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how to copy or backup files ignoring dot files Let's stop displaying a user's accept rate Akhil showed that the  is the same as the continuum, using as a step the observation that continuous functions that agree at rational points must agree everywhere, since the rationals are dense in the reals.  This isn't an obvious step, so why is it true? How do I upgrade from 14.04 LTS to 16.04.1 LTS? Procedure for reducing the degrees of freedom of an arbitrary system 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. How to install Python 3.4 on Ubuntu? I'd like to know if there is any alternative to Deep Freeze for Linux that still under development, because I've read some things on the internet and looks like the same company which developed Deep Freeze had a Linux version of it, but the project was discontinued. says that a photon of  to $10^{-62}$ kg has been detected:     10×10−62 kg   Mass equivalent of the energy of the lightest photon   detected [citation needed]   This equates ($mc^2=E=hf=h\frac{c}{\lambda}$) to a wavelength of $\lambda=2.2\times 10^{20}$ m (roughly a million ly)! Can anyone provide a citation for this measurement? And how can such a large wavelength/low energy photon be detected?  Edit  Apart from the quotation (true/false un/reliable un/documented ....), I'd like to learn about the lightest photon detected, or about the instrumental limit: what is the lower limit of energy that can be registerd by an intrument (or the greatest wavelength), and how it is done? For example, can you detect a radiowave of 1 Hz? Can I change the color of the last selected face, so that it is the same as the other selected faces?  Here, I've selected the left face then the right face. Note the right face is some sort of checkered or dithered pattern, and just the outline has the nice orange 'selected' color.    Here I've selected the top face, note the right face has now the nice color.    And here I've deselected the top face. Now, both of the remaining selected faces have the nice color. This is the result I'd rather see instead of image 1. Erdős-Straus conjecture The  (ESC), states that for every natural number $n \geq 2$, there exists a set of natural numbers $a, b, c$ , such that the following equation is satisfied:  $$\frac{4}{n}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\tag{1}$$  The basic approach to solving this problem outlined by Mordell [Ref1] is described below  By defining $t$ and $m$ as positive integers greater than zero and $q$ a positive integer greater than one we can observe that  a) There is always a solution for even $n$, since if $n=2^qt$ we have the trivial solution $$\frac{4}{4t}=\frac{1}{t}$$  In the remaining case $n=2(2t+1)$, a solution in the form of two Egyptian fractions can always be found  e.g. $$\frac{4}{2(2t+1)}=\frac{2}{2t+1}=\frac{1}{t+1}+\frac{1}{(t+1)(2t+1)}$$  b) If $(1)$ is a solution for some particular prime $n$ then all composite numbers $mn$ divisible by $n$ are also solutions, thus  $$\frac{4}{mn}=\frac{1}{ma}+\frac{1}{mb}+\frac{1}{mc}$$  will also be a solution. This means that we can simplify the analysis to the cases where $n$ is a prime greater than 2.  Using Mordell's approach we have just shown that we only need to consider the cases where $n$ is prime and where $n \equiv 1 \pmod{2} \;\;[meaning \;\;n=2t+1]$  The argument continues...  Mordell goes on to show in turn that the search can be reduced further to the cases when $$n \equiv 1 \pmod{4} \;\;[meaning \;numbers \;\;n=4t+1]$$ $$n \equiv 1 \pmod{8} \;\;[meaning \;numbers \;\;n=8t+1]$$ $$n \equiv 1 \pmod{3} \;\;[meaning \;numbers \;\;n=3t+1]$$ $$n \equiv 1,2,4 \pmod{7} \;\;[meaning \;numbers \;\;n=7t+1,n=7t+2 \;or\;n=7t+4 ]$$ $$n \equiv 1,4 \pmod{5}  \;\;[meaning \;numbers \;\; n=5t+1 \;or\;n=5t+4]$$  Assembling these results together, Mordell showed that the conjecture can be proved in this context except for the cases when $$n \equiv 1,11^2,13^2,17^2,19^2,23^2 \pmod{840}$$  Mordell stated that since the first prime meeting this condition is 1009, this is proof that the conjecture holds for $n&lt;1009$.  This basic approach can be pursued further. Other workers have shown that the conjecture holds for much higher values of $n$ using similar methods as can be seen on the above Wikipedia page.   Note that other intermediate results can be constructed from the above congruence's, e.g. $n \equiv 1 \pmod{24}$.  The question is:  Are there any other elementary approaches to solving this problem than the one outlined by Mordell (and described above)?  [Ref1] Louis J. Mordell (1969) Diophantine Equations, Academic Press, London, pp. 287-290. If a person holds prejudice against people because of their nationality, would that be considered racist? Would it be considered racist if a store owner believes all Canadians are thieves and does not let any Canadians into his store? Racism pertains to discriminating based on race, and (correct me if I'm wrong) Canadians are not a race. What would be an appropriate word to describe an individual such as the  store owner?  The discrimination is specific to Canadians, not foreigners in general. I'm looking for a word that could be applied to someone who lives in the country they discriminate against. For example if a Canadian announces "all Canadian culture is stupid!" what would that be called? I can run faster than _____. (1) him (2) he? Keyboard Shortcuts no longer working on GNOME 3.4.1 Refreshing SFDC page from VF frame: CORS issue How to schedule jobs in Sql server 2008 for less than 10 sec? I want to run a job every 3 seconds, however in SQL Server 2008 we cannot define an interval of less than 10 seconds.  The job is used to insert/update visitor information, and segmentation information into a database which is tracked by google search.   There are up to about 100 rows inserted in a 2 or 3 seconds. That job inserts and update the table in a database. Is there any way to schedule it using sp job scheduling configuration? How do I remove objects from an array in Java? Graphical interface for generating presentation slides Is there a good graphical interface, similar to PowerPoint or LibreOffice Impress, for generating presentation slides?  When writing documents I prefer to write my text and LaTeX-markups using a text-editor and not using a graphical tool like LyX. However, in the case of presentation slides I want to see the layout and to have the ability to immediately see what you get e.g. by moving a picture with arrow keys.  ADDITION: The background to my question is as follows. I have used PowerPoint for more than a decade and like to use a WYSIWYG tool when making presentation slides. However, I can not use PowerPoint on my current computer and I think the output from LibreOffice Impress is inferior. As a long-time user of LaTeX, I have considered using SliTeX or Beamer but unfortunately I do not like the way of working. The end result is of course superior, but I found it very time-consuming and tiresome to e.g. adjust the position and size of pictures. Can I make `find` return non-0 when no matching files are found? How can I get octal file permissions from command line?