Differential functional equation
Solving functional differential equation $f'(x)=2f(2x)-f(x)$
A real nxn matrix always has a real eigenvalue when n is odd what do it mean by "A real nxn matrix always has a real eigenvalue when n is odd?" Shouldnt it be that regardless of odd or even there will always have a real root?  hope to hear from you guys soon:) As of now, my desktop has begun showing the contents of my home folder (~) instead of the contents of ~/desktop. I must have changed something, but I have no idea what, or what I was doing exactly when it happened.  How do I re-point gnome to the right folder?  I'm running Ubuntu 11.04. "Arnold raced out of the door": grammatical or not? Why wasn't Restricted Section of the library better protected? "IllegalFormatConversionException: d != java.lang.String" when padding number with 0s? The characteristic and minimal polynomial of a companion matrix of a monic polynomial $f \in \mathbb F\left[x\right]$ in $1$ variable $x$ over a field $\mathbb F$ plays an important role in understanding the structure of finite dimensional $\mathbb F[x]$-modules.  It is an important fact that the characteristic polynomial and the minimal polynomial of $C(f)$ are both equal to $f$. This can be seen quite easily by induction on the degree of $f$.  Does anyone know a different proof of this fact? I would love to see a graph theoretic proof or a non inductive algebraic proof, but I would be happy with anything that makes it seem like more than a coincidence! I am writing out some parameters to JSON files using pythontex, but would like to add context information in form of section numbers (for example \thesection or \thesubsubsection, perhaps also the page number or other counters).  Is there a straightforward way to pass the values of the section counters to Python?   Josef Subscribe to a particular question by email (not RSS) Is there a standard place for placing custom Linux scripts? How to answer a negative question without ambiguity? I faced a problem to answer a negative question, for example, when someone asks you:      Don't you have any money?   It's a yes/no question but how should one answer the question without ambiguity?  When you answer "yes", does it mean "yes, I don't have any money"? or the other way "Yes, I do have money"? the questioner may think you are agreeing to the negative, that yes, you do not have any money.  I know it's better to answer with "on the contrary" but is it possible to answer yes or no? Custom post type - posts list - white screen of death i am getting a weird error - white screen in the list of posts for a specific Custom post type (just for that one)   tried deactivating all the plugins tried checking for error (debugging = true)   Still nothing the page just doesnt echos anything... (nothing in source too)  I am talking about such a url in the admin:     Here is register_post_type part i am using:    function register_submodelcpt() {     $labels = array(         'name'                  =&gt; __('Sub Models', THEME_NAME),         'singular_name'         =&gt; __('Sub Models', THEME_NAME),         'add_new'               =&gt; __('New Model', THEME_NAME),         'add_new_item'          =&gt; __('Add new Model', THEME_NAME),         'edit_item'             =&gt; __('Edit Model', THEME_NAME),         'new_item'              =&gt; __('New Model', THEME_NAME),         'all_items'             =&gt; __('All Sub Models', THEME_NAME),         'view_item'             =&gt; __('Watch Model', THEME_NAME),         'search_items'          =&gt; __('Search Models', THEME_NAME),         'not_found'             =&gt;  __('No Models found', THEME_NAME),         'not_found_in_trash'    =&gt; __('No Models found in trash', THEME_NAME),          'parent_item_colon'     =&gt; '',         'menu_name'             =&gt; __('Sub Models', THEME_NAME),      );      $args = array(         'labels'                =&gt; $labels,         'public'                =&gt; true,         'publicly_queryable'    =&gt; true,         'show_ui'               =&gt; true,          'show_in_menu'          =&gt; true,          'query_var'             =&gt; true,         'rewrite'               =&gt; array('slug' =&gt; 'submodels'),         'capability_type'       =&gt; 'post',         'has_archive'           =&gt; true,          'hierarchical'          =&gt; true,         'menu_position'         =&gt; 5,         'menu_icon'             =&gt; get_stylesheet_directory_uri().'/images/cpt/subcars.png',                     'supports'              =&gt; array('title', 'thumbnail', 'revisions', 'page-attributes')     );      register_post_type('submodelscpt',$args); } add_action('init', 'register_submodelcpt');   Did anyone encounter such an issuse? can you think of a reason this might happen?   Another weird thing when i change this:    To this:     The posts list loads correctly... Are submodules of finitely generated free modules always free? I don't believe it's true that all submodules of a finitely generated free module are free just based on results from google. Is there a canonical simple example of a finitely generated free module with a submodule that is not free? Do I make money in the stock market from other people losing money? What am I doing when I separate the variables of a differential equation? I see an equation like this:  $$y\frac{\textrm{d}y}{\textrm{d}x} = e^x$$  and solve it by "separating variables" like this:  $$y\textrm{d}y = e^x\textrm{d}x$$ $$\int y\textrm{d}y = \int e^x\textrm{d}x$$ $$y^2/2  = e^x + c$$  What am I doing when I solve an equation this way?  Because $\textrm{d}y/\textrm{d}x$ actually means  $$\lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}$$  they are not really separate entities I can multiply around algebraically.    I can check the solution when I'm done this procedure, and I've never run into problems with it.  Nonetheless, what is the justification behind it?  What I thought of to do in this particular case is write  $$\int y \frac{\textrm{d}y}{\textrm{d}x}\textrm{d}x = \int e^x\textrm{d}x$$ $$\int \frac{\textrm{d}}{\textrm{d}x}(y^2/2)\textrm{d}x = e^x + c$$  then by the fundamental theorem of calculus  $$y^2/2 = e^x + c$$  Is this correct?  Will such a procedure work every time I can find a way to separate variables? I want to transfer my current system hard drive to a larger hard drive. Doing so, I thought of creating an image of my system hard drive which is 320 GB in size.   Would I be able to restore this image on a larger hard drive? I plan buying a 1TB hard drive.  If yes, how? I prefer no data loss.  I am using Windows 7 How did Walter White poison that character? I've seen Breaking Bad complete series 2-3 times, but I never found out how Walter White was able to poison Brock.  I mean did he himself directly feed the Valley of the Lilly berries to Brock or did he let Saul do the work? I can't figure it out. Can I run a natural gas dryer from a portable propane tank? How do open files behave on linux systems? I have Solaris 8 OS installed in French.  Is it possible to switch from French to English without reinstalling the OS ? If yes how ?  When locale -a i have this :  POSIX common en_US.UTF-8 C iso_8859_1 en_CA en_CA.ISO8859-1 en_US en_US.ISO8859-1 en_US.ISO8859-15 en_US.ISO8859-15@euro fr_CA fr_CA.ISO8859-1 iso_8859_15 th th_TH th_TH.TIS620   Even when I try to edit /etc/default/init with :  LANG=en_US.ISO8859-15 LC_COLLATE=en_US.ISO8859-15 LC_CTYPE=en_US.ISO8859-15 LC_MESSAGES=en_US.ISO8859-15 LC_MONETARY=en_US.ISO8859-15 LC_NUMERIC=en_US.ISO8859-15 LC_TIME=en_US.ISO8859-15 LC_ALL=en_US.ISO8859-15   and reboot : nothing happens.  To verify the result i always use date and when i reboot : i also have the date in french.  P.S : I have to do this configuration in a computer which isn't here in my office, so i have to this manipulation in a an another computer here in my office and if it works, i'll do it to the other computer.  So the computer here is configured in English and i have to switch it to French. Here is the content of my ~./dt :  C                     errorlog              sessionlogs Desktop               errorlog.old          sessions Trash                 errorlog.older        simulateur.dtwmrc appconfig             help                  startlog appmanager            icons                 startlog.old asr.dtwmrc            outils.dtwmrc         startlog.older bin                   palettes              tmp bookmarks             sdtfonts              types dtwmrc                sdtpcaction.conf      wsmenu en_US.ISO8859-15      sdtpcaction.conf.bak   Thanks TeXnicCenter & Adobe Acrobat 10