I wish to write the name of pdfTeX's author:    I am not able to figure out how to write the middle name. I triedTh\'{\^{e}}, but it doesn't return the desired output.  It's different from the similar double accent question:  since the answer there (using TIPA) doesn't work here. This is a very specific situation.
As linguistics student, I have to put more than one thing on a character every now and then. For example, I need to type ā̆. I thought I could simply do that by typing \={\u{a}}, but then the macron is placed above an empty space in front of the character.  How can I solve this? Thanks  P.S. I'm using MiKTeX 2.9, running on Windows 8; in case it might be of use.
find all $(x,y,z)$ such that $27^{3x^2 + 2y}+27^{3y^2 + 2z}+27^{3z^2 + 2x}=1$ Find all ($x,y,z$) such that $$ 27^{3x^2 + 2y}+27^{3y^2 + 2z}+27^{3z^2 + 2x}=1$$  I am a high school student and would appreciate it if anyone could solve it using high school mathematics. here is what I have tried till now: $$ 3x^2 +2y &lt; 0 $$ (this can also be said for the other 3 equation. it also means that x,y,z&lt;0) $$ -2y&gt;3x^2 $$ $$ 4y^2&gt;9x^2 $$ ( -2y and 3x^2 are both positive) $$ 3y^2&gt;27/4 x^2 $$ $$ -2z&gt;3y^2&gt;27/4 x^4 $$ $$ 4z^2 &gt; 729/16 x^8 $$ $$ 3z^2&gt; 2187/64 x^8 $$ $$ -128/2187&lt;x^7 $$ $$ -2/3 &lt; x $$ $$ -2/3&lt; x,y,z &lt; 0 $$ i tried this but as you can see didn't do much good increasing impedance of headphones I have headphones with differential input and impedance of 8 ohms. I need to drive this headphone with some DAC with built in headphone driver (Currently I have chosen ADAU1772). DAC's datasheet mentions that the minimum impedance of headphones it supports is 16 ohms. Can I increase impedance of my headphones so that I can drive them through this chip? What will happen if I drive this 8 ohm headphone through a chip supporting minimum impedance of 16 Ohms? How to render from Eevee in Blender 2.8? I have the Blender 2.8 version from the 21st Sep 2018 I was looking forward to render a test sequence but cannot find a render button anywhere? Does anyone know where to find it? How to set a JavaScript breakpoint from code in Chrome? Science Fiction novel or novels about starship that becomes a god, colonizes hostile planet Plot Summary/Details  The sharpest memory I have of this one is that it was unusually dense reading. Much more difficult going than most of the sci-fi stuff I'd read by that time (I was 10 or 11, I think).  What I remember in terms of plot is that there is a starship, sent either to explore, or colonize, a distant star system.  I don't remember the names of any of the characters, but I think maybe they discover they are clones?  In any case, something happens to the computer system that the onboard AI becomes sentient and develops a measure of omniscience and omnipotence.  It effectively becomes a god of sorts.  The next part I can remember, and I'm not sure this is the same book or not, is that the ship has forcibly settled the crew on a hostile planet.  All sorts of nasty indigenous life forms live here, and guards are post on the wall outside the settlement to destroy them as they try to enter.  I remember there is a female character standing watch, and she goes over the bestiary in her mind.  One particularly nasty creature paralyzes you, and then burrows up your spine into your brain (or something like that) if it gets a hold of you.  That's all I can recall.  Not a lot of detail, unfortunately, but I'm having a tough time remembering much about this one.  I never finished the book(s), as they were mostly "over my head" at that age. Where did newtonian size setting go in 2.79a I have a list of cards for a deck I want to build or buy. What should I do to check whether that deck is legal in a particular format (Standard, for example)? What is the difference between <%# and <%= in ASP.NET MVC? Custom Tools not Saving in Toolbar on Startup/ Normal.mxt? I know cell phone cameras are the lowest rung, but when reading reviews of phones, the reviewers always have sample shots that are much better than what I can manage.  What are some ways to take decent shots with a cell phone camera?  (I'm thinking of the higher end Android or iPhone cameras). Is my phone liable to explode if I charge it with a charger that came with a different phone? Is is true &lt;h1&gt; tag should not have more than 1 on every page for SEO?   Every pages on the header, it includes and &lt;h1&gt; tag. Website Name which show an image from logo class, like this:  &lt;div id="header"&gt;   &lt;h1 class="logo"&gt;      &lt;a href="#"&gt;Website Name&lt;/a&gt;   &lt;/h1&gt; &lt;/div&gt;   and I also include &lt;h1&gt; on the contact page, help, etc and article page for example:  &lt;h1&gt;Contact Us&lt;/h1&gt; &lt;h1&gt;Name of the Article Title here&lt;/h1&gt;   On the homepage, it just has one &lt;h1&gt; for the logo Site Name... other pages have 2 &lt;h1&gt; tags Please consider the integral:  $$\int_{-a}^{a}x^2dx=\frac{2a^3}{3}$$  I would like to know why I can't make the substitution:  $$u=x^2$$  When I make the substitution, the limits of the integral will be the same, and the integral itself will be zero, which is the wrong answer. So why does this simple change of variables not work as I have expected?  Please note that I do not want help solving the integral, I know how to solve it several ways. My question is why does this specific attempt at a solution not work? Suppose $f$ is an isometric (i.e., distance preserving) function on $\mathbb{E}^2$ such that $f(0,0) = (0,0)$.  Then I want to show that $f$ is necessarily linear.  Now $f$ is linear iff $f$ is both additive and homogenous.  The following is an attempted proof for the homogeneity of f (missing the last step); still more, I have no idea how to argue for the additivity of $f$.  Any ideas?  Let $x \in \mathbb{E}^2$ and $\alpha \in \mathbb{R}$   We know that $\forall x \in \mathbb{E}^2$, $\Vert x - 0 \Vert = \Vert f(x) - f(0)\Vert = \Vert f(x) - 0 \Vert$ so that $\Vert x\Vert = \Vert f(x)\Vert$.  From this we immediately have the following facts:  $\Vert x \Vert = \Vert f(x) \Vert$  $\Vert \alpha x \Vert = \Vert f(\alpha x) \Vert$  We can then argue that since $\Vert \alpha x\Vert = |\alpha| \Vert x \Vert = |\alpha| \Vert f(x) \Vert = \Vert \alpha f(x) \Vert$, we also have that $\Vert f(\alpha x) \Vert = \Vert \alpha f(x)\Vert$.  Finally, we have that  $\Vert \alpha x - x \Vert = \Vert \alpha f(x) - f(x) \Vert$   iff $ \Vert (\alpha - 1)x \Vert = \Vert (\alpha - 1) f(x) \Vert$   iff $|\alpha - 1| \Vert x \Vert = |\alpha - 1| \Vert f(x) \Vert$  Since the last of these statements is in fact true, we now have $\Vert \alpha x - x \Vert = \Vert \alpha f(x) - f(x) \Vert$ as desired.  Now at this point it seems like I have all of the facts required to assert that $f(\alpha x) = \alpha f(x)$, but I can't figure out how to formally state why without illegally appealing to visual intuition.  Any ideas? Is energy content of a system different depending on the observer? For the sake of simplicity, let's imagine that the entire universe is empty except for a single lump of (classical) matter with mass $m$. In its center of momentum frame, it is clear that the total energy is simply $E_\text{CoM}=mc^2$. However, in a frame moving relative to it with speed $v$, we have $E_\text{moving}=\sqrt{m^2c^4+p^2c^2}&gt; mc^2$ for all nonzero $v$.  Are we to infer that the energy content of a system can be different relative to the observer? Does this not violate the first law of thermodynamics? Is the Ohm's law violated here? And also why is electricity generated at 11,000 V in India? Significance of starting the Fibonacci sequence with 0, 1.... 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. Why am I still being asked for an ssh password when I'm using private key authentication? Can I downgrade to macOS Mojave if I buy the new 2019 MacBook Pro? Why not use a WAMP stack?