I have an equation defined as  $$m^*(E) \leq \sum_{k=1}^{\infty} l(I_k) &lt; m^*(E) + \varepsilon \text{ and } E \subseteq \cup_{k=1}^{\infty} I_k.$$    but I am receiving an uncontrolled sequence error. Is there a special package I need to use \text{ and }? If me equation is   $$m^*(E) \leq \sum_{k=1}^{\infty} l(I_k) &lt; m^*(E) + \varepsilon E \subseteq \cup_{k=1}^{\infty} I_k.$$    I do not receive an error.
I'm getting this error:  ! Undefined control sequence. l.64 ...p(- \frac{E_j - E_i}{k_B T}) &amp; \quad \text                                                   {:  E_j &gt; E_i}\\ ?  ! Undefined control sequence. l.65     1 &amp; \quad \text                         {:  E_j&lt;E_i}\\ ?    which is from this:  \begin{equation}\label{eq:hop} w_{i,j}=w_0 exp(-2 \gamma R_{i,j})\left\{    \begin{array}{l l}     exp(- \frac{E_j - E_i}{k_B T}) &amp; \quad \text{:  E_j &gt; E_i}\\     1 &amp; \quad \text{:  E_j&lt;E_i}\\   \end{array} \right. \end{equation}   But I don't understand why I get the error. This is my header:  \documentclass[11pt]{iopart} %\newcommand{\gguide}{{\it Preparing graphics for IOP journals}} %Uncomment next line if AMS fonts required \usepackage{iopams} \usepackage{graphicx, wrapfig} \usepackage{fixltx2e} \graphicspath{{images/}} \DeclareGraphicsExtensions{.pdf,.png,.jpg,.gif} \makeatletter \g@addto@macro\@floatboxreset\centering %\def\@cite#1{\textsuperscript{[#1]}} \makeatother   And my class file is the standard IoP one from   Can anyone help me get read of this error?
How to set Google+ photos to be Public-Unlisted (as you could do with PicasaWeb)? Previously, if I uploaded photos from Picasa to PicasaWeb, I could specify them as Public but Unlisted. So you had to have the link to view them but no login was required.  I don't see that option now that Picasa uploads to Google+.  Any ideas? I've seen them maneuver. They definitely can go backwards. How fast can they go in reverse? Is warp speed possible, or is reverse limited to impulse power? If it is limited to impulse power, can they travel backwards under impulse power as fast as they travel forwards under impulse power? If I'm standing at the equator, jump, and land 1 second later, the  Earth does NOT move 1000mph (or .28 miles per second) relative to me,  since my velocity while jumping is also 1000mph.   However, the Earth is moving in a circle (albeit a very large one),  while I, while jumping, am moving in a straight line.   How much do I move relative to my starting point because of this? I  realize it will be a miniscule amount, and not noticeable in practise,  but I'd be interested in the theoretical answer. This question is from a set of optional, much harder problems from my first year analysis course, but the subject material is norms on $\mathbb R^K$.  (c) Show that there exists a constant $C &gt; 0$ such that for all $\mathbf x ∈ \mathbb R^k$, $||\mathbf x||\le C||\mathbf x||_\infty$  Hint: Use the standard unit vectors to write $\mathbf x = x_1\mathbf e_1 +. . .+x_n \mathbf e_n$, and use the triangle inequality.  (d) Show that there also exists a constant $c &gt; 0$ such that for all $x ∈ \mathbb R^k$, $||\mathbf x||_\infty \le c||\mathbf x||$  Hint: If it isn’t true, then you can find a sequence $⟨\mathbf x_n⟩$ such that $||\mathbf x_n||$ is bounded but $c_n := ||x_n||_∞ → ∞$. (Why?) Think about the sequence $⟨\mathbf x_n/c_n⟩$. The Bolzano-Weierstrass theorem may be of assistance.  Note that the unspecified norm represents any norm for $\mathbb R^k$. I've done part c), but am stuck on part d). I've had a look for proofs on other questions on MSE, but none of them seem relevant to the hint given, and frequently the terminology is too advanced for me.  I tried considering the case if it isn't true, as suggested, but I can't see how to bound any sequence using that. Any help would be much appreciated. Why does pdfTeX hang on this file? Answer textbox's content starts overlapping when adding new lines in middle on Android app When typing/editing an answer, sometimes if I scroll the editor textbox, go upwards and add lines, the text will start overlapping each other. The behaviour is that when you add a newline, the text below it does not move downwards.  Minimizing soft keyboard fixes this.  This does not affect the Ask Question box in my test.    I am using Android 4.1.2 What is the possibility of a railgun assisted orbital launch? Basic facts: The  is 2.4 miles deep.  Railguns  of a projectile on the order of 7.5 km/s.  The Earth's  is 11.2 km/s.  It seems to me that a railgun style launch device built into a deep shaft such as an abandoned mine could reasonably launch a vehicle into space.  I have not run the calculations and I wouldn't doubt that there might be issues with high G's that limit the potential for astronauts on such a vehicle, but even still it seems like it would be cheaper to build such a launch device and place a powerplant nearby to run it than it is to build and fuel single-use rockets.  So, what is the possibility of a railgun assisted orbital launch?   What am I missing here?  Why hasn't this concept received more attention? I'm curious why PCBs have one square pad in row for 0.1" headers. What is purpose of putting one square pad? What it indicates? Can you push more amps through square pad than round? bash if -a vs -e option Both about -a and -e options in  is said:  -a file     True if file exists. -e file     True if file exists.    Trying to get what the difference is I ran the following script:  resin_dir=/Test/Resin_wheleph/Results  if [ -e ${resin_dir} ] ; then     echo "-e "; fi  if [ ! -e ${resin_dir} ] ; then     echo "! -e"; fi  if [ -a ${resin_dir} ] ; then     echo "-a"; fi  if [ ! -a ${resin_dir} ] ; then     echo "! -a"; fi   /Test/Resin_wheleph/Results exists and is a directory. And this is what I get:  -e -a ! -a   which seems to be a little strange (notice -a and  ! -a). But when I use double brackets (e. g. if [[ -e ${resin_dir} ]]) in the similar script it gives reasonable output:  -e -a   So:    What is a difference between -a and -e options? Why -a produces a strange result when used inside single brackets? How long will foods that have "Best by: XX-XX-XX" on the product last past that date?  I have tried looking online, and all I can find is anecdotal evidence, which isn't very assuring for me since there seems to be no specific "x food will expire y weeks after its best by date".  Is there a rule of thumb or some guide out there that can tell me how long a "best by" food will last? Or is it safe to assume that they never expire, since it's not actually labelled on the product? Today while troubleshooting a service broker problem, I discovered that the database owner was the Windows login of an employee who had left the company. His login had been removed and thus the query notifications were failing.   Supposedly the best practice for dealing with this is to make 'sa' the database owner. We changed it and that cleared out the queue.   My (very elementary) question: what is the database owner and what is its purpose? It is well established that:   'In quantum mechanics, the behavior of an electron in an atom is described by an orbital, which is a probability distribution rather than an orbit.   There are also many graphs describing this fact: : (hydrogen atomic orbital - one electron) In the figure, the shading indicates the relative probability to "find" the electron, having the energy corresponding to the given quantum numbers, at that point.  My question is: How do these symmetries shown in the above article occur?                 What about the 'preferable' axis of symmetries? Why these? How to view the system console message after Blender crashes? I am testing a script in Blender game engine. I can view the helpful message on the external system console when the script throws exception. Sometimes the bugs of the script cause the Blender to crash and close the console immediately.    Is there any way to view the message after the Blender crashes? How to write the message to a text file for later viewing? Any suggestion? Return matched elements' attribute ar array using jQuery Why does range(start, end) not include end? How to kill The Twins In Terraria In Terraria I often try to defeat spazmatism first, but when he transformed, his flamethrower killed me. What is easiest way to kill The Twins? How do I create a link? Say I am extending The blockBase class to create a custom block, and I am implementing the blockBuild method to create some markup for my block. Something like this:   class YourModuleBlock extends BlockBase {     /**      * Implements \Drupal\block\BlockBase::blockBuild().      */      public function build() {       return array(         '#markup' =&gt; 'This is a block!',       );      }    }   If I wanted to provide a link in this markup, in D7 I would have used the l function, but this is no longer available (). So, I need to make available the new D8 method for generating links. I could just use an &lt;a&gt; tag, but this was never best practice in D7.  So, what is the right method to use for creating links and how do I make it available to my function? Removing spaces between "words" in math mode Is it possible to kill people indirectly with the Death Note? in the Death Note states:        Whether the cause of the individual's death is either a suicide or accident, if the death leads to the death of more than the intended, the person will simply die of a heart attack. This is to ensure that other lives are not influenced.      However,  states:        Even though only one name is written in the Death Note, if it influences and causes other humans that are not written in it to die, the victim’s cause of death will be a heart attack      Besides the fact that I find these 2 rules to be contradicting (correct me if I'm wrong), it still made me curious: Is it possible to kill people indirectly with the Death Note?  For example, writing a heart surgeon's name during a operation, or a pilot's name while mid-flight. Roman numerals become “too wide” in table of contents Following minimal document:  \documentclass{report}  \begin{document} \renewcommand*\thechapter{\Roman{chapter}} \tableofcontents \setcounter{chapter}{6} % Problem starts at chapter 7 \chapter{Seven} \chapter{Eight} \section{Eight-one} \section{Eight-two} \end{document}   yields this output (cut to size for your convenience):    Clearly, the chapter (and section) headings hang into the chapter (section) numbers. For the previous chapter numbers, this isn’t a problem since all chapter titles are aligned to the same column and the numbers I–VI are sufficiently narrow.  (The same happens regardless of document type, I’m actually using scrreprt with the same result.)  How can I prevent this?