I'm writing an presentation of the project where I took a "standard" equation and modified it slightly. I would like to therefore show this by replacing the standard equation with its modified version.  I've seen a few solutions here, but they all deal with RHS replacements and don't work with the LHS.  I would like (this is merely as an example)  A &amp;= B   to be replaced by   A + C &amp;= B^D  while maintaining the alignment around the equations. I've tried using  \alt&lt;2-&gt;{A + C}{A} &amp;= \alt&lt;2-&gt;{B^D}{B}  but while \alt solves RHS replacement (especially if used with \phantom to deal with possible vertical erros), with a variable LHS the result still wobbles. How can this be solved?
The beamer command \alt&lt;*overlay specification*&gt;{foo}{bar} will insert foo if the current slide is within the given overlay specification, and bar otherwise.  It's equivalent to   \only&lt;*overlay specification*&gt;{foo}\only&lt;*complementary overlay specification*&gt;{bar}   Here is a sample document using it:  \documentclass{beamer} \begin{document} \begin{frame} \begin{align*} y &amp;= \frac{(x^2+1)\sqrt{x+3}}{x-1} \\ \ln y &amp;= \ln (x^2+1) + \frac{1}{2} \ln(x+3) - \ln(x-1) \\ \frac{1}{y} \frac{dy}{dx}       &amp;= \frac{2x}{x^2+1} + \frac{1}{2(x+3)} - \frac{1}{x-1} \end{align*} So \[ \begin{split} \frac{dy}{dx} &amp;= \left(\frac{2x}{x^2+1} + \frac{1}{2(x+3)} - \frac{1}{x-1} \right) \alt&lt;2&gt;{\frac{(x^2+1)\sqrt{x+3}}{x-1}}{y} \end{split} \] \end{frame} \end{document}   This is very useful and saves typing.  But if one of the alternatives is larger than the other, it leads to jiggling slides.    What I would like is a overlay-specification-aware command \altvisible that would take the same amount of space on each slide.  So it would have to insert a box as big as the bigger of the two, and then set the correct material.  So the above document with \altvisible instead of \alt would not jiggle.  Any takers?
find $\left( \frac{x}{x+y} \right)^{2007} + \left( \frac{y}{x+y} \right)^{2007}$ tikz trees: How to not draw a single edge Why doesn't the Moon fall onto the Earth? DISCLAIMER: I do not deal with in-depth mathematics on a daily basis as some of you may, so please pardon my ignorance or lack of coherence on this topic.  QUESTION: What is the significance of starting the Fibonacci sequence with $0,1$ ?  For instance, if I picked any two random integers, say 2 and 7, to start a sequence would I actually be creating some multiple or derivation of the Fibonacci sequence?  Is there a general mathematical explanation for the relationship between any sequence represented by $a[0] = x, a[1] = y, a[n] = a[n-1] + a[n-2]$ and the Fibonacci sequence?  Or, back to my example sequence, is there a general mathematical relationship between:  $2,7,9,16,25,41,66,107,173,280...$  and  $0,1,1,2,3,5,8,13,21,34...$  Perhaps the Golden Ratio explains it somehow?  Any help would be appreciated. Do Indian passport holders with UK Tier 2 need to get a tourist visa for Mexico? I'm an Indian passport holder currently resident in the UK under a Tier 2 (General) visa and planning on going to Mexico on a holiday. So I was looking into the rules on the Mexican embassy in the UK and :     According to the new regulations who entered into effect on 18th, May   2016 (article 26 of the Guidelines and Requirements for Migratory   Services) regarding foreign nationals visiting Mexico, holders of a   valid UK visa, regardless their nationality, are not required to apply   for a Mexican visa as a tourist, business (Non-Lucrative Activities)   or transit visitors for a stay of up to 6 months. This regulation does   not apply to British Travel Document holders.   However, :     PERMANENT RESIDENT IN THE UK (ILR / ILE / PERMANENT RESIDENTS)        According to Mexican regulations which came into force in June 2009,   Permanent residents in the United Kingdom wishing to travel to Mexico   do not require a visa to enter the country as tourists or business   visitors for up to 180 days and as visitors in transit for up to 30   days, regardless their nationality.   So which one is correct? Are Tier 2 holders with an Indian passport allowed visa-free / visa on-arrival entry to Mexico? There are many beings that have very big powers. There are beings that are worshipped as gods (Asgardians; and I would lump Azazel into that as well since Marvel seems to imply that he's - while a mutant - someone people consider to be "Devil"). There are mutants whose power would clearly have been considered as "god like" by people worshipping Greek or other polytheistic pantheons where the threshold to what made you a god was pretty low.  But are there any actual major "Gods" in Marvel universe?  Since there are many different definition of what a "god" is, the one that is pertinent to this question:   Power wise, being able to create Universe(s); e.g. gods more in a sense of Christianity/Judaism scale rather than "Pan" or "Hestia" in Greek pantheon who merely have some limited supernatural powers over small domain of natural events. Effectively immortal, at least excluding specific exotic attacks. Origin-wise, be "supernatural", not merely a human mutant or a powerful alien with advanced technology. Desire/demand/like followers' worship or prayers. Stop jQuery .load response from being cached I have the following code making a GET request on a URL:  $('#searchButton').click(function() {     $('#inquiry').load('/portal/?f=searchBilling&amp;pid=' + $('#query').val());             });   But the returned result is not always reflected. For example, I made a change in the response that spit out a stack trace but the stack trace did not appear when I clicked on the search button. I looked at the underlying PHP code that controls the ajax response and it had the correct code and visiting the page directly showed the correct result but the output returned by .load was old.  If I close the browser and reopen it it works once and then starts to return the stale information. Can I control this by jQuery or do I need to have my PHP script output headers to control caching? Interpretation of ROC curve I have a ROC curve like the figure below:   What can be inferred given this kind of curve in general?  What are the differences of states 1, 2 and 3 in the figure?  What causes the diagram to jump straight from state 1 to state 3? Most of the ROC curves on the internet look like the figure below: How do I tunnel and browse the server webpage on my laptop? I run a web app in one of my lab servers, and I have already setup X11 Forwarding on those machines. Other lab members can tunnel through SSH, and browse that web app on their local browser at home.  I can't. Last time I checked with them, there is almost nothing I need to do.  When I type 192.168.1.113/webapp I get nothing.   Any tips?  THanks.    I ended up using the second method :)  ssh -L 8080:&lt;server-ip-address&gt;:80 &lt;username&gt;@&lt;remote-addr&gt; -N Trigger an event with Prototype and is such interpretation the norm?  When something went from 4 units to 8 units, most authoritative sources seem to agree with the use of "a two-fold increase", even though what was actually increased is more like "one-fold", i.e. the original quantity.  But if the "two-fold increase" is the correct usage, why most people seem to interpret "a 100% increase" the same thing? Suppose that $(U,V)$ has the following joint pdf: $$f_{U,V}(u,v)=\exp(-\theta u-\theta^{-1}v)$$ , where $u\geq0$, $v\geq0$, $\theta&gt;0$. Define $X=UV$ and $Y=U/V$. Find the marginal pdf of $X$ and $Y$.  With transformation, I got $U=\sqrt{XY}$ and $V=\sqrt{X/Y}$ and the absolute value of Jacob is $1/2Y$. Then, the joint pdf of $(X,Y)$ is  $$f_{X,Y}(x,y)=\exp(-\theta \sqrt{XY}-\theta^{-1}\sqrt{X/Y})1/2Y, X,Y&gt;0.$$  But I am not sure how to get the marginal pdf?  Thank you! Which one is the formula of angular velocity? Is it $\omega= vr$? If not then why does the source below use $mvr=nh/2\pi$, where $mvr$ is angular momentum and $vr$ is angular velocity? Again $\omega=v/r$ shows radian per second. I saw $\omega= vr$ in one book and $\omega= v/r$ in another! What are the “spam” and “rude or abusive” (offensive) flags, and how do they work? Compute $P(X_1+\cdots+X_k\lt 1)$ for $(X_i)$ i.i.d. uniform on $(0,1)$ Consider $N=\min\{n: S_n&gt;1\}$, where $S_n=X_1+\cdots+X_n$ and $(X_i)_{i=1}^\infty$ is i.i.d. uniform on $(0,1)$. So, $N$ is the first time that $(S_n)_{n=1}^\infty$ crosses $1$. I'd like to calculate $E(N)$. To this end I'd like to calculate $\Pr(N\gt k)=\Pr(S_k\lt 1)$.  Is there a way to actually do this for any arbitrary $k$? I mean, certainly there is as I know about the distribution of $S_n$ but the formula is just formidable when you move with $k$ toward $\infty$ and even though tractable with a computer, I don't think it's tractable without it.  Is there maybe a better way to calculate the expectation? Thanks for any help. PhD without previous academic degree: truth or myth? Nicely force 66 characters per line Based on newtons third law If an elephant can apply 250N force and a rabbit can apply 25N force , and if they are pulling each other , then elephant will pull with 250N force and according to newtons third law the rabbit should also pull the elephant with 250N force.then from where do the rabbit got the extra 225N i.e.(250-25=225) force??? can anyone please explain. How do I set bold and italic on UILabel of iPhone/iPad? Why does the mirror modifier sometimes give me an overlapping mesh? When I add a mirror modifier it sometimes doesn't mirror correctly, giving me an overlapping mesh. How can I fix this?