I am trying to understand why the provided sentence makes sense. I understand a grammar rule: the pronoun in the sentence should match the noun in the sentence. However, how can we use &quot;they&quot; for &quot;a prisoner&quot;?  Even if a prisoner has committed a serious crime, they deserve humane treatment.  To me, the following sentences make more sense based on the grammar rule.  Even if a prisoner has committed a serious crime, she or he deserves humane treatment. Even if prisoners have committed a serious crime, they deserve humane treatment.
Is it good English to say "They have just left", when talking about a single person (perhaps someone you don't know the gender of)?  (I am a native English speaker, I'm looking for the view held by lexicographers).
Prevent external devices being locked to launcher If I connect an external device (such as a USB stick or android smartphone) it will automatically open in nautilus and get a corresponding icon locked to unity launcher. Is there any way to prevent this?  I'm using Ubuntu 14.04 I am on a Mac with MacTex 2020 and ran into a strange problem with Biber. Working on a document all was fine, I did not change the bibliography (says my git) and only fixing typos (not even adding cites) and suddenly latexmk stopped working after a Biber run, while that looked like  INFO - This is Biber 2.14 INFO - Logfile is 'doc.blg' INFO - Reading 'doc.bcf' INFO - Found 31 citekeys in bib section 0 INFO - Processing section 0 INFO - Globbing data source 'literature.bib' INFO - Globbed data source 'literature.bib' to literature.bib INFO - Looking for bibtex format file 'literature.bib' for section 0 INFO - LaTeX decoding ... INFO - Found BibTeX data source 'literature.bib'   so harmless in my view. Then with --debug I additionally get in the end.  INFO - LaTeX decoding ... warning: overriding existing definition of macro "jun" warning: overriding existing definition of macro "jul" warning: overriding existing definition of macro "sep" warning: overriding existing definition of macro "jan" [...] warning: overriding existing definition of macro "nov" INFO - Found BibTeX data source 'literature.bib' Unicode::UCD: failed to find unicore/version in /var/folders/hm/gt63cn0j2r7bwbzw7c1hww1r0000gn/T/par-626572676d616e6e/cache-2f8a664c3c933a44d096bcc8d018a5e92bced897/inc/lib /var/folders/hm/gt63cn0j2r7bwbzw7c1hww1r0000gn/T/par-626572676d616e6e/cache-2f8a664c3c933a44d096bcc8d018a5e92bced897/inc CODE(0x7fd026aeb5a8) CODE(0x7fd026aebb90) at /var/folders/hm/gt63cn0j2r7bwbzw7c1hww1r0000gn/T/par-626572676d616e6e/cache-2f8a664c3c933a44d096bcc8d018a5e92bced897/inc/lib/Biber/Input/file/bibtex.pm line 1011.   It seems unrelated to the library itself since deleting a few entries (going through deleting one half, then the other), the problem persists. It does not happen for an empty literature, but as soon as a first entry is added (just author/journal/title/year/volume/pages - no utf8-only chars) this error message appears.  what does this last error message mean?  How can I solve this? Proving an inequality by induction, how to figure out intermediate inductive steps? I'm working on proving the following statement using induction:  $$ \sum_{r=1}^n \frac{1}{r^2} \le \frac{2n}{n+1} $$  Fair enough. I'll start with the basis step:  Basis Step: (n=1) $$ \sum_{r=1}^n \frac{1}{r^2} \le \frac{2n}{n+1} $$ $$ \frac{1}{1^2} \le \frac{2}{1+1} $$ $$ 1 \le 1  \checkmark  $$  Inductive Step: $$ \sum_{r=1}^{n+1} \frac{1}{r^2} \le \frac{2(n+1)}{(n+1)+1} $$ $$ \sum_{r=1}^{n+1} \frac{1}{r^2} \le \frac{2(n+1)}{n+2} $$  My goal is to prove $\forall_{n\ge1} s(n) \implies s(n+1) $ or that this inequality holds true for all $n\ge1$.  I'm not quite sure to go from here on the inductive step. I understand that I need to basically work some clever substitution and manipulation into the problem to end up with: $$ \sum_{r=1}^{n+1} \frac{1}{r^2} \le \frac{2n}{n+1} $$  However, I'm not quite sure what needs to done to obtain this after attempting a few times. Im trying to get my head around complex integration/complex line integrals. Real integration can be thought of as the area under a curve or the opposite of differentiation. Thinking of it geometrically as the area under a curve or the volume under a surface in 3 dimension is very intuitive.   So is there a geometric way of thinking about complex integration? Or should I just be viewing it as process that reverses differentiation? Or has integration other meanings in complex analysis? Here is an example, could someone explain this to me - Here's the definition of the integral along a curve gamma in C, parameterized by $w:[a, b] -&gt;C$ \begin{equation} \int_\gamma f(z)dz = \int_a^b f(w(t)).w{(t)}'dt \end{equation}   So I have -  $\gamma$ is the unit circle with anti-clockwise orientation parameterized by  $w:[0, 2\pi]\to C$  $w(t) = e ^{it} = Cos(t) + iSin(t)$  So if use the definition of the integral,   $\int_\gamma f(z)dz = \int^b_a f(w(t)).w{(t)}&#39;dt$,  and work this out it comes to  $\int^{2\pi}_0 i dt = 2{\pi}i$  So what does this $2{\pi}i$ represent? Does it mean anything geometrically, like if a regular integral works out to be 10 that means the area under the curve between 2 points is 10... How can I parse integers passed to an application as command line arguments if the app is unicode?  Unicode apps have a main like this:  int _tmain(int argc, _TCHAR* argv[])   argv[?] is a wchar_t*. That means i can't use atoi. How can I convert it to an integer? Is stringstream the best option? How good is it for SEO if you have a widget that lives on other sites? I made a widget that would ideally live on other sites.  Here is an example:   I guess since the widget would link back to me, it would be an SEO boost for my site.  Is that correct?  Or would it be just an SEO boost for that particular URL?  If it is just an SEO boost for the particular URL, it does me little good since that page does not link to any of my other pages.  Am I thinking about this correctly?  How are these things typically handled so that there is  a benefit to my site's SEO? Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$ Suppose that $H$ and $K$ are normal subgroups of a group $G$ such that $HK=G$. I need to show that  $G/(H\cap K)\cong (G/H)\times (G/K)$.  So from the second isomorphism theorem we have that:  $HK/H\cong H/(H\cap K)$ which gives that $G/H\cong H/(H\cap K)$  $HK/K\cong K/(H\cap K)$ which gives that $G/K\cong K/(H\cap K)$  So we must now show that:  $H/(H\cap K)\times K/(H\cap K)\cong G/(H\cap K)$  So consider the map $\theta:H/(H\cap K)\times K/(H\cap K)\rightarrow G/(H\cap K)$ such that $\theta(h(H\cap K)\times k(H\cap K))=hk(H\cap K)$  Now this is a homomorphism and is surjective. To check injectiviy we see that if:  $\theta(h_1(H\cap K)\times k_1(H\cap K))=\theta(h_2(H\cap K)\times k_2(H\cap K))$ then we have that:  $(h_1k_1(H\cap K))=(h_2k_2(H\cap K))$ so that $(h_1k_1)(h_2k_2)^{-1}(H\cap K)=(H\cap K)$ which gives that $h_1k_1(H\cap K)=h_2k_2(H\cap K)$ So we are done.  Is the above correct?  Thanks for any help I have a bunch of magnets (one of those game-board thingies) given to me when I was a school-going lad over 20 years ago, and the magnets feel just as strong as it was the day it was given.   As a corollary to this question , is there a way to determine how long a permanent magnet will remain a magnet?   Addendum: Would two magnets remain a magnet for a shorter duration if they were glued in close proximity with like poles facing each other? This is what I have come up with so far, but I am rather lost at lines 3-4...  $$\begin{align} (a,b)\in A\times (B\setminus C)\iff&amp; a\in A \land b\in (B\setminus C)\\ \iff&amp; a\in A \land (b\in B \land \lnot(b\in C))\\ \iff&amp; (a\in A \land b\in B) \land (a\in A \land b\notin C)\\ \iff&amp; (a\in A \land b\in B)\setminus (a\in A \land b\in C)\\ \iff&amp; (a,b)\in (A\times B)\setminus ((a,b)\in A\times C)\\ \iff&amp; (a,b)\in (A\times B)\setminus (A\times C) \end{align}$$ How can I disable the “News and Interests” Widget on the Windows 10 Taskbar? On Windows 10 version 1909 and newer releases, Microsoft has added a &quot;News and Interests&quot; widget on the Taskbar (see ):  How can I remove this Widget from the Taskbar? When do you use Java's @Override annotation and why? What are the best practices for using Java's @Override annotation and why?     It seems like it would be overkill to mark every single overridden method with the @Override annotation.   Are there certain programming situations that call for using the @Override and others that should never use the @Override? I have recently upgraded my OS to Ubuntu 18.04 (fresh install via boot device). However, when trying the command:  sudo apt-get upgrade   It works fine until ~75% when it stops and says:  snapd.snap-repair.service is a disabled or a static unit, not starting it.   I'm not quite sure what this means and if I Crtl-Z to get out of it, any time I try to install anything I get:  E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it?   and have to restart my computer to install anything. Short sci-fi story of plan devised by marooned spaceship pilot to save paradise world from development Spaceship crashes on beautiful, remote planet. The pilot survives and lives quite well on the beautiful "island paradise" world amongst friendly, good-natured people... but, one day (while relaxing in a hammock near a beach) he "realized he was dying" (actually, that he would eventually die, then being unable to help the people he had come to love). He fears future "discovery" of his adopted world and the inevitable plundering of the resources and people by "developers"... so he devises... "a plan" "convinced island elders to support his plan" "his students taught others" "achieved 80% literacy... a remarkable feat" "established world government" "more generous than developer expected" "successfully argued for independent status" "established 100% taxation rate" "finished resort buildings converted to school" "developer hired to build resort in isolated area"  ...'not having luck finding it... my recollection of the story is good, but apparently not EXACT/searchable phrases How can one express frequentist p-value in terms of Bayesian concepts? "Neither", "none", "no one" + [of them] + verb-s In a comment on English Language &amp; Usage I read the following answer responding to a(n) asker's question: &quot;Neither sound natural.&quot; I have always had more than one doubt on the &quot;neither&quot; usage and I would like understand(ing) the &quot;secrets&quot; to use this word better or, at the best, correctly. So, let us consider the following examples:  1 Neither sound natural. 2 None sound natural. 3 No one sound natural. 4 Neither of them sound natural. 5 None of them sound natural. 6 No one of them sound natural. 7 Neither sounds natural. 8 None sounds natural. 9 No one sounds natural. 10 Neither of them sounds natural. 11 None of them sounds natural. 12 No one of them sounds natural.  Comparing the above sentences (one) with each other, can anybody explain which is grammatical and why? How to insert strings containing slashes with sed? Is there a technical reason Android update story is so bad? Is there a technical reason why Android phones general lag a lot behind the stable released version of Android?    This applies to both new phones, for example a recent trip to the phone shop everything was 4.0 to 4.2.1, KitKat could not be seen. And also old phones, my girlfriend's iPhone 4 had an OTA update to the latest OS, this is a July 2010 phone, whilst a July 2010 Android is basically a paperweight.    Presumably Android itself doesn't concern itself with the actual hardware, and thus talks to the OS via abstractions? I guess then the handset maker just provides the drivers for the specific hardware, thus I can't see the issue with pushing OTA updates if the ABI remains stable (my phone doesn't grow new hardware features). Which command controls the open file limits? What is a "good fit" Brier score and Harrell's C Index I’m currently working on a solar powered boat with a modest sized team of people. For our competition we are only allowed to have 3 12v batteries on board but we are allowed to have up to 52v at any point in our setup. We are hoping to kick up the speed of our outboard motor for the sprint portion of the completion and are looking into using a boost converter for this.   After doing a little research I’m a bit confused about how they fundamentally work. From what I can tell they take in a voltage and current and put out a higher voltage with a lower current with some level of efficiency. But it seems to be independent from the load( in this case the motor) which doesn’t make much sense to me because I thought the current would be determined by whatever my load is. How do loads actually interact with boost converters?( The simpler the better.)  For reference we are using the Saietta 119r motor system and I’m considering using the MPS MPQ3425 boost converter.