QGIS print composer layout with several data frames: is it possible?
Adding Multiple Maps in QGIS Composer?
Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$ I was surprised to find that standalone package can not compile a document with an equation:  \documentclass{standalone} \begin{document} \begin{equation} % not working! F(V, T) = E(V) + D(T) \end{equation} \end{document}   Is there an option or some workaround that allows this? The current error is something like:   ! Missing $ inserted.   in line 4. (The idea of course is that the including (main) document can just \input the standalone without knowing if is going to be an equation or something else) Correct formula for LED current-limiting resistor? How to ensure all data has been physically written to disk? I understand that .NET FileStream's Flush method only writes the current buffer to disk, but dependent on Windows' disk driver and the hard disk firmware this is no guarantee that the data is actually physically written to disk.  Is there a .NET or Win32 method that can give me this guarantee? So if there is power loss one nanosecond after the call to this method comes back, I can still be sure that everything is OK? Which OpenType Math fonts are available? To give you some background, I have a grasp on the basics of statistics and probability theory and even remember touching Bayes theorem at the university data mining course. But being a few years away from the university made my math got extremely rusty (so much for last-minute pre-exam cramming). While I remember various random basic concepts, there are a lot of gaps in my understanding of them.  What would be a good material (a book, a site, or otherwise equally accessible medium) to revise the fundamentals and go beyond basics? I'd like a book that can be actually read as a book (most statistics books are really dry and are close to being reference material, rather than a book). Is this a correct demonstration for why elements above untriseptium cannot exist? With the confirmation that elements 113, 115, 117, and 118 are indeed fundamental elements that are now to be named on the periodic table, the next question is: what is the highest atomic number possible for an element? Feynman had a go at this years ago, and he derived (according to my limited understanding) that above element-137 (informally denoted 'Feynmanium') the electrons in the nearest orbit about the nucleus would be traveling at a velocity greater than the speed of light. (Note I am considering the Bohr model of the atom in this question.) I wished to demonstrate to my friends why this is and I came up with the following explanation.  According to Bohr's quantum condition, the angular momentum of an electron about the nucleus is given by $$ L=m_evr_n=n\hslash \implies r_n=\frac{n\hslash}{m_ev},$$ where $m_e$ is the mass of the electron, $v$ its velocity, $n$ an integer, and $r_n$ the radius of the $n$th possible orbit. Because we are concerned with the nearest orbit to the nucleus, $n=1$; and thus $$r=\frac{\hslash}{m_ev}.$$   Now, according to Coulomb's law, if the electron orbits about the nucleus the centripetal motion can be described by $$\frac{Ze^2}{4\pi\epsilon_or}=m_ev^2, $$ where $Z$ denotes the number of protons in the nucleus (the atomic number), and $e$ the elementary charge. Solving for $Z$ and substituting in $r$ from above yields $$Z=\frac{4\pi\epsilon_o \hslash v}{e^2}. $$ But what is $v$? Well, the maximum velocity an electron could ever have is the speed of light, and we wish to find the atomic number associated with an orbiting electron traveling at this speed, so we set $v=c$ and obtain our final result of $$Z=\frac{4\pi\epsilon_o\hslash c}{e^2}\approx 137.521,$$ which implies that for $Z&gt;137$, the electrons at a position of $n=1$ in the Bohr model would have a velocity $&gt;c$; and thus the highest atomic number achievable on the periodic table is 137.  Again, I just want to make sure this is a correct method for deriving element-137 before presenting. Perhaps one could explain how relativity plays a role here. I know Feynman used the Dirac equation to get this result...so could anyone (subsequently of course) expatiate on this in a simplistic manner? Thanks! How to force restart an iPhone with broken home button Earlier today I was on my iPhone and it randomly froze so I turned it off. When I went to unlock it it wouldn't move. I couldn't unlock it or tap anything. So now I can only stay on the lock screen. I read on the Apple website that I should "force restart" it by pressing my home button and power button at the same time. The problem is my home button is stuck and doesn't work. What should I do? Collage of six photos, not Facebook Lookback movie Update Manager is constantly offering me updates (e.g. security fixes, updates from PPAs).  How can I tell my Ubuntu installation to automatically download and install updates whenever they become available? How can I copy the contents of a folder to another folder in a different directory using terminal? I am trying to copy the contents of a folder to another folder in a different directory using terminal.  Would somebody be able to provide me an example of the command line syntax required to achieve this? I'm getting the following error when i try and install MSSQL 2008 on Windows Server Standard 2008 R2: Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$ If $x_1,...,x_n$ are positive real numbers and if $y_k=1/x_k$, prove that $$\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2.$$   I've been learning induction, and I've come across this problem that I really can't even break down and begin to think about. I've been told it has something to do with Cauchy-Schwarz, but I cannot figure out how to apply it. I would appreciate help figuring out how to go about and formulate this proof. Thanks! Get e-mail addresses from Gmail messages received I have no idea how prove that $$\{(z_0,\ldots,z_n)\in\mathbb{C}^{n+1} \quad| \quad z_0^d+z_1^2\ldots+z_n^2=0, \quad |z_0|^2+|z_1|^2\ldots+|z_n|^2=2\}$$ is a $(2n-1)$-compact manifold.  How give the charts. For $n=1$ and $d=2$ not distinguish which 1- manifdold is? Showing that $\displaystyle\lim_{s \to{1+}}{(s-1)\zeta(s)}=1$ I need prove the following: ($\zeta(s)$ is the Riemann zeta function)  $\displaystyle\lim_{s \to{1+}}{(s-1)\zeta(s)}=1$  I really don't know, I have tried hard, but have obtained nothing for now. Expected value of sums Suppose we draw cards out of a deck without replacement. How many cards do we expect to draw out before we get an ace? I'm attempting to get a better understanding of cryptography and have run into some questions about bcrypt.   Bcrypt relies on the blowfish cipher, which is a reversible method of encryption. But bcrypt is not reversible. How is that possible? Or am I mistaken? What does bcrypt do on top of blowfish to make it irreversible? Why does bcrypt use blowfish instead of twofish or threefish? Can we apply for a Schengen tourist visa while visiting another country on a short-stay visa? We are Indians and will be visiting UK on short-stay visas for about five months.  Can we apply for Schengen tourist visas while we are in London? Is there a better alternative to ambiguous for a word with a wide range of meanings, difficult to find, because they become different in connection with person's opinion.