While browzing through my Windows directory, I found the Panther subdirectory, which had this icon:    Does anyone know what this signifies? I was able to open it normally, and it was, to all appearances, a normal directory.
On some icons I am seeing a two blue arrows at the top the right pointing towards each other. I first noticed it on the icons on folders which I archived which happened randomly. I archived the folder and the text went blue as expected, then when I went to the folder again the text was black and the folder icon has these arrows. When I just recently installed Office 2007, I noticed the same arrows on the icons for the programs. OS: Windows 10 Pro 64-bit (the latest update: 1115) Application: Microsoft Office 2007 suite and file explorer
Prove 24 divides $u^3-u$ for all odd natural numbers $u$ At our college, a professor told us to prove by a semi-formal demonstration (without complete induction):   For every odd natural: $24\mid(u^3-u)$   He said that that example was taken from a high school book - maybe I din't get something, but I really have no idea to prove that without using complete induction.  Any idea of smart demonstration?  Thanks for your help. (Excuse my bad English.) When and how did "pretty" enter English as an intensifying adverb? I created a simple service layer polygon in network analyst (ArcGIS Desktop 10.2) with no hierarchies set in the street network. Now I don't understand why is this polygon created along some particular streets?   Why isn't is properly spread out? For example, why doesn't the polygon cover the areas/streets I have marked in red? Obviously those marked areas are also within 1 km.  The impedance is 1 km and 2 km respectively.   The streets are also well connected individual line elements as you can see the junctions. How would you go about proving that $$\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$$  for any two integers $a$ and $b$?  Intuitively it is true because when you divide $a$ and $b$ by $\gcd(a,b)$ you cancel out any common factors between them resulting in them becoming coprime. However, how would you prove this rigorously and mathematically? Filling a conical tank I have been working on this problem for about 2 hours and I can't seem to get it, here is exactly what the question reads. "Water is poured into the top of a conical tank at the constant rate of 1 cubic inch per second and flows out of an opening at the3 bottom at a rate of .5 cubic inches per second. The tank has a height of 4 inches, and a radius of 2 inches at the top. How fast is the water level changing when the water is 2 inches high?" When do we still need the table and figure environments when we don't want the enclosed objects to float? The LaTeX Wikibook :     Please understand: you do not have to use floating tables. It only   looks more professional. If you want to place your tables where they   lie in your source code, do not use table at all! This is a very   common misunderstanding among newcomers.   LaTeX works with an intricate , but I often prefer immediate placement with the H placement specifier (enabled by the float package).  My understanding is that captions and table/figure numbering require the table/figure environments. Is this really so, or are there ways around that? What other reasons are there for using table/figure if we know that we don't want a particular object to float? From the limit definition of differentiability, determine where the function $f(x) = \sqrt{x}$ is differentiable? For the function $f(x) = \sqrt{x}, \hspace{2 mm} f: [0, \infty) \rightarrow \mathbb{R}$, I wish to find all points $a$ at which $f(x)$ is differentiable, from the definition $$ f'(x) = \lim_{x \rightarrow a}\frac{f(x)-f(a)}{x-a} $$  Clearly, for our function $f(x) = \sqrt{x}$, this gives us $$ f'(x) = \lim_{x\to a}\frac{\sqrt{x} - \sqrt{a}}{x-a} $$  So the question boils down to showing for what values of $a$ this limit exists. How would this be done? Intuitively, I know that the answer is that the limit exists for all $a \in [0, \infty)$ and is given by $\frac{1}{2 \sqrt{a}}$, but I'm unsure of how to prove this from the limit definition of differentiability. Fill the area determined by two pgfplots graphs I need to fill the region determined by two (Gaussian) curves and the right red line (the region is brushed in green in the figure below). I also wonder what is the best way to draw vertical line which goes through the intersection of both graphs (the left red line on the figure).  Any pointers would be greatly appreciated.    My initial attemt is pasted below.  \documentclass{standalone} \usepackage{pgfplots}  \begin{document}  \pgfmathdeclarefunction{dnorm}{2}{%   \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}% }  \begin{tikzpicture} \begin{axis}[domain=0:12, samples=100, height=5cm, width=10cm] % Fill aread under the curves \addplot [fill=red!20, draw=none, domain=0:6] {dnorm(6.5,1.5)} \closedcycle; \addplot [fill=blue!20, draw=none, domain=6:10] {dnorm(4,1)} \closedcycle; % Draw curves \addplot [thick] {dnorm(4,1)}; \addplot [thick] {dnorm(6.5,1.5)}; \end{axis} \end{tikzpicture}  \end{document}   My solution  A picture is worth a thousand words. Code is pasted below.   \documentclass{article} \usepackage{tkz-fct} \usetikzlibrary{intersections}  \begin{document}  \tikzset{    name plot/.style={every path/.style={name path global=#1}} }  % Extract coordinates for point X \makeatletter \newcommand{\gettikzxy}[3]{%   \tikz@scan@one@point\pgfutil@firstofone#1\relax   \edef#2{\the\pgf@x}%   \edef#3{\the\pgf@y}% } \makeatother  % Dimlines \def\Dimline[#1][#2][#3][#4]{ \begin{scope}[thin, &gt;=stealth'] % redefine as flechas \draw let \p1=#1, \p2=#2, \n0={veclen(\x2-\x1,\y2-\y1)} in [|&lt;-&gt;|, decoration={markings,mark=at position .5 with {\node[#3] at (0,0) {#4};}, }, postaction=decorate] #1 -- #2 ; \end{scope} }  \begin{tikzpicture}[scale=1,font=\small] \tkzInit[xmin=0,xmax=12,ymin=0,ymax=.3,ystep=.05] % Draw coordinates \draw[&gt;=stealth', &lt;-&gt;] (0,6) node[above] {$y$} -- (0,0) --  (12.5,0) node[right] {$x$}; % Draw functions and areas \tkzFct[name plot=A,thick,color=red,domain=0:12]{1/(1.5*sqrt(2*pi))*exp(-((x-4.5)**2)/(2*1.5**1))} \tkzDrawArea[opacity=.3,color=blue,domain = 7:12] \tkzFct[name plot=B,thick,color=blue,domain=0:12]{1/(2*sqrt(2*pi))*exp(-((x-7)**2)/(2*2**1))} \tkzDrawArea[opacity=.3,color=red,domain=0:7] \tkzDrawAreafg[between=b and a,opacity=.3,color=green,domain = 0:7] % Intersection between curves \path [name intersections={of=A and B,by=C}]; % Extract coordinates of C \gettikzxy{(C)}{\cx}{\cy} % Vertical lines \draw [thick,dashed, black] (\cx,0) -- (\cx,5.5) node [above] {$x_{0}$}; \draw [thick,dashed, black] (7,0) -- (7,5.5) node [above] {$\hat{x}$}; % Define regions \Dimline[($(0,0)+(0,-.6)$)][($(7,0)+(0,-.6)$)][above,black][$\mathcal{R}_{1}$]; \Dimline[($(7,0)+(0,-.6)$)][($(12,0)+(0,-.6)$)][above, black][$\mathcal{R}_{2}$]; \end{tikzpicture}  \end{document} How to download a whole FTP site using command line? I need to download an FTP site (a web site source code actually) containing a very high quantity of relatively small files (downloading it with FileZilla took more than a day, but I believe it could be downloaded much faster if many files were downloaded at once). Unfortunately there is no SSH access to the site and no way to archive the files on the server side.  So at least the question is how to download a whole FTP site into a folder using command line tools. A better it'd be if the download could be parallelized by downloading many files simultaneously instead of one by one. I have a ListBox DataTemplate in WPF. I want one item to be tight against the left side of the ListBox and another item to be tight against the right side, but I can't figure out how to do this.  So far I have a Grid with three columns, the left and right ones have content and the center is a placeholder with it's width set to "*". Where am I going wrong?  Here is the code:  &lt;DataTemplate x:Key="SmallCustomerListItem"&gt;     &lt;Grid HorizontalAlignment="Stretch"&gt;         &lt;Grid.RowDefinitions&gt;             &lt;RowDefinition/&gt;         &lt;/Grid.RowDefinitions&gt;         &lt;Grid.ColumnDefinitions&gt;             &lt;ColumnDefinition/&gt;             &lt;ColumnDefinition Width="*"/&gt;             &lt;ColumnDefinition/&gt;         &lt;/Grid.ColumnDefinitions&gt;         &lt;WrapPanel HorizontalAlignment="Stretch" Margin="0"&gt;             &lt;!--Some content here--&gt;             &lt;TextBlock Text="{Binding Path=LastName}" TextWrapping="Wrap" FontSize="24"/&gt;             &lt;TextBlock Text=", " TextWrapping="Wrap" FontSize="24"/&gt;             &lt;TextBlock Text="{Binding Path=FirstName}" TextWrapping="Wrap" FontSize="24"/&gt;          &lt;/WrapPanel&gt;         &lt;ListBox ItemsSource="{Binding Path=PhoneNumbers}" Grid.Column="2" d:DesignWidth="100" d:DesignHeight="50"      Margin="8,0" Background="Transparent" BorderBrush="Transparent" IsHitTestVisible="False" HorizontalAlignment="Stretch"/&gt;     &lt;/Grid&gt; &lt;/DataTemplate&gt; If $(1), (log_yx), (log_zy), (-15log_xz)$ are in Arithmetic Progression... If $(1), (log_yx), (log_zy), (-15log_xz)$ are in AP then...   (A)$z^3=x$   (B)$x=y^{-1}$   (C)$z^{-3}=y$   (D)$x=y^{-1}=z^3$   (Multiple answers may be correct)   I tried many approaches, one of them being: $1+log_zy=2log_yx$ $log_zz+log_zy=log_yx^2$ $log_z(yz)=log_yx^2$ But the fact that the bases are different is causing the main problem as I don't know how to proceed further. It would be great if anybody could give me a hint for solving such questions. I know the usage of     This is a new car.   This is singular.     These are some books for you.   These is plural.  Shall we use   There exists some people who agree with me. There exist some people who agree with me.   Which one is the correct usage and why? If we have a point charge and outside of it we have a non-conducting Gaussian sphere, then Gauss's law says that the net flux should be zero. I agree that the total field lines coming in are equal to the number of field lines coming out, but isn't it true that the magnitude of the electric field at those segments of the sphere where the field is coming in is greater than those where it is coming out? So when we integrate, wouldn't these areas, having a greater electric field, contribute more to the net flux? I don't see why they would cancel each other out. How can I stand on the ground? EM or/and Pauli? "Improve" treated as improper response to proper response to audit I have recently installed a custom ROM and cannot find the Play Store. It seems like all apps that belong to Google are missing.  How can I install the Google Apps Package (Play Store, ...) on my Android device? Is there a way to disable recovery mode so it won't be possible to factory reset your phone?  Basically what I am trying to do, is that it should be impossible to factory reset the phone as there is no recovery partition.  (Example format the recovery partition, or hide the option of factory reset on the recovery menu, build a custom recovery etc.)  P.S.. I was thinking of maybe removing a system app (example package installer) and making it a user app, and therefore when you factory reset the phone it won't start cause the system app is missing, but when I tried that, the phone wouldn't start even without resetting it, as the system needs the system app to start, ( I thought that maybe even though I removed the app from being a system app, the phone would still start as it's still there as a user app, and only after resetting the phone - that the user apps get deleted, the phone won't start as it's missing the app).  Thanks in advance Is $\exists x(x=a)$ a valid formula in first order logic with equality? How do I extract all the external links of a web page and save them to a file? regexp in ksh for extensions tgz, tar.tgz I'm trying to get a regexp (in ksh) to identify files with only the following extensions: tgz, tar.gz, TGZ and TAR.GZ. I tried several but can't get them to work. I'm using this regexp to select only files files with those extensions to do some work with them:  if [ -f $myregexp ]; then    .....  fi