Using a string as reference to object
Dynamically access object property using variable
LaTeX/BibTex not arranging citations by order of appearance A current I flows through a solenoid (with n turns). Self inductance is $L$. If the magnetic flux is $\phi$, I am taught that $-n\phi=LI$  I dont understand the part with $n$, why do we have multiply by $n$? $\phi$ itself represents the whole magnetic flux there, if $\phi$ implied the flux only occurred by one coil, then it would be correct.   Moreover, flux change by a coil ($n$ turns) in $dt$ time is $d\phi$, so the induced electromagnetic force is   $$dE=n \cdot \frac{d\phi}{dt}$$   Why do we multiply by $n$ here? If $\phi$ means the whole flux, then why multiply? Fspy add-on not installing Conversion Error setting value for 'null Converter' - Why do I need a Converter in JSF? How can you sync Blender configs between multiple machines? I run Blender on several machines, it is a hassle to copy configs around, in order that you don't have to configure everything from scratch every time. Is there a sync functionality that does this? How to get the path of a running JAR file? 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} Counterexample: $G \times K \cong H \times K \implies G \cong H$ I am having a hard time finding a counterexample for the statement: $G \times K \cong H \times K \implies G \cong H$  I think this should be true for abelian, finite groups. But is this true in general? What would be a counterexample?  Any hints appreciated!  Thanks Learning development with Force platform. Any good books? I'm a bit familiar with Java and SQL, any good books to get on coding in Apex for salesforce? Function overloading in C How could I retrive full internal storage of an Android smartphone in order to restore data? A secant inequality for convex functions I just learned that using CBC encryption with an IV which is predictable is not secure.  From what I understand, using certain plain texts, and then guessing the IV that it uses, the attacker can verify if the IV he guessed was right. How does this qualify as an attack? The default font is too small on my screen at the resolution I have it, so I like to reset the font to size 12, but it appears I have to do this everytime I launch the program.  How do I make it remember my preferences? Automatically run commands over SSH on many servers There is a list of IP addresses in a .txt file, ex.:  1.1.1.1 2.2.2.2 3.3.3.3   Behind every IP address there is a server, and on every server there is an sshd running on port 22. Not every server is in the known_hosts list (on my PC, Ubuntu 10.04 LTS/bash).  How can I run commands on these servers, and collect the output?  Ideally, I'd like to run the commands in parallel on all the servers.  I'll be using public key authentication on all the servers.  Here are some potential pitfalls:   The ssh prompts me to put the given servers ssh key to my known_hosts file. The given commands might return a nonzero exit code, indicating that the output is potentially invalid. I need to recognize that. A connection might fail to be established to a given server, for example because of a network error. There should be a timeout, in case the command runs for longer than expected or the server goes down while running the command.   The servers are AIX/ksh (but I think that doesn't really matter. Python 3 with QGIS on Mac? I need to start learning Python, and I want to learn with version 3.x. I understand that QGIS--at least some plug-ins--relies on Python and Tcl/Tk, and probably on specific versions. Assuming that QGIS is dependent on Python 2, can anyone tell me how to set up parallel installations of Python 3 and Tcl/Tk such that QGIS will have what it needs and I can use Python 3 for other purposes? How do I completely remove Ubuntu? How to change Windows 7 date format? Is it possible to configure Windows 7 to use YYYY-MM-DD instead of DD/MM/YYYY as the date format? How? Where? Can X.org Load Two Different Drivers? (Triple-Head Setup with Intel and NVidia Card) We want to set up a 3 screens with an onboard intel graphics adapter and an nvidia card.  Both cards are recognized in lspci   01:00.0 VGA compatible controller: NVIDIA Corporation GT218 [GeForce 210] (rev a2) 00:02.0 Display controller: Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller (rev 09)   And bascially work: If I switch to the console, I see output on the Intel card, X is only running on the Nvidia card.  But when I type xrandr | grep conn I get only one connected port:   DVI-I-0 disconnected (normal left inverted right x axis y axis) VGA-0 disconnected (normal left inverted right x axis y axis) DVI-I-1 connected 1920x1200+0+0 (normal left inverted right x axis y axis) 518mm x 324mm HDMI-0 disconnected (normal left inverted right x axis y axis)   I am on Ubuntu 12.10 (and XFCE) and installed the proprietary nvidia driver.  I was assuming that X maybe has a problem to autodetect both cards, so I thought the following xorg.conf could help:   Section "ServerLayout"     Identifier     "Layout0"     Screen      0  "Screen0"     Screen      1  "Screen1"     InputDevice    "Keyboard0" "CoreKeyboard"     InputDevice    "Mouse0" "CorePointer" EndSection  Section "Files" EndSection  Section "InputDevice"     # generated from default     Identifier     "Mouse0"     Driver         "mouse"     Option         "Protocol" "auto"     Option         "Device" "/dev/psaux"     Option         "Emulate3Buttons" "no"     Option         "ZAxisMapping" "4 5" EndSection  Section "InputDevice"     # generated from default     Identifier     "Keyboard0"     Driver         "kbd" EndSection  Section "Monitor"     Identifier     "Monitor0"     VendorName     "Unknown"     ModelName      "Unknown"     HorizSync       28.0 - 33.0     VertRefresh     43.0 - 72.0     Option         "DPMS" EndSection  Section "Device"     Identifier     "Device0"     Driver         "nvidia"     VendorName     "NVIDIA Corporation"     BoardName      "GeForce 210" EndSection  Section "Screen"     Identifier     "Screen0"     Device         "Device0"     Monitor        "Monitor0"     DefaultDepth    24     SubSection     "Display"         Depth       24     EndSubSection EndSection   Section "Monitor"     Identifier     "Monitor1"     VendorName     "Unknown"     ModelName      "Unknown"     HorizSync       28.0 - 33.0     VertRefresh     43.0 - 72.0     Option         "DPMS" EndSection  Section "Device"     Identifier     "Device1"     Driver         "intel"     VendorName     "Intel"     BoardName      "Internal Intel Graphics" EndSection  Section "Screen"     Identifier     "Screen1"     Device         "Device1"     Monitor        "Monitor1"     DefaultDepth    24     SubSection     "Display"         Depth       24     EndSubSection EndSection   But it is still not working.   Is this generally possible to use two different drivers in X ? Is it necessary to create an xorg.conf manually then? (because Ubuntu 12.10 normally works without the xorg.conf) Are there any errors in my xorg.conf? Show that $a_n=\sin(n)$ does not converge     My idea:  Take two subsequences: $a_{n_k}=\sin(\frac {\pi k} 2)$ , $a_{n_l}=\sin(\frac {2\pi l} 3)$  So: $\forall n$ : $\lim_{n\to\infty} a_{n_k}=1$, $\lim_{n\to\infty} a_{n_l}=-1$  So two inifinite subsequence converge to different limits thus the sequence $a_n$ doesn't converge.   Is that correct ?  Edit:   The contrapositive of the defintion of a limit of a sequence:   $\exists\epsilon&gt;0 : \forall n\in N : \exists n&gt;N \Rightarrow |x_n-L|&gt;\epsilon$  Take $\epsilon =1$ and we know that $\sin(n)$ is bounded so lets take it's supermum: 1  $|1-1|&gt;\epsilon=1\Rightarrow 0&gt;1 \Rightarrow$ Contradiction.