Depends on lib32gcc1 , libc6-i386 , can't install neither
How do I resolve unmet dependencies after adding a PPA?
I am not mathematician by any means so this question might be rather stupid. I came across this Wikipedia article on  and found this bewildering formula,   $$1 + 2 + 3 + \dots  = - \frac1{12}$$  The article also says that "Ramanujan summation of a divergent series is not a sum in the traditional sense". I am wondering then what this summation actually implies?  Is there any interpretation of this confounding result in the physical world that someone not so math-savvy can understand? Convolution operator has norm 1 with respect to $L^2$ norm Let $C_c(\mathbb{R})$ be the following:  $$C_c = \{ f \in C(\mathbb{R}) \mid \exists \text{ } T &gt; 0 \text{ s.t. } f(t) = 0  \text{ for } |t| \geq T\}$$  Let $T_n \in L(C_c(\mathbb{R}))$ be a linear operator such that:  $$T_n u = \delta_n *u, \forall u \in C_c(\mathbb{R}),$$  where  $$ \delta_n(t)= \begin{cases}        n^2(t+1/n) &amp; -1/n \leq t \leq 0 \\       -n^2(t-1/n) &amp; 0 &lt; t \leq 1/n \\       0 &amp; \text{elsewhere}     \end{cases} $$  I have to prove that with respect to the 2-norm, the operator $T_n$ has $\|T_n\| = 1$ and I have succeeded in proving that $\|T_nu\|_2 \leq \|u\|_2, \forall u \in C_c(\mathbb{R}).$  Now, I remained  to prove that $\exists \text{ } u \in C_c(\mathbb{R}) \text{ s.t. } \|T_nu\|_2 = \|u\|_2$, but I really don't get how $u$ should be shaped in order to satisfy it. Simulating the Windows key on an old keyboard Is (rest) mass conserved in special relativity? I don't understand why it is said that the (rest) mass of a system is not conserved in relativity. I mean, the momentum of a system is conserved (i.e.: it remains constant in a frame of reference without any external influence). Also the energy of a system is conserved in relativity: it doesn't change without any external agency  and the (rest) mass of a system is just  $$m^2=E^2-p^2$$  $E$ is constant, $p$ is constant, how can $m$ change?  For example, entropy is not conserved in a system, that means that the entropy of the system will increase spontaneously with time, which is really the case. But, is this true for mass?   here is the problem from Griffiths and exact solution as given in the Griffiths,  Two lumps of clay, each of rest mass $m$, collide head-on at $3c/5$ and they stick together. Question: what is the rest mass $M$ of the composite lump?  Solution: In this case conservation of momentum is trivial it is zero before and zero after. The energy of each lump prior to the collision is $$mc^2/\sqrt{1-v^2/c^2} =5mc^2/4.$$ The energy of the composite lump after the collision is $Mc^2$ (since its at rest). so the conservation of energy says: $5mc^2/4 + 5mc^2/4 =Mc^2$ and hence $M=5m/2$.  Notice that this is greater than the sum of the initial masses! Mass was not conserved in this collision; kinetic energy was converted into rest energy, so the rest mass increased. Transfering money from NRE to saving account is taxable or not I have the following problem: Let $(M, \omega)$ be a symplectic manifold. How can I show $$\omega^n=\underbrace{\omega\wedge \ldots\wedge \omega}_{n-times},$$ satisfies $\omega^n(p)\neq 0$ for all $p\in M$. I believe that is not too dificult but I'm not used with exterior product.. Any help will be valuable...  This is important because the nondegeneracy condition on $ω$ is equivalent to the condition that M has an even dimension $2n$ and the top wedge product $\omega^n$ is nowhere vanishing on M, i.e., $ω^n$ is a volume form. In particular, $M$ must be orientable and is canonically oriented by $\omega^n$. I have a current view set up that displays a feed of stories and is sorted in descending order. I now need to have the first 4 stories display as a different style then the remaining ones. I have pagination set to 10. I only want the first 4 to show differently on page 1, and then the current style will show on the remaining pages. Is there a way to do this? Rescuing/Compiling old TeX file starting with “\input amstex” I have come across an ancient (1995) LaTeX file which was (surely) once compliant, but now does not compile at all. Is there any way to rescue it?  My actual question is much more precise. I want a copy of the follow paper on the arXiv:    Downloading the pdf source produces something which looks like a document on a4 paper printed on US letter (the bottoms of some pages are cut off). However, if you download the TeX source from the arXiv, then it doesn't compile (even adding .tex, naturally). I'm using an up to date version of TeXshop on a mac. We work heavily with serialization and having to specify Serializable tag on every object we use is kind of a burden. Especially when it's a 3rd-party class that we can't really change.  The question is: since Serializable is an empty interface and Java provides robust serialization once you add  implements Serializable - why didn't they make everything serializable and that's it?    What am I missing? Can't access pre populated SQLite database using PhoneGap/Cordova in Android Logistic regression is predicting all 1, and no 0 I am running an analysis on the probability of loan default using logistic regression and random forests.    When I use logistic regression, the prediction is always all '1' (which means good loan).  I have never seen this before, and do not know where to start in terms of trying to sort out the issue.  There are 22 columns with 600K rows.  When I decrease the # of columns I get the same result with logistic regression.   Why could the logistic regression be so wrong?  **Actual from the data**  0 :   41932  1 :   573426  **Logistic regression output**   prediction for 1 when actually 0: 41932 prediction for 1 when actually 1:573426  A**s you can see, it always predicts a 1**   **Random forests does better:**  actual 0, pred 0 : 38800  actual 1, pred 0 : 27  actual 0, pred 1 : 3132 actual 1, pred 1 : 573399 Good tools for drawing schematics I was going to add a bit of information to my post on a previous day using schematics and some instructions. What programs are being employed for this purpose?  I mostly want to see what others are using and that I can easily use to give descriptive schematics.  In a perfect world, and I know this is a case of me wishing, it would be:   Free. Extremely easy to draw schematics in. Allows simple production of waveforms for the inputs/outputs. Mask and inherit the same systemd unit Suppose a package provides whatever.service file so certain events (including whatever.socket) cause a daemon to start with a certain configuration.  I want to disable this completely. In particular, I want the old socket and any other unit files that might refer to this service by name to be unable to start the daemon.  Instead, I want to create my own unit files for this daemon with a different .socket unit and different environment variables. I also want my override to automatically take account of possible upstream updates to the original unit file (which my current solution of copying whatever.service as whatever-modified.service and editing it unfortunately does not provide).  If I create the following symlinks and files: /etc/systemd/system/whatever.service → /dev/null /etc/systemd/system/whatever-modified.service → /usr/lib/systemd/system/whatever.service /etc/systemd/system/whatever-modified.service.d/fix.conf  systemd considers the new service to be masked as well and refuses to start it. How to avoid this? Can someone use DC generator along with electric motor to make electricity along with mechanical energy? I know this might sound stupid and maybe stupid totally, but I need some clarification....  I came through electric motor principle.  and then I came across the following link on DC generators    Now my question is, can't we combine them both to provide DC current with little DC used in motor side? By "combine," I mean using a DC generator coil only at the other side of the coil of the motor in the motor itself. The condition is that the 2 coils are connected via some apparatus that causes the 2nd coil to move along with the 1st coil.   In this way we can use both the mechanical energy produced by the 1st coil and the electrical energy produced by the 2nd coil, right?   This is a great concept if it works, right? Please throw some light on this. How to increase Scrollback lines in Ubuntu(14.04.2) server edition? I can see only limited lines on terminal by using shift+ pageup. in Ubuntu desktop version, there is option to make scroll-back lines unlimited. how to do it in Ubuntu server version. please suggest. java.lang.IllegalArgumentException: Invalid  in servlet mapping &lt;servlet&gt;     &lt;servlet-name&gt;myservlet&lt;/servlet-name&gt;     &lt;servlet-class&gt;workflow.WDispatcher&lt;/servlet-class&gt;     &lt;load-on-startup&gt;2&lt;/load-on-startup&gt; &lt;/servlet&gt;  &lt;servlet-mapping&gt;     &lt;servlet-name&gt;myservlet&lt;/servlet-name&gt;     &lt;url-pattern&gt;*NEXTEVENT*&lt;/url-pattern&gt; &lt;/servlet-mapping&gt;   Above is the snippet from Tomcat's web.xml. The URL pattern *NEXTEVENT* on start up throws     java.lang.IllegalArgumentException: Invalid &lt;url-pattern> in servlet mapping   It will be greatly appreciated if someone can hint at the error. ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ How to prove wave nature of large object? I've just installed Ubuntu 14.04 and am trying to install php 5.3. But when I run   apt-get install php5    it's installing php 5.5.9-1ubuntu4. I need to use php 5.3 in the system because the application I'm working on is built with php 5.3.   How can I achieve this? I've got an MP4 video file and I want to add another AAC audio track to it. I've tried YAMB and MeGUI (frontends for MP4Box) and it plays correctly in Zoom Player, but it picks the wrong track in WMP and plays both at once in Quicktime. I think this might have to do with designating the default audio track somehow.  Does anyone know how to specify the default audio track with YAMB/MeGUI or know of another way of adding a track to an MP4 file? Is expression for law of equipartion of energy valid for real gas? I know that according to law of equipartion of energy ,energy per molecule per degree of freedom is 1/2 Kb T I wanted to know if it is true for a real gas ?