this modification? Because I'm using a tool to Simulate virtual platforms that use flex licensing and the authentication need to be in eth0 interface name.  Any suggestion?  The command ip link returns:  user@laptop:~$ ip link  1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN mode DEFAULT group default qlen 1 link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00 2: enp6s0: &lt;NO-CARRIER,BROADCAST,MULTICAST,UP&gt; mtu 1500 qdisc pfifo_fast state DOWN mode DEFAULT group default qlen 1000 link/ether b8:2a:xx:yy:xx:yy brd ff:ff:ff:ff:ff:ff 3: wlp7s0: &lt;BROADCAST,MULTICAST,UP,LOWER_UP&gt; mtu 1500 qdisc mq state UP mode DORMANT group default qlen 1000 link/ether 5c:e0:xx:yy:xx:yy brd ff:ff:ff:ff:ff:ff  user@laptop:~$ ifconfig  enp6s0    Link encap:Ethernet  HWaddr b8:2a:xx:yy:xx:yy   lo        Link encap:Local Loopback   wlp7s0    Link encap:Ethernet  HWaddr 5c:e0:xx:yy:xx:yy     (Some information were ignored and suppressed)  I already tried some links: From the Cracks in time and space story arc it's known that if a TARDIS is blown up (possibly while in the Time Vortex) it rips creation itself apart. Also, from the Stolen Earth / Journey's End we learn the Daleks' masterplan which is subjugating creation itself via destroying it with the Reality Bomb (unfading Z-neutrino energy radiation).  In the Last Great Time War all sorts of temporal weapons were used and it's known that Daleks have the ability of time travel as well. Why didn't they use the Time Vortex back then to win the war once and for all via detonating a TARDIS while inside? Show that $|f(z_1)|=|f(z_2)|≤|z_1|^2=|z_2|^2$. Let $f\in H(B(0,1))$, $f(0)=0$, $f(B(0,1))\subset B(0,1)$. Suppose there are 2 different points $z_1$,$z_2\in B(0,1)$, s.t. $|z_1|=|z_2|$, $f(z_1)=f(z_2)$. Show that $|f(z_1)|=|f(z_2)|≤|z_1|^2=|z_2|^2$.    I have used the Schwarz-Pick Proposition to prove that $|f(z_1)|=|f(z_2)|≤|z_1|=|z_2|$ directly, but that is not enough. Thank you for help! Clear 301-redirect cache in Firefox Is it possible to clear only 301-redirects from Firefox's cache? CTRL+F5 doesn't do the job since you just reload the target without caching but do not clear the cached redirect.  An option to disable caching of those redirects completely would be fine, too - but some way (possibly through an extension) to remove those cached redirects would be better.  Note: I'm not looking for answers that disable all caching (including CSS, JS, etc.) Do we have different badges in different SE sites How to run a command that involves redirecting or piping with sudo? How to Highlight a Row on Active Status I have a column which should define in list if the issue is in status: -Not Started, Active, Completed.   I would like to ideally add some colour to this by the row for example if completed it is green or active it is red. Then it highlights the whole row, do you know if this can be edited within the columns settings or if there any step by step instructions that can be followed to make this change? (ideally for someone new to sharepoint)  Thank You I add js file with drupal_add_js in hook_form_alter, it is ok and I see it in list of js loaded in page, but when I submit form and form not validate and return to that form (after validation failed) I don't see js files that added to form, why this happened? and how can add my js file in that form after validation failed ?   some part of my code   function mymodle_form_alter(&amp;$form, $form_state, $form_id) {   if ($form_id == 'news_node_form') {     drupal_add_js(drupal_get_path('module', 'mymodule') . '/js/mymodulejsfile.js'); //, array('scope' =&gt; 'footer','weight' =&gt; 10));   } }   code work correctly in add and edit form, but when form submit and validation failed it show validation error but my js file not loaded in page (I checked html source and check firebug script files), but there is not my js file,