Separating plural possessive apostrophe from closing double-quote
How do you end with a single quote followed by a double quote?
In a  a doubt was voiced about my answer, which claims GCM to requires $2^{128}$ for a successful forgery. The doubt was that the square root needs to be taken meaning the security would be $2^{64}$.  So of course I immediately checked the relevant security theorem ():  $$\mathbf{Adv}^{\text{auth}}_{\operatorname{GCM}[\operatorname{Perm}(n),\tau]}(\mathcal A)\leq \frac{0.5(\sigma+q+q'+1)^2}{2^n}+\frac{q'(\ell_A+1)}{2^\tau}$$  with $\sigma$ being the total plaintext size in blocks, $q$ being the total number of encryption queries, $q'$ being the total number of decryption queries, $n$ being the size in bits of the underlying permutation, $\ell_A$ being maximum authenticated input length in blocks and $\tau$ being the tag size in bits.  Now clearly from this we can see that performing $2^{n/2}=2^{64}$ queries yields a strong enough advantage for a break.  Now my question is: When talking about "n-bits of security" or "needs $2^n$ operations to break", do we usually talk about "online" security, ie queries to an oracle can be done and cost $1$ or "offline" security where no oracles are available or do we need to make this decision depending on the situation?  TL;DR: Does GCM offer 64 or 128 bit security? Functions of Independent Random Variables Is the claim that functions of independent random variables are themselves independent, true?   I have seen that result often used implicitly in some proofs, for example in the proof of independence between the sample mean and the sample variance of a normal distribution, but I have not been able to find justification for it. It seems that some authors take it as given but I am not certain that this is always the case. How to detect using c# if a pendrive is plugged into a USB port? Is there a way to find out when in a LAN anyone plugs in a pendrive to the USB port?  Programatically (in C# preferably) or through some tool. Basically I'd imagine a client application sits on each terminal and monitors the USB ports and sends the information to the server.   a.) Can I get the details of the file(s) being copied? b.) Is there a way to do this without a client application?   EDIT  I dont want to disable the USB port entirely. its to be on a need to have basis. Basically just want the users on the LAN to share data responsibly and know that whatever data is tranfered is monitored and logged and can be questioned later. How do I solve $$x'=e^{it}\overline{x}?$$  This is a complex differential equation, but I don't see how to solve it.  Edit: the original ODE is given by $$(x', y')=\begin{pmatrix}\cos t&amp; \sin t\\ \sin t&amp;-\cos t\end{pmatrix}(x,y)$$ I want to show that solutions of this ODE do not remain bounded for all $t$, and the idea was to solve the complex equation. How to typeset subscript in usual text mode? It's easy to make subscripts in math mode: $a_i$.   How do I make a subscript outside math environment, likethis? Can I use the Twig template engine? I do a lot of  development and I like their templating language. , the , looks very much like it.  How can I use Twig in Drupal 7 or even Drupal 6? Difference between '>' and '-gt' What's the difference between these:  SEC=$(mysql -hxxx -Pxxx -uxxx -pxxx -se "SELECT Seconds FROM tablename")  SEC=100   Both return the same result (100). But when I test it with:  if [ ${SEC} &gt; 1 ] then     echo "SEC GT 1" else     echo "SEC LT 1" fi   The first one returns:  "SEC GT 1"   The second one returns:  "SEC LT 1"   If however, I change it to:  if [ ${SEC} -gt 1 ]   then the result is reversed.  I'm assuming it's got something to do with the datatype, and that I presumbaly need to cast one or the other to get the same result.  It's just that at present it's messing up my testing, as I have to remember to change the IF section every time. How can I use docker without sudo? On Docker's documentation pages, all example commands are shown without sudo, like this one:  docker ps   On Ubuntu, the binary is called docker.io. It also does not work without sudo:  sudo docker.io ps   How can I configure Docker so that I don't need to prefix every Docker command with sudo? Why do you add +1 in counting test questions? If $0$ is the zero-object $ \Longrightarrow F(0) $ is the zero object when $F$ additive Find the center of the symmetry group $S_n$. Find the center of the symmetry group $S_n$.   Attempt:  By definition, the center is $Z(S_n) = \{ a \in S_n : ag = ga \forall\  g \in S_n\}$. Then we know the identity $e$ is in $S_n$ since there is always the trivial permutation. Suppose $a$ is in $S_n$, but not equal to identity. Now we can imagine the permutation as bijective function that maps from $\{1,2,\dotsc,n\}$ to $\{1,2,\dotsc,n\}$.  So suppose $p$ is a permutation map. Then $p$ maps from a location $i$ to a location $j$. Take $p(i) = j$ where $i\neq j$. Let $k$ be in $\{1,2,\dotsc,n\}$, where $k$, $i$ and $j$ are all different elements. The cycle $r = (jk)$, then we will see if this commutes.  $rp(i) = rj$    Can someone please help me, I am stuck?  Thank you. Pageblocktable to be rendered as table in PDF I have a VF code below where I am trying to display the related list of an object using  and  command. I am rendering this page as PDF , doing that in my PDF I am unable to see the content in a tabular format. How can I make the content appear in a table?      &lt;apex:pageBlockSection columns="1" title="TECHNICAL ASSESSMENT"&gt;          &lt;apex:repeat value="{!interviewSkillReviews}" var="interview"&gt;              &lt;table border="1" cellpadding="6"&gt;                 &lt;apex:pageblockTable value="{!interview.Skill_review__r}" var="skillreview"&gt;                      &lt;apex:column headerValue="Skill Name"&gt;                                                         &lt;apex:outputText value="{!skillreview.Skill__r.Name}"/&gt;                     &lt;/apex:column&gt;                 &lt;apex:column headerValue="Recommended Level"&gt;                     &lt;apex:outputText value="{!skillreview.Level__r.Name}"/&gt;                 &lt;/apex:column&gt;                  &lt;apex:column headerValue="Rating"&gt;                     &lt;apex:outputField value="{!skillreview.RatingCopy__c}" rendered="{!NOT(interviewerMode)}" /&gt;                     &lt;apex:selectList value="{!rating}" multiselect="false" size="1" rendered="{!interviewerMode}"&gt;                         &lt;apex:selectOption itemValue="1" itemLabel="1"/&gt;                         &lt;apex:selectOption itemValue="2" itemLabel="2"/&gt;                         &lt;apex:selectOption itemValue="3" itemLabel="3"/&gt;                         &lt;apex:selectOption itemValue="4" itemLabel="4"/&gt;                         &lt;apex:selectOption itemValue="5" itemLabel="5"/&gt;                     &lt;/apex:selectList&gt;                 &lt;/apex:column&gt;                  &lt;apex:column headerValue="Rating Level Description"&gt;                     &lt;apex:outputText value="{!skillreview.Skill_Level_Description__c}"/&gt;                 &lt;/apex:column&gt;               &lt;/apex:pageblockTable&gt;         &lt;/table&gt;      &lt;/apex:repeat&gt; &lt;/apex:pageBlockSection&gt;   I tried using &lt;table&gt; command of HTML but I just get a border around the pageblocktable.    Example of table look and feel: For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$ The definition of a Fibonacci number is as follows:  $$F_0=0\\F_1=1\\F_n=F_{n-1}+F_{n-2}\text{ for } n\geq 2$$   Prove the given property of the Fibonacci numbers for all n greater than or equal to 1. $$F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$$  I am pretty sure I should use weak induction to solve this. My professor got me used to solving it in the following format, which I would like to use because it help me map everything out...  This is what I have so far:  Base Case: Solve for $F_0$ and $F_1$ for the following function: $F_nF_{n+1}$.  Inductive Hypothesis:  What I need to show: I need to show $F_{n+1}F_{n+1+1}$ will satisfy the given property. Proof Proper:  (didn't get to it yet)  Any intro. tips and pointers? WoeUSB Error Code 256 with NTFS formatted USB Login with Facebook using Stack Exchange Android App jsp:useBean scope iCloud has sucked up all my laptop's files - can you transfer files directly from iCloud to Google Drive? I'm trying to disconnect my macbook from iCloud, as it's been creating some problems.  I was told by an Apple Support employee that doing so is only recommended once you've backed up everything from your Mac somewhere, to ensure you don't lose any files - so my goal is to upload everything to Google Drive before messing with my laptop's iCloud settings. The problem is, almost none of the projects that I want to back up to Google Drive are truly on my laptop - instead I mostly just have folders full of file names, which are placeholders for the real files that have been sucked into iCloud. This means I have to re-download everything to my computer before uploading it all to Google Drive. Another crucial piece of information is that I only have 1 GB of storage left on my macbook, which prevents me from re-downloading any complete projects/folders at a time. So unfortunately my current method is this: downloading 1-5 files at a time, uploading these few things to Google Drive, deleting the copies from my laptop and trash, repeat (thousands of times). So, I was wondering if anyone could offer any alternative methods for uploading stuff to Google Drive in this situation - for example, is there a way to transfer files directly from iCloud to Google Drive without having to download them to my laptop first? I should probably mention that I've scoured my laptop for duplicated files and applications I no longer use, make sure to empty my trash regularly, etc (I also asked Apple Support to help me make sure I wasn't missing out on any other ways to maximize storage space). The most obvious culprit of my lack of space is the massive 150 GB iCloud folder on my laptop, which appears to contain duplicates of everything on my computer. I can't seem to do anything about it until I've disconnected from iCloud itself (its reasons for existence are unclear to me in the first place...but that's beside the point lol). Im using a program called Daisy Disk to see what is taking up space in my Mac and I find that the /cores directory is taking up 77gb.   Is that a problem? Can I get rid of it to regain the space? Should I remove Adult Dependent from my 2019 tax return so they will receive a COVID Stimulus Check? On my 2019 Tax Return I claimed my 28 year old girlfriend as a dependent. This makes her ineligible to receive a COVID Stimulus Check. My return was already accepted and I have already received my refund. Should I amend my return, remove her as a dependent? Would she then be eligible to receive the stimulus check? Can the milky way actually be photographed ? I know the image is manipulated, and is probably a composite, but how do you capture such contrast in the milky way? Is an equitorially mounted scope required? Any advice or pointers are welcome, thanks.  I'm heading out towards much less light polluted areas middle of next week and I want to try some nighttime sky captures with my 7D.  Additional info: I just found  on wikipedia that says: 54s, tripod mounted 5D, 16mm lens, f/2.8, ISO800. What else do I need to be aware of? My 7D is only an APS-C and the widest lens I have is 19mm. I'm thinking that might not be wide enough to capture an interesting shot?