Can I leave a garden hose under pressure for long periods of time?
Is there a setup where I can leave the water on all summer?
General solution to the PDE $xU_x+yU_y=0$ Solve the equation $xU_x+yU_y=0$.   From Partial Differential Equations: An Introduction, 2nd Ed. (Strauss, pg. 10). There are no boundary conditions.  Solution: The PDE can be written $(x,y)\cdot\nabla U(x,y)=0$, implying that the vector $(x,y)$ is tangent to the PDE's characteristic equation. Then I can write $dy/dx=y/x$, and to solve this ODE,  $$\frac{dy}{dx}=\frac yx \\ \ln y=\ln x+c_1 \\ y=cx \\ y/x=c$$  Hence, the PDE is dependent on $c$ and I can write $U(x,y)=f(y/x)$ for some function $f$, solving the problem.  Question: Is this solution correct? The hint for the question (supplied by the professor) said I should use a substitution of variables, but this seems reasonably valid. How to write (La)TeX (with parentheses) [or any other TeX-related logo] Java: creating a date object from a string and inserting into MySQL how to make a 360 video (turntable) of an Object using a python script I want to install lubuntu on my current (pre-existing) Ubuntu Install because of it's light-weight footprint.   Can I preserve currently installed apps after installation? Working with a huge file. Illustrator is super slow. What can I do to ease the load? How does the Deposit-User work? On SU there's the  which is suspended for quite some time. And I also know that it is used for spammers, but how does it work? Does the account of the spammer get 'linked' to Deposit? Do the answers get moved there? Can commuting matrices $X,Y$ always be written as polynomials of some matrix $A$? Consider square matrices over a field $K$. I don't think additional assumptions about $K$ like algebraically closed or characteristic $0$ are pertinent, but feel free to make them for comfort. For any such matrix $A$, the set $K[A]$ of polynomials in $A$ is a commutative subalgebra of $M_n(K)$; the question is whether for any pair of commuting matrices $X,Y$ at least one such commutative subalgebra can be found that contains both $X$ and $Y$.  I was asking myself this in connection with frequently recurring requests to completely characterise commuting pairs of matrices, like . While providing a useful characterisation seems impossible, a positive anwer to the current question would at least provide some answer.  Note that in many rather likely situations one can in fact take $A$ to be one of the matrices $X,Y$, for instance when one of the matrices , or more generally if its  (so coincides with the characteristic polynomial). However this is not always possible, as can be easily seen for instance for diagonal matrices $X=\operatorname{diag}(0,0,1)$ and $Y=\operatorname{diag}(0,1,1)$. However in that case both will be polynomials in $A=\operatorname{diag}(x,y,z)$ for any distinct values $x,y,z$ (then $K[A]$ consists of all diagonal matrices); although in the example in  the matrices are not both diagonalisable, an appropriate $A$ can be found there as well.   I thought for some time that any maximal commutative subalgebra of $M_n(K)$ was of the form $K[A]$ (which would imply a positive answer) for some $A$ with minimal polynomial of degree$~n$, and that a positive answer to my question was in fact instrumental in proving this. However I was wrong on both counts: there exist (for $n\geq 4$) commutative subalgebras of dimension${}&gt;n$ (whereas $\dim_KK[A]\leq n$ for all $A\in M_n(K)$) as shown in , and I was forced to correct  in the light of this; however it seems (at least in the cases I looked at) that many (all?) pairs of matrices $X,Y$ in such a subalgebra still admit a matrix $A$ (which in general is not in the subalgebra) such that $X,Y\in K[A]$. This indicates that a positive answer to my question would not contradict the existence of such large commutative subalgebras: it would just mean that to obtain a maximal dimensional subalgebra containing $X,Y$ one should in general avoid throwing in an $A$ with $X,Y\in K[A]$. I do think these large subalgebras easily show that my question but for three commuting matrices has a negative answer.  Finally I note that  to the cited MO question mentions a result by Gerstenhaber that the dimension of the subalgebra generated two commuting matrices in $M_n(K)$ cannot exceed$~n$. This unfortunately does not settle my question (if $X,Y$ would generate a subalgebra of dimension${}&gt;n$, it would have proved a negative answer); it just might be that the mentioned result is true because of the existence of $A$ (I don't have access to a proof right now, but given the formulation it seems unlikely that it was done this way).  OK, I've tried to build up the suspense. Honesty demands that I say that I do know the answer to my question, since a colleague of mine provided a convincing one. I will however not give this answer right away, but post it once there has been some time for gathering answers here; who knows somebody will prove a different answer than the one I have (heaven forbid), or at least give the same answer with a different justification. I want to remove all empty lines from a file. Even if the line contains spaces or tabs it should also be removed. How to define a Bijection between $(A^B)^C$ and $A^{B \times C}$ Clarifications about Gstreamer I'm a bit confused about what Gstreamer does.   Does it come installed by default with Ubuntu ?  If so which version  is the default for 14.04?  Does it provide hardware accelerated video playback (decoding) ?   If so does it work with VA-API and VDPAU or is it an alternative to those?    Thanks for your help I'm currently unable to access anything via the Stack Exchange app under iOS; is this a known issue? What does InitializeComponent() do, and how does it work in WPF? What does InitializeComponent() do, and how does it work in WPF?  In general first, but I would especially be interested to know the gory details of order of construction, and what happens when there are Attached Properties. How can I check for Python version in a program that uses new language features? If I have a Python script that requires at least a particular version of Python, what is the correct way to fail gracefully when an earlier version of Python is used to launch the script?  How do I get control early enough to issue an error message and exit?  For example, I have a program that uses the ternery operator (new in 2.5) and "with" blocks (new in 2.6).  I wrote a simple little interpreter-version checker routine which is the first thing the script would call ... except it doesn't get that far. Instead, the script fails during python compilation, before my routines are even called. Thus the user of the script sees some very obscure synax error tracebacks - which pretty much require an expert to deduce that it is simply the case of running the wrong version of Python.  I know how to check the version of Python. The issue is that some syntax is illegal in older versions of Python. Consider this program:  import sys if sys.version_info &lt; (2, 4):     raise "must use python 2.5 or greater" else:     # syntax error in 2.4, ok in 2.5     x = 1 if True else 2     print x   When run under 2.4, I want this result  $ ~/bin/python2.4 tern.py  must use python 2.5 or greater   and not this result:  $ ~/bin/python2.4 tern.py    File "tern.py", line 5     x = 1 if True else 2            ^ SyntaxError: invalid syntax   (Channeling for a coworker.) Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove $\operatorname{trace}(A) = \operatorname{trace}(B)$.  I'm not sure where to go on this. So far I have this:  If $A$ is similar to $B$, then      $B=P^{-1}AP$ and $A=PBP^{-1}$   This implies that:     $\operatorname{trace}(B) = \operatorname{trace}(P^{-1}AP)$ and $\operatorname{trace}(A) = \operatorname{trace}(PBP^{-1})$   Not sure where to go from here Question title overlap in new design when title is longer Today I noticed that in new design view count is getting overlapped with question title on scifi.se for longer title:    But it's not site specific as same problem happen in Beta site too ( Hinduism.se):    That's why asked in main meta. Does "Erase Disk and Install Ubuntu" replace the default boot screen? I am new here. And I may replace a laptop's hard disk with Ubuntu. It's an HP Compaq notebook which has Windows 7 installed. So If I choose that install option, will it replace the screen that says F12 for boot options [actually it was esc]. I am just asking. I know that choosing that options erases your other partitions. I am assuming it gets replaced by grub2? Geometric proof that a Pythagorean triple has a number divisible by $3$? Can I infer from “If $a,b \in \mathbb{N}$ such that $(a,3)=(b,3)=1$ then $a^2+b^2\neq c^2$ for any $c\in\mathbb{N}$” that any pythagorean triple has a number which is divisible by $3$? If so, how can this relationship be proved geometrically? Best way to center a  on a page vertically and horizontally? Best way to center a &lt;div&gt; element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too? Integral of $\int \frac{dx}{\sqrt{x^2 -9}}$