So, when I installed Ubuntu 20.04 LTS onto my PC firstly I removed Nautilus (Because I prefer to use Nemo) and after this action my system has a lot of broken files that can't be removed (I tried and it's said that I have more and more broken files) and the command sudo apt install -f doesn't work at all. How can I fix it? I cannot install even Steam now also my system is up to date! PS. aptitude doesn't work as well as apt. sudo apt install steam sudo password for lambleeg: Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  steam:i386 : Depends: libgl1-mesa-dri:i386 (&gt;= 17.3) but it is not going to be installed or                        libtxc-dxtn0:i386 but it is not installable               Depends: libgl1-mesa-dri:i386 but it is not going to be installed               Depends: libgl1-mesa-glx:i386 but it is not going to be installed               Depends: libudev1:i386 but  but it is not going to be installed E: Unable to correct problems, you have held broken packages.
After upgrading from 10.04 to 12.04 I am trying to install different packages.  For instance ia32-libs and skype (4.0).  When trying to install these, I am getting the 'Unable to correct problems, you have held broken packages' error message.   Output of commands:  sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   After running this:  sudo dpkg --configure -a foo@foo:~$ sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
Leave bash script running on remote terminal while not logged in? I have a bash script that takes several hours to run.  While it's running, I would like to do other things, which may involve logging out or disconnecting from the internet (my script runs network tests on various computers).  I understand that there is a command that would allow me to run my tests from a remote terminal and logout of the terminal while it runs.  Does anyone know what this command is? I have a directory which contains numbered image files, something like this:  01.png 02.png 03.png 03.svg 04.png 05.png 06.jpg 07.png 08.png 09.png 09.svg 10.png   Sometimes there may be multiple versions of a file in different formats (eg. a png and svg version of the 03 and 09 files above) but the numbers are otherwise consecutive.  Typically there are 40-80 such files in each directory.  The numbers correspond to the order these images appear in a manuscript (a Word document, but that's not important).  There is no other way to determine the order of the images.  If I add a new image to the manuscript I need to place a copy of the image in this directory with the correct numbering.  So if the new image is the fifth in the manuscript I need to rename the files in the directory to this in order to make room for it:  01.png 02.png 03.png 03.svg 04.png 06.png 07.jpg 08.png 09.png 10.png 10.svg 11.png   What is the most straightforward way from the command line, or from a script or macro to renumber all the files starting at a certain number?  I have a standard Fedora Linux install using bash. How to prove $x^a-1\mid x^b-1 \iff a \mid b$, where $x \ge 2$ and $a,b,x \in \Bbb Z$.  I've tried the following in attempting to solve this:  $$a\mid b \Rightarrow aq=b \Rightarrow x^{aq}=x^b \Rightarrow x^ax^q=x^b$$  Because $x^q \in \Bbb Z$, it follows that $x^a\mid x^b$.  This is as far as I have gotten; any help getting further is appreciated.  Note: It may be that this identity is not true at all? A method for evaluating sums/discrete functions by assuming they can be made continuous and differentiable? Suppose I had a function that satisfied the property $f(x)=f(x-1)+g(x)$.  For any $x\in\mathbb N$, it is easy enough to see that this boils down to the statement  $$f(x)=f(0)+\sum_{k=1}^xg(k)$$  If we return to our functional equation and differentiate it $n$ times, we get  $$f^{(n)}(x)=f^{(n)}(x-1)+g^{(n)}(x)$$  Once again, for any $x\in\mathbb N$, we have  $$f^{(n)}(x)=f^{(n)}(0)+\sum_{k=1}^xg^{(n)}(k)$$  One could then integrate both sides.  For example, this asserts that  $$\sum_{k=1}^xg(k)=xf'(0)+\int_0^x\sum_{k=1}^tg'(k)dt$$  If the sum inside the intagral is generalized to any upper bound.  How would I justify this for discrete functions?    An example of this is letting $f_p(x)=\sum_{k=1}^xk^p$, as it seems to follow the above result.  We can see from the above that  $$f_p(x)=a_px+p\int_0^xf_{p-1}(t)dt$$  $$a_p=1-p\int_0^1f_{p-1}(t)dt$$  which appears to be a true recursive formula.    Under what conditions can I extend discrete functions $f(x)$ and $g(x)$ into continuous differentiable functions and apply this method? If I have flagged a post, show me a "flags" link in my profile WinForms: How to programmatically fire an event handler? I want to programmatically invoke an event handler for a control. For example:  DateTimePicker dtpLastConsummated;   I want to trigger the TextChanged event handler for the dtpLastConsummated, how can i do it?  In other languages I would call something akin to:  dtpLastConsummated.TextChanged(this, new EventArgs());   but in .NET you can have multiple event handlers:  dtpLastConsummated.Click +=new EventHandler(dtpLastConsummated_TextChanged); dtpLastConsummated.Click +=new EventHandler(dtpLastConsummated_AnotherHandler); dtpLastConsummated.Click +=new EventHandler(dtpLastConsummated_MoreHandlers); ... dtpLastConsummated.Click +=new EventHandler(dtpLastConsummated_Nminus1);   so you need a way to trigger all the attached event handlers.    Answer  The following code will fire the event:  Toolkit.FireEvent(dtpLastConsummated, "TextChanged", new EventArgs());   And here's the code of the static toolkit function:  /// &lt;summary&gt; /// Programatically fire an event handler of an object /// &lt;/summary&gt; /// &lt;param name="targetObject"&gt;&lt;/param&gt; /// &lt;param name="eventName"&gt;&lt;/param&gt; /// &lt;param name="e"&gt;&lt;/param&gt; public static void FireEvent(Object targetObject, string eventName, EventArgs e) {    /*     * By convention event handlers are internally called by a protected     * method called OnEventName     * e.g.     *     public event TextChanged     * is triggered by     *     protected void OnTextChanged     *      * If the object didn't create an OnXxxx protected method,     * then you're screwed. But your alternative was over override     * the method and call it - so you'd be screwed the other way too.     */     //Event thrower method name //e.g. OnTextChanged    String methodName = "On" + eventName;     MethodInfo mi = targetObject.GetType().GetMethod(          methodName,           BindingFlags.Instance | BindingFlags.NonPublic);     if (mi == null)       throw new ArgumentException("Cannot find event thrower named "+methodName);     mi.Invoke(targetObject, new object[] { e }); }     Note: I'm not creating a subclass of every control in the .NET framework, and every 3rd party control, and convincing an enterprise worth of developers to retrofit every form to use my custom controls. How to evaluate $\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta) d\theta$? For $\alpha \in \mathbb{R}$, define $\displaystyle I(\alpha):=\int_{0}^{2\pi}e^{\alpha \cos \theta}\cos(\alpha \sin \theta)\; d\theta$. Calculate $I(0)$. Hence evaluate $\displaystyle\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta)\; d\theta$.  Hint: To evaluate the integral that expresses $\displaystyle\frac{dI}{d\alpha}$, consider $\displaystyle\frac{\partial}{\partial \theta}(e^{\alpha \cos \theta}\sin(\alpha \sin \theta))$.  How do I do this question? I think this might have something to do with the Fundamental Theorem of Calculus, but I'm not sure.  I computed $\displaystyle I(0)=\int_{0}^{2\pi} d\theta=2 \pi$, and $\displaystyle I(1)=\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta) d\theta$. Following the hint I get  $$\begin{align} \frac{\partial}{\partial \theta}(e^{\alpha \cos \theta}\sin(\alpha \sin \theta)) &amp; =\alpha e^{\alpha \cos \theta} \sin (\alpha \sin \theta) + e^{\alpha \cos \theta}\cos(\alpha \sin \theta) \alpha \cos \theta \\ &amp; =  \alpha e^{\alpha \cos \theta} \sin (\alpha \sin \theta) + \frac{dI}{d \alpha} \cos \theta. \\ \end{align}$$  Is this correct so far?  The answers in the question referred as a duplicate does not help. I'm in a course dealing with real values, not complex. Ubuntu with spyware? Richard Stallman states that Ubuntu "has installed surveillance code". See:   Is this true?   I agree with him that "Any excuse Canonical offers is inadequate....". For some or other reason, typing @ᔕᖺᘎᕊ in a chat room pings everyone who's been in that chat room for the last 7 days...    Seems to work in all chat rooms (I only tested 2 as I don't want to upset too many people...)  How should we proceed? Line numbering paragraph oriented? I'm using the lineno package with the pagewise option but I need a way to get the numbering restart every paragraph break. I need a general solution to pass to the latex command, e.g.:  latex "\AtBeginDocument{\RequirePackage[pagewise]{lineno}\linenumbers}\input{mydocument.tex}"   I read the lineno manual but the package does not provide this feature. Is there any trick to do that? I have come across a question about determining possible minimal polynomials for a rank one linear operator and I am wondering if I am using the correct proof method.  I think that the facts needed to solve this problem come from the section on Nilpotent operators from Hoffman and Kunze's "Linear Algebra".     Question: Let $V$ be a vector space of dimension $n$ over the field $F$ and consider a linear operator $T$ on $V$ such that $\mathrm{rank}(T) = 1$.  List all possible minimal polynomials for $T$.   Sketch of Proof:   If $T$ is nilpotent then the minimal polynomial of $T$ is $x^k$ for some $k\leq n$.  So suppose $T$ is not nilpotent, then we can argue that $T$ is diagonalizable based on the fact that $T$ must have one nonzero eigenvalue otherwise it would be nilpotent (I am leaving details of the proof of diagonalization but it is the observation that the characteristic space of the nonzero eigenvalue is the range of T and has dimension $1$).  Thus the minimal polynomial of $T$ is just a linear term $x-c$.    Did I make a mistake assuming that $T$ can have only one nonzero eigenvalue?  Thanks for your help I have been playing for almost 2 days, and today it is asking me to sign up again.  I have all my game saved in my google account, but I wonder if I just log in from a trainer account will I keep my progress? Finding all solutions for a system of equations with constraint on the sum of absolute values I am looking for a fast algorithm to find all integer solutions for the following system of linear equations ($c_1,\ldots,c_n \in \mathbb{Z}$ and $r\in \mathbb{N}$ ):  $x_1+x_2=c_1$  $x_3+x_4=c_2$  ...  $x_{2n-1}+x_{2n}=c_n$  $|x_1|+|x_2|+\ldots+|x_{2n}|=r$  $x_1,\ldots,x_{2n} \in \mathbb{Z}$   Also can we find the number of solutions before solving the system? How to pad zeroes to a string? My Applications are not showing after upgrading from Ubuntu 18.04 to 20.04 I did an upgrade today to the latest version of ubuntu. Everything looked good and fine only for me to discover that I cannot find my applications after clicking the 'Show Applications' icon. The same applies when I search for an application in the search bar, I do not see it. It shows me an endless search.  These are the screenshot images of the problem:      In the meantime, I access my applications from the menu at the top bar and also use the terminal to run applications with CLI. The Bash man page describes use of ${!a} to return the contents of the variable whose name is the contents of a (a level of indirection).  I'd like to know how to return all elements in an array using this, i.e.,  a=(one two three) echo ${a[*]}   returns  one two three   I would like for:  b=a echo ${!b[*]}   to return the same.  Unfortunately, it doesn't, but returns 0 instead.  Update  Given the replies, I now realise that my example was too simple, since of course, something like:  b=("${a[@]}")   Will achieve exactly what I said I needed.  So, here's what I was trying to do:  LIST_lys=(lys1 lys2) LIST_diaspar=(diaspar1 diaspar2)  whichone=$1   # 'lys' or 'diaspar'  _LIST=LIST_$whichone LIST=${!_LIST[*]}   Of course, carefully reading the Bash man page shows that this won't work as expected because the last line simply returns the indices of the "array" $_LIST (not an array at all).  In any case, the following should do the job (as pointed out):  LIST=($(eval echo \${$_LIST[*]}))   or ... (the route that I went, eventually):  LIST_lys="lys1 lys2" ... LIST=(${!_LIST})   Assuming, of course, that elements don't contain whitespace. Show that $$\int_{0}^{\infty} \frac{x - \sin(x)}{x^3} \, dx = \frac{\pi}{4}$$   My attempt is as follows: Let $$f(z) = \frac{z - i e^{iz}}{z^3}$$ and consider the contour on $[\epsilon, R]$ followed by a semicircular arc in the counter clockwise direction, then on $[-R, -\epsilon]$, then the semicircular clockwise contour avoiding the origin. We have, then, that  $$0 = \int_{\Gamma} f(z) dz = \int_{[\epsilon, R]} f(t) dt + \int_{C_R}f(Re^{it})Rie^{it}dt + \int_{[-R, -\epsilon]}f(t)dt + \int_{C_{\epsilon}}f(\epsilon e^{-it})\epsilon i e^{-it} dt$$  Then the first and third integrals ( $I_1$ and $I_3$) combine so that  $$I_1 + I_3 = 2\int_{\epsilon}^R \frac{t - \sin{t}}{t^3}\,dt$$  Further,   $$|I_{C_R}| \leq \int_0^\pi \left|\frac{Re^{it} - ie^{-R\sin{t}}e^{iRcos{t}}}{R^2 e^{2it}} \right|dt \rightarrow 0 \text{ as } R\rightarrow \infty$$  (I've omitted the details, it isn't too bad to bound)  However, I'm having trouble computing the limit  $$\lim_{\epsilon \rightarrow 0}\int_{C_{\epsilon}} f(\epsilon e^{-it})\epsilon i e^{-it} dt$$  No matter which way I look at it, it seems like this limit does not exist. Perhaps I'm seeing something wrong or have I chosen a bad $f(z)$? Produce an explicit bijection between rationals and naturals? Why $\dim U+\dim U^\perp=\dim V$? How do I get a file extension in PHP?