In publications the wording often resembles the following: "We found that our results followed what we found in our previous research."  I am now writing a publication alone, with no co-authors.  Is it bad form to use "my" in place of "our" in such cases?
Which personal pronoun is appropriate in single-author papers - 'I' or 'we'? Could the use of 'I' be considered egotistical? Or will the use of 'we' be considered to be grammatically incorrect?
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.   I have already figured out that $|Z(G)| = p$, and that $G'=[G,G] \lhd G$.  Also, $|G'| = p$ or $p²$.  I suppose I'd have to prove that $G' \subset Z(G)$, but I've been trying and I have no idea how. Any hints? Thanks! How to generate a 2D array data structure in tikz? I need to illustrate a 2D array data structure in my document. This is a picture I found on the internet. I want something similar.    I also want to show the memory layout in the illustration. Something like this:   Can someone help me with drawing them in Tikz? Thanks in advance.  MWE  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{tikz} \usetikzlibrary{matrix,backgrounds}  \begin{document} \begin{tikzpicture}[font=\ttfamily, array/.style={matrix of nodes,nodes={draw, minimum size=7mm, fill=green!30},column sep=-\pgflinewidth, row sep=0.5mm, nodes in empty cells, row 1/.style={nodes={draw=none, fill=none, minimum size=5mm}}, row 1 column 1/.style={nodes={draw}}}]  \matrix[array] (array) { 0 &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; 6 &amp; 7 &amp; 8 &amp; 9\\   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;  \\}; \node[draw, fill=gray, minimum size=4mm] at (array-2-9) (box) {};  \begin{scope}[on background layer] \fill[green!10] (array-1-1.north west) rectangle (array-1-10.south east); \end{scope}  \draw (array-1-1.north)--++(90:3mm) node [above] (first) {First index}; \draw (array-1-10.east)--++(0:3mm) node [right]{Indices}; \node [align=center, anchor=south] at (array-2-9.north west|-first.south) (8) {Element\\ (at index 8)}; \draw (8)--(box); % \end{tikzpicture} \\ \begin{tikzpicture}[font=\ttfamily, array/.style={matrix of nodes,nodes={draw, minimum size=7mm, fill=red!30},column sep=-\pgflinewidth, row sep=0.5mm, nodes in empty cells, row 1/.style={nodes={draw=none, fill=none, minimum size=5mm}}, row 1 column 1/.style={nodes={draw}}}]  \matrix[array] (array) {  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp; \\  &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;  \\}; % \end{tikzpicture} \\ \begin{tikzpicture}[font=\ttfamily, array/.style={matrix of nodes,nodes={draw, minimum size=7mm, fill=blue!30},column sep=-\pgflinewidth, row sep=0.5mm, nodes in empty cells, row 1/.style={nodes={draw=none, fill=none, minimum size=5mm}}, row 1 column 1/.style={nodes={draw}}}]  \matrix[array] (array) {  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp; \\  &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;  \\}; % \end{tikzpicture} \end{document} Recovering lost text which was copy pasted from a website to MS Word I have a file with ANSI colors.  test.txt: \e[0;31mExample\e[0m  I would like to display the content of this file in a terminal, like cat does, but I would like to display the colors as well. How do I remove Windows 7 from my dual boot system with Ubuntu? Hello can someone give me short tutorial how to:   Remove Windows 7 from my dual boot system (Ubuntu/Windows7) Let me use free space as new partition for data (so I don't need to extend Ubuntu itself here) Remove windows 7 option from boot screen   Update:  Thanks to Lekensteyn answer I successfully deleted windows. Now I created new partition (formatted to ext4), but I can not use it. I cannot copy files there, only as root.  Also when booting, Ubuntu complains it didn't find /windows partition (of course it didn't, I removed it). I feel like I should update some tables or what, any ideas? When trying to view  via the iOS app, I get this:        It's consistent, retrying does not help and the request always fail.  All other questions load just fine, so I highly suspect the cause is the Emoji icons used in there, especially in the comments that contain lots of them.  Beta channel, version 1.0.1.85  Update: still happening in 1.0.1.88 and I also found that the "preview" seen for example in tag search shows the Emoji just fine: How do I prove that $m(TE)=\left|\det(T)\right|m(E)$? Let $m$ be the $n$-dimensional Lebesgue measure and $T$ be a linear operator on $\mathbb{R}^n$. Let $\Sigma$ be the sigma-algebra of Lebesgue measurable sets. How do prove that (1) $\forall E\in\Sigma, T(E)\in \Sigma$ and $m(T(E))=\left|\det(T)\right|m(E)|$? Since the $\sigma$-algebra of Lebesgue measurable sets is strictly larger than the borel algebra, I think it cannot be proven by showing that $T$ is continuous. How do I prove this formally? I have a script from UC Davis and every thing is proven precisely here, except for one lemma which is critical for rest proofs in the script. That is,  Define $\mathbb{B}=\big\{\prod_{i=1}^n [a_i,b_i) : a_i,b_i\in\mathbb{R}\big\}$. Let $T$ be a unitary operator on $\mathbb{R}^n$. Let $A\in \mathbb{B}$ and $\{A_k\}_{1≦k≦m}$ be a finite disjoint sequence such that $\bigcup_{1≦k≦m} A_k \subset T(A)$. Then $\sum_{1≦k≦m} m(A_k) ≦ m(A)$.  It's written in the script: &quot;This result is geometrically obvious, but a formal proof seems to require a fuller discussion of the volume function on elementary geometrical sets, which is included in the theory of valuation in convex geometry. We omit the details&quot; It's okay to me to go through full discussion of volume function if that is precise. If it cannot be proven another easier way(so I can prove it in a day), please recommend me a &quot;convex geometry&quot; text which explains this. "A/An" preceding a parenthetical statement When a/an precedes a parenthetical aside (sometimes seen in informal/conversational writing), should the vowel rule depend on the first word in parentheses, or the next word in the "regular" flow of the sentence?     I need a (memorable) idiom (preceding an m word; use a)   or     I need an (memorable) idiom (preceding an i word; use an) I'm using terminal-ide  which is basically a terminal for android with all sorts of utilities. One is able to create bash scripts for example. Is there a way to create an icon on the home screen that will launch one of these scripts? Beamer: change header background color I have decided to switch from Powerpoint to Beamer, and for my first presentation I'd like to use the , and the same colors as in this goggle slide template:  .  I tried to do some research about it, the closest answers I found are the question  and the . I tried this code:  \documentclass{beamer} \usepackage[frenchb]{babel} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc}  \usetheme{metropolis}  \definecolor{bluegreen}{rgb}{3, 166, 155} \definecolor{pitchblack}{rgb}{0, 0, 0} \definecolor{lightbeige}{rgb}{255, 251, 241} \definecolor{mediumgray}{rgb}{183, 183, 183}  \setbeamercolor{background canvas}{bg=pitchblack} \setbeamercolor{normal text}{fg=lightbeige} \setbeamercolor{headline}{bg=bluegreen, fg=mediumgray}  \begin{document} \begin{frame}     \frametitle{The title}     Lorem ipsum... \end{frame} \end{document}   I does everything I want, except that the title bar's background color is lightbeige:    What did I do wrong? Or what argument should I pass to \setbeamercolor to get it right? Thanks in advance :-). Numbering equations If I am writing a LaTeX document on TexMaker and I want to number my equation but most probably I will be adding details later on and I do not want to fall into retyping it all over again. So if for example I have an equation and currently called equation (1.2) that I want to refer later as in the following sentence "As you can see in (1.2)" but then I had to edit my document in a way that it becomes (1.3) now instead of (1.2) what should I do in order to avoid editing large number of equations and my reference to them? How can a Photon have a "frequency"? I picture light ray as a composition of photons with an energy equal to the frequency of the light ray according to $E=hf$. Is this the good way to picture this? Although I can solve elementary problems with the formulas, I've never really been comfortable with the idea of an object having or being related to a "frequency". Do I need to learn quantum field theory to really understand this? Does a car use friction to move? When a car's engine injects fuel into the cylinder chambers, the reaction creates a force that generates rotational momentum to the shaft and over the transmission, it translates that power to the wheels, right?  But, something's bothering me, how does the car actually move, is it dependent on the force of friction? Wheels have a contact with the road in one exact point and when the drive gets to rotate them, a force is exerted on the road in the direction of movement and there is friction that is counteracting it.  Is the key to get a car properly moving to have the drive force equal or less than the force of friction to keep that point locked to the ground and use the rolling of the wheel for translational displacement ie. moving forward? If it's bigger than the force of friction, that would cause the wheels to spin in place?  Am I completely off or am I getting something right? If there's a knowledgeable person on this topic, I'd greatly appreciate some insight, perhaps even a bigger response with some basic vehicle physics. Is there any way to check whether a file is locked without using a try/catch block?    Right now, the only way I know of is to just open the file and catch any System.IO.IOException. Etymology of Tor and Ext Functors The names of the derived functors $\operatorname{Tor}$ and $\operatorname{Ext}$ seem quite cryptic to me. Does anyone know what these abbreviations stand for? I would be glad if someone could tell me where these names come from. Spatial query to return multiple values I have a woodland scheme advice layer that has a polygon for each area of advice (brown layer in the picture). I also have a polygon layer of UK local authorities (red boundary layer in the picture). I would like to perform a spatial query which returns the local authority name for each woodland advice scheme. This would work fine if each woodland advice scheme was found in just one local authority boundary. However many are found across a boundary of two different authorities. For instance, one scheme sits across the boundaries of the authorities of Fife and Angus. The scheme is the yellow selected polygon in the picture and the red line is the authority boundary. How do I get the spatial join to return a value of Fife; Angus (or something similar to identify two values) instead of just Fife or Angus. Parse JSON with R I'm trying to prove whether or not the Laurent polynomials $\mathbb{Z}[x, x^{-1}]$ with coefficients in $\mathbb{Z}$ form a principal ideal domain.    I know that $\mathbb{F}[x, x^{-1}]$ is a PID when $\mathbb{F}$ is a field, but clearly $\mathbb{Z}$ is not a field so I cannot appeal to this result. And my intuitions are not serving me very well at the moment. Can anyone provide a hint or direction to take? Multiplicative order and powers Let's consider two number $a$ and $b$ such as $gcd(a,b)=1$. Can you explain me intuitively why there exist $n&gt;0$ such as $a^{n} \equiv 1 \space (mod \space b)$  ? What is the difference between "gender" and "sex"? What is the difference between gender and sex?  says that gender is The mental analog of sex but that's too high English for me.  Basically, I'm developing a web-application that stores people's profile along with a field for gender/sex. Which name would be more appropriate?  __  [UPDATE]  After getting these good answers, I can figure out that,   Sex - Biological characteristics  Gender - Social characteristics   And, well, for my web-application, I went with the term sex, as it sounds more scientific and less political. P.S. Values for sex are clearly defined and can be easily validated (only two values * + an optional blank value).  * plus some anomalies.