Improve security of contact form
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Aromatic rings resized with chemfig When I want to reduce the size of a molecule drawn with  I usually put a [scale=0.xx] before the argument of the command. However when I deal with aromatic rings this method doesn't work well, in fact only the carbon skeleton is resized: the 'aromaticity' is not and it's also out of center.  For example:  \chemfig[][scale=0.75]{**6(-------)}\quad   gives me:     How do I achieve a complete resize? Derivation of survival copula $$ \begin{align}F(x,y) &amp;= P(X\leq x, Y\leq y) \\  &amp;= C(F(x), F(y)) \end{align}$$ The copula of a bivariate distribution is equal to its CDF, $C(u,v) = F(x,y)$. The density of the data's CDF therefore can be expressed as $$f(x,y) = c(u,v) \times f_X(x) f_Y(y)$$ where $c(u,v)$ is the copula density and $f_X(x)$ is a marginal. If $\hat{C}(u,v)$ is the survival copula for determining $$ \begin{align}\bar{F}(x,y) &amp;= P(X&gt; x, Y &gt; y) \\  &amp;= \hat{C}(1-F(x), 1-F(y)) \end{align}$$ how is the first equation of the ordinary copula, $C(u,v)$, linked to the survival copula as $$\hat{C}(u,v) = u + v - 1 + C(1-u,1-v)$$ are $u$ and $v$ merely vectors containing the (ranked) observations of the uniform marginals? A derivation in integrals and probabilities (rather than $F$s) would be good. Possible Duplicate:          I tried to color only a cell of my table but I don't know how do it. I found the method to color an entire row.How could I color only a cell of my table of a precise color? Finishing a proof: $f$ is injective if and only if it has a left inverse I've already done a lot of searching (in particular: ) to try to prove this statement:      $f: A \to B$ is injective if and only if it has a left inverse. [I'm going to also assume $A$ and $B$ are nonempty.]   My attempt so far:     $\Leftarrow$ Suppose $f$ has a left inverse and $f(a_1) = f(a_2)$ for    $a_1, a_2 \in A$. Then there is a function $g: B \to A$ such that   $g\left(f(a_1)\right) = a_1$ and $g\left(f(a_2)\right) = a_2$. Since   $g$ is well-defined, it follows that $g\left(f(a_1)\right) =  g\left(f(a_2)\right)$, and hence $a_1 = a_2$.         $\Rightarrow$Now   suppose $f$ is injective. Then $f(a_1) = f(a_2) \implies a_1 = a_2$.   Furthermore, since $A$ is nonempty, there is an element $x \in A$.   Define $g: B \to A$ by  \begin{equation*} g(b) = \begin{cases}  f^{-1}(b), &amp; b \in \text{Im}(f) \\ x, &amp; b \in A \setminus  \text{Im}(f)\text{.} \end{cases} \end{equation*} This mapping is   well-defined, since if $f$ is injective, $f^{-1}(b)$ is unique.   My main question: does this imply that if $f: A \to B$ is injective that any mapping $g: \text{Im}(f) \to A$ is bijective? Otherwise, I don't understand why we can even use $f^{-1}$ on an element. [Please read the link above for more details - in proof 1.] Linear functional on a Banach space is discontinuous then its nullspace is dense. Drawing a square root spiral What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results? The closest I can get to making mesh lights affect their environment in Blender Eevee is giving them an Emission material and turning on "Bloom". But this isn't emitting proper light, it just looks like it is, but it doesn't light the surroundings whatsoever.     I would like to be able to light a scene with meshes without having to put point lamps everywhere just to make them emit light. Let $\Bbb R^+$ be the set of positive real numbers. Use Zorn's Lemma to show that $\Bbb R^+$ is the union of two disjoint, non-empty subsets, each closed under addition. How can I recover deleted photos from an SD Card? My technophobe mother returned from a European trip to discover she'd erased all but 15 images from a nearly full 2GB card. As I am the computer guy in the family, she posted the card to me and asked that I make something magical happen.  The photos were taken with and deleted by a Nikon Coolpix. (I don't know the model.)  I am a Linux guy, but there is a Windows Vista box at my disposal.  What is my best strategy to try to recover something? I am using eclipse and i get this error--I think it's an error with the way i imported becker.robots Should I include a link to my Stack Overflow profile on my résumé? Various \textcolor within lstlisting? I'm a bit confused about what Gstreamer does.   Does it come installed by default with Ubuntu ?  If so which version  is the default for 14.04?  Does it provide hardware accelerated video playback (decoding) ?   If so does it work with VA-API and VDPAU or is it an alternative to those?    Thanks for your help $X$ and $Y$ are independent rv having pdf $f(t)=\frac{1}{\pi} \frac{1}{1+t^2}$ determine pdf of $Z=\frac{X+Y}{3}$ Using restroom on airplane while fasten seatbelt light is on? This question about  over on  made me wonder what a passenger is supposed to do when they urgently have to use the restroom while the fasten seat belt light is on. FAA regulations require passengers to obey the seat-belt sign, even if flight attendants do not.  I saw this happen on a flight where an older gentleman asked the flight attendant if he could use the restroom, and she said "not until the light is off". The flight had been free of turbulence for 15 minutes or so by this time, and the flight attendants were walking freely throughout the cabin, collecting post-meal trash, etc. The gentleman who asked to use the restroom appeared to be in quite some discomfort, and practically ran to the restroom when the light went off 10 minutes later.  So what is a passenger supposed to do when he isn't permitted to use the lavatory, when he has to go and can't wait? Just go in their seat? How does a credit card company make any money off of me using their card if there are no fees associated with the card (I don't pay any extra) and I pay off my balance on time every month (so I don't pay any fees ever for this either).  Are they just banking on the fact that many people don't do this and end up owing them money? What terminal command or program can list an SSD's Power On Hours? I'm looking to script using the unix shell the retrieval of SSD (and HDD) data that disk utility shows in the information window.    I'm immediately interested in the Power On Hours and Power Cycle, but if all the data comes from one data structure or tool, so much the better. The usual tools diskutil info disk0 and ioreg -l are not producing the "of interest" values listed in the screen shot above.  Is this information available from any of the built in OS X terminal tools or do I need to locate an open-source package that makes the same API calls to get this level of detail about a Mac drive? Why Multiplication of zero by any number is zero? If I multiply $a$ by $0$, it means $a$ is added $0$ times, but I am not able to visualize $0$ times! Is the uncertainty principle just saying something about what an observer can know or is it a fundamental property of nature? I ask this question because I have read two different quotes on the  that don't seem to match very well. There are similar questions around here but I would like an explanation that reconciles these two interpretations specifically:   Feynman talks about the uncertainty principle in one of his lectures and mentions it as the reason why electrons don't crash into the atom's nucleus: If they did they would have an exact location and momentum which is not allowed by the uncertainty principle. In saying this it is clear that the uncertainty principle is a fundamental property of nature because it has an effect on where an electron can reside. Recently I read - somewhere else but I forgot where exactly - an account of the uncertainty principle where there was explained how we can measure position of a particle by firing another particle into it, the collision disturbs the velocity of the observed particle therefore we can not know its momentum anymore.   Now, 2) very much seems like a limitation of what the observer can know, while 1) attributes a fundamental property of nature to it (electrons don't crash into the nucleus). What is the correct way to think about this?