Irreducible polynomials?
Family of irreducible polynomials
After running a VM and logging out, I got a black screen. I powered off and re-started but got the same after the bios option in start up passed. Several attempts went bye with the same result. So I fiddled with bios boot options a bit and was able to get to a different looking Ubuntu start up screen which, after entering pass key would run a series of commands that were too numerous and frantic to make out. They appeared to be overlapped/layered (the text that is) and seemingly repeating endlessly. I had to power down to get it to stop and re-booting just had the same effect. Finally, I hit the down arrow key when prompted for "disk sda5_crypt" at the pseudo Ubuntu log-in screen I mentioned before. This brought me to an all black screen which read something like:  lvmetad not active cannot process volume group "umbuntu-vg" unlock disk sda5_crypt**   From here I entered a password and Ubuntu start up ran.  That was an unsettling hour or so and I'd like to avoid that in the future. Any ideas what caused it and how to avoid it going forward?  Should have said this before but Ubuntu is the only OS on my machine and my optical drive cannot be opened manually. I would like to be able to change the default CSS used by chrome, such as removing the underlines for links, etc. However, I cannot find the default CSS file used by Chrome. Does anyone know where it is? How to launch the default (native) application for a given file from Java? In Walter Rudin's Principles of mathematical analysis Exercise 5.21, it is proved that for any closed subset $E\subseteq \mathbb{R}$, there exists a smooth function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$.   Since $E^c$ is open in $\mathbb{R}$, $E^c$ is a countable disjoint union of open intervals $(a_i,b_i)$. On an interval $(a,b)$, if we let $f(x)=\exp(\frac{1}{(x-a)(x-b)})$, $x\in(a,b)$; $f(x)=0$, $x\notin(a,b)$, ($f(x)=\exp(\frac{1}{(x-a)})$ or $f(x)=\exp(\frac{1}{(x-b)})$ on $(a,\infty)$ and $(-\infty,b)$ resp.), then $f$ is smooth. Hence we can get a smooth function on $\mathbb{R}$ such that $E$ is the zero point sets of $f$.  (1). How about a closed subset $E$ of $\mathbb{R}^n$? is it true that for any closed subset $E\subseteq \mathbb{R}^n$, there exists a smooth function $f$ on $\mathbb{R}^n$ such that $E=\{x\in \mathbb{R}^n\mid f(x)=0\}$?  An open set in $\mathbb{R}^n$ cannot be written as a disjoint union of countable open balls hence the proof above is not valid. The partition of unity only claims that for an  open set $U$, there exists open $V$ in $U$ such that $\bar V\subseteq U$ and a smooth function $f$ on $\mathbb{R}^n$ such that $supp f\subseteq U$, $f|_V=1$.   (2). The taylor series of $f(x)=\exp(\frac{1}{(x-a)(x-b)})$ does not converge around points $a,b$ hence $f$ is not analytic at $a,b$. Is it true that for any closed subset $E\subseteq \mathbb{R}$, there exists an analytic function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$? Not all files are visible over MTP I have LG L5 (e610 model) device with Cyanogenmod 10. When I connect the phone to a computer with Linux (I have mtpfs installed), I can see both internal storage and the SD card.  However when I navigate inside them, I can't see some of the files.  For example, if I open file manager app on the phone, I can see several files in the Internal storage/Notifications directory, however the directory on the computer only shows one of those files.  If I switch USB connection type to PTP (camera) - as OS X doesn't support MTP natively - Image Capture sees the phone as a camera, however it can only see about a third of all the images present on the phone.  I don't have a Windows machine to try, but I suspect the results would be similar.  I tried upgrading Cyanogenmod to the latest nightly, clearing and reinstalling it - same results.  Any idea as to what is going on?  How can I make all files appear on the host computer? Is there a better name for this than "emphatic and"? In semi-poetic writing, I have had occasion to deviate from the standard prose list practice (interpose commas or semicolons between items, with an "and" preceding the final item), by utilizing a second or third and to separate three or four items.  That is,       Bob likes beer, wine and liquor.   The variant would be:     Bob likes beer and wine and liquor.   Now, the usage is obviously nonstandard and should be avoided in formal writing, but for those instances where poetic variation may be justified.    What is it called?  "Emphatic And" is the best I can coin on my own, but I wonder if there is a more established name for this variation. How can one refute John Searle's "syntax is not semantics" argument against strong AI? I think we need a button that says Edit and Close added to the Review Close button options.  Many of these closed posts will be around forever (and should be, closed should not just be a path to deletion), so they need editing.  If I edit it now it goes away, with the only option being a back click to get back to the review, and then click into the post and edit it.  We have an Edit and Reopen button, so this would fit in just fine. Multiple two pin multi-color LEDs pattern - how does this work? Let's say I have Table A: BookingsPerPerson  Person_Id    ArrivalDate    DepartureDate 123456       2012-01-01     2012-01-04 213415       2012-01-02     2012-01-07   What I need to achieve with a view is the following:  Person_Id    ArrivalDate    DepartureDate    Jan-01    Jan-02    Jan-03    Jan-04    Jan-05    Jan-06    Jan-07 123456       2012-01-01     2012-01-04       1         1         1         1 213415       2012-01-02     2012-01-07                 1         1         1         1         1         1   The system is for events, so each hotel booking could take anything between 1 to 15 days but no more than that. Any ideas would be very much appreciated. How to increase the width and height of the Rich Text area field in Visual force Page? Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.   I was thinking of showing $A$ is not invertible, meaning it has an eigenvalue of $0$. Since no matter the power you give to $A$, it is still not the identity, you can deduce that at least one eigenvalue is indeed $0$. However this doesn't work if you have different eigenvalues in the Matrix, so I got stuck.  Help will be most appreciated. How can I escape white space in a bash loop list? I have a bash shell script that loops through all child directories (but not files) of a certain directory.  The problem is that some of the directory names contain spaces.    Here are the contents of my test directory:  $ls -F test Baltimore/  Cherry Hill/  Edison/  New York City/  Philadelphia/  cities.txt   And the code that loops through the directories:  for f in `find test/* -type d`; do   echo $f done   Here's the output:   test/Baltimore test/Cherry Hill test/Edison  test/New York City test/Philadelphia   Cherry Hill and New York City are treated as 2 or 3 separate entries.  I tried quoting the filenames, like so:  for f in `find test/* -type d | sed -e 's/^/\"/' | sed -e 's/$/\"/'`; do   echo $f done   but to no avail.  There's got to be a simple way to do this.    The answers below are great.  But to make this more complicated - I don't always want to use the directories listed in my test directory.  Sometimes I want to pass in the directory names as command-line parameters instead.  I took Charles' suggestion of setting the IFS and came up with the following:  dirlist="${@}" (   [[ -z "$dirlist" ]] &amp;&amp; dirlist=`find test -mindepth 1 -type d` &amp;&amp; IFS=$'\n'   for d in $dirlist; do     echo $d   done )   and this works just fine unless there are spaces in the command line arguments (even if those arguments are quoted).  For example, calling the script like this: test.sh "Cherry Hill" "New York City" produces the following output:   Cherry Hill New York City Help with math symbols in BibTeX I am writing a PhD thesis using LaTeX. Every thing is going fine, but I have problem with the output of the mathematical symbols in the references lists. I copy one example from the Pdf file to make it clear for you. You can see that the fraction remains the same.      [1] Mezzacapo, F. and Cirac, J. I. (2010) Ground-state properties of   the spin-\frac{1}{2} antiferromagnetic Heisenberg model on the   triangular lattice: a variational study based on entangled-plaquette   states. New. J. Phys., 12,   103039.   You can see below the all the packages I use:  \documentclass[12pt,PhD,twoside,a4paper]{GB_muthesis}%[10pt,PhD, singlespace] \usepackage[pdftex]{graphicx} \usepackage[bookmarks=true,colorlinks=true,linkcolor=blue, urlcolor=blue,citecolor=blue]{hyperref} \usepackage[numbers,comma, sort&amp;compress]{natbib} \usepackage{amsmath} \usepackage{amssymb} \usepackage{mathtools} \usepackage{rotating} %\usepackage{GE_manthesis} \usepackage{GB_thesis} \usepackage{bm} \usepackage{fmtcount} \usepackage{setspace} \usepackage{chapterbib} \usepackage{subfigure}% allow subfigures \usepackage{amsfonts} \usepackage{url, enumitem} \usepackage{lscape} \usepackage{notoccite}%This package is for ingnoring the citation in the caption of the figures and tables. \begin{document} What to do when I get an "attempt to read or write outside of disk 'hd0'" error and Boot Repair does not solve the problem? How can I have a different input method for each app window on windows 8. When I change input language to ENG all app window also uses this method and I don't want that. Like windows 7 that has a different input method for this purpose. thanks Using wp_query is it possible to orderby taxonomy? My question is simple, I'm using WP_Query to retrieve some custom type posts filtering by a taxonomy using tax_query.  Now my problem is I would like to orderby the taxonomy, but from documentation and searching on the web I can't find a solution.  The orderby in WP_Query lets you order by a bunch of fields even custom meta fields but it doesn't seem to support taxonomy.  Any pointers in the right direction?  Thank you all. SED: insert text after the last line? This  inserts a tag to the beginning of a file:  sed -i "1s/^/&lt;?php /" file   How can I insert something to the end of each file with sed? Using Squeeze Theorem to show the following limits Consider a function f (x) defined on R satisfying:   for all x distinct 0.  Calculate: lim f(x) with x→∞ and limf(x) with x→−∞   Issue information:   if x → ∞ then we can consider | x | = x  if x → -∞ then we can consider | x | = -x  I can use x² = | x |? Simplify $\sum (x_i- \mu)^2$ How can I simplify this relation? $$\sum_{i = 1}^m(X_i-\mu)^2=\sum_{i = 1}^m(X_i-\bar{X}_m)^2+m(\bar{X}_m-\mu)^2$$ I know how to set up: $$\sum_{i = 1}^m(X_i-\mu)^2=\sum_{i = 1}^m[(X_i-\bar{X}_m)+(\bar{X}_m-\mu)]^2$$ but when I open the bracket, how do I handle the mixed term? $$2\sum_{i = 1}^m(X_i-\bar{X}_m)(\bar{X}_m-\mu)$$  Thank you!