Which is the correct form of the sentence?      There has been many instances of outbreaks in vaccinated populations    vs.     There have been many instances of outbreaks in vaccinated populations?   The question that this is supposed to be a duplicate of does not mention there has or there have. We have many learners here who are not going to be able to deduce much of anything from it.
For example:     There's two options here   or     There are two options here   I hear a lot of people say the first line (or something similar), but isn't that incorrect? Isn't it plural and therefore you should use "there are"?
Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$ Does anybody know how to add the shapefile name to a field in the file's attribute table?  I've found a description:     'You have to use inline variable in CalculateField like %Name% in   expresssion so that whatever the name of the file is, the string will   be inserted based on Name of the dbase file !'   I've tried to CalculateField tool with %Name%, but I got message:  Executing: CalculateField "2011-11-6 15_41_point" DBFName %Name% PYTHON # Start Time: Thu Dec 08 23:34:23 2011 WARNING 000405: No records within table Succeeded at Thu Dec 08 23:34:24 2011 (Elapsed Time: 1.00 seconds)   Where is my mistake? Living forever in D&D (via spells)? I was thinking of a way for a humanoid (PC or NPC) to live forever in a D&amp;D setting, but through rather "common" and reproducible means, such that they will be available to many. By this logic I exclude cases such as a god giving immortality (or some other intervention) or a unique item granting an endless lifespan etc.  To cover all bases I will note that miracle and wish cannot do this directly, nor can true resurrection (and its lesser brethren) "restore to life a creature who has died of old age".  I had came up with the following ruse:   Reach your deathbed with at least 2 HD (or levels). Have someone kill you so that the cause of death will not be "old age". Have a druid cast reincarnate on you into a young body. You "recall the majority of your former life". I assume your memories, personality/identity and experiences are preserved.   Rinse and repeat. It's not that difficult to recover the 1 HD lost through the course of almost a lifetime. The material components are worth 1,000 gp - might not be easy to get, but surely possible.  Furthermore, it is stated that "A wish or a miracle spell can restore a reincarnated character to his or her original form.". I assume the "original form" is the aged humanoid at his or her deathbed - not the direction we are looking for, unless it means that the humanoid restores his race only.  Is there a flaw in this plan? Is there another way of doing it? I have Lubuntu 16.10 installed on my disk mounted as /.  The problem is that the CUPS log file( /var/log/cups/error.log)  grows all the time until I no have free space left on the disk...   So when I delete that file, the space on disk freed up again  I already tried:    fsck disk usage analyzer every apt-cleaning/autocleaning, and dependencies fixing.    How should I proceed?  du -sxh:  9,0G    .  Model: ATA ST3160815AS (scsi) Disk /dev/sda: 160GB Sector size (logical/physical): 512B/512B Partition Table: msdos Disk Flags:   Number  Start   End     Size    Type      File system     Flags  1      32,3kB  50,3GB  50,3GB  primary   ext4            boot  2      50,3GB  160GB   110GB   extended  5      50,3GB  158GB   108GB   logical   ext4  6      158GB   160GB   2136MB  logical   linux-swap(v1)   parted --list &amp;&amp; sudo df -h:  Model: ATA ST3160815AS (scsi) Disk /dev/sda: 160GB Sector size (logical/physical): 512B/512B Partition Table: msdos Disk Flags:   Number  Start   End     Size    Type     File system  Flags  1      32,3kB  50,3GB  50,3GB  primary  ext4         boot  2      50,3GB  160GB   110GB   primary  ext4   Filesystem      Size  Used Avail Use% Mounted on udev            985M     0  985M   0% /dev tmpfs           201M  6,3M  195M   4% /run /dev/sda1        46G   43G  709M  99% / tmpfs          1003M  188K 1003M   1% /dev/shm tmpfs           5,0M  4,0K  5,0M   1% /run/lock tmpfs          1003M     0 1003M   0% /sys/fs/cgroup tmpfs           201M   36K  201M   1% /run/user/1000 /dev/sda2       101G   60M   96G   1% /media/aram/ What are the numbers / symbols to the right of my reputation counter? How come the PHP private class var is not private? How do I manually install Adobe Flash player for Chromium? I am a super newbie for Ubuntu and basically need Ubuntu for a Python package.  I would like to run a Python file in say e:/username/folder1/folder2/python.py. I tried every method online and the only reply is bash: cd./e: No such file or directory. I am not sure whether it is because of the bash windows or virtualenv.  When I use bash on Ubuntu on Windows, ls, it says VIRTUALENV_DIR. cd, it says /home/username. The cd .. etc changes the directory a little, but not another drive, nor the folder I would like it to find. I'm trying to write an automated test of an application that basically translates a custom message format into an XML message and sends it out the other end.  I've got a good set of input/output message pairs so all I need to do is send the input messages in and listen for the XML message to come out the other end.  When it comes time to compare the actual output to the expected output I'm running into some problems.  My first thought was just to do string comparisons on the expected and actual messages.  This doens't work very well because the example data we have isn't always formatted consistently and there are often times different aliases used for the XML namespace (and sometimes namespaces aren't used at all.)  I know I can parse both strings and then walk through each element and compare them myself and this wouldn't be too difficult to do, but I get the feeling there's a better way or a library I could leverage.   So, boiled down, the question is:  Given two Java Strings which both contain valid XML how would you go about determining if they are semantically equivalent?  Bonus points if you have a way to determine what the differences are. Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$ I am trying to find a closed form for  $$\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx = 0.094561677526995723016 \cdots$$  It seems that the answer is $$\frac{\pi^2}{12}\left( 1-\sqrt{3}\right)+\log(2) \log \left(1+\sqrt{3} \right)$$  Mathematica is unable to give a closed form for the indefinite integral.  How can we prove this result? Please help me.  EDIT  Apart from this result, the following equalities are also known to exist: $$\begin{align*} \int_0^1 \frac{\log \left( 1+x^{4+\sqrt{15}}\right)}{1+x}\mathrm dx &amp;=\frac{\pi^2}{12} \left( 2-\sqrt{15}\right)+\log \left( \frac{1+\sqrt{5}}{2}\right)\log \left(2+\sqrt{3} \right) \\ &amp;\quad +\log(2)\log\left( \sqrt{3}+\sqrt{5}\right) \\ \int_0^1 \frac{\log \left( 1+x^{6+\sqrt{35}}\right)}{1+x}\mathrm dx &amp;= \frac{\pi^2}{12} \left( 3-\sqrt{35}\right)+\log \left(\frac{1+\sqrt{5}}{2} \right)\log \left(8+3\sqrt{7} \right) \\ &amp;\quad +\log(2) \log \left( \sqrt{5}+\sqrt{7}\right) \end{align*}$$  Please take a look . List all my drafts In GMAIL you can list all your boss-tell-off and wife-cuss-out emails by clicking Drafts    I'd like to see my started-but-never-finished responses, possibly between x Answers and y Votes in /&lt;&lt;user&gt;&gt;/Stats/? Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$ Let $a\ge 2$ be an integer. Show that for positive integers $m,n$, we have $a^n - 1$ divides $a^m - 1$ if and only if $n$ divides $m$.   I am having trouble showing this. I've seen a similar problem on here but it only shows one direction for the proof. I would like to see both directions.  This is what I have so far: Let $m = nq + r$, then $a^m - 1 = a^{nq + r}- 1 = a^{nq}a^r - 1 = a^{nq}a^r - a^r + a^r - 1 = a^r(a^{nq} - 1) + a^r - 1$. Since $0\le r\lt n$, $r = 0$ then $a^m - 1$ = $a^{nq} - 1$ so $a^m$ = $a^{nq}$ . Thus $m = nq$ hence $n\mid m$. Prevent Windows 10 installer from using the preinstalled serial key without disabling UEFI My laptop (a Lenovo Flex 2 15) came preinstalled with Windows 8 Standard (with the serial key preinstalled into the BIOS), and I've since installed an SSD (a Samsung Evo 840 120GB) &amp; upgraded to Windows 10.  When the laptop still had its hard drive, I upgraded it to Professional so I could use the resources provided by the domain on my homeserver; because of this, I can only use the Professional editions of Windows (Home can't join domains).  I bought Windows 10 Professional &amp; completed a fresh-install (complete reinstallation) of Windows, only that it installed Windows 10 Home instead of Professional. I'm guessing this is due to the Windows 8 Standard Edition serial key preinstalled in the BIOS.  I then downloaded an All-In-One ISO image of Windows 10 from MSDN (of which I have limited access to), transferred the installer onto a USB stick, &amp; reinstalled (a clean install again). However it's still installing Windows 10 Home.  If I try to install using the AIO image from within Windows, the installer does not present me with a list of options for the edition I want to install; instead, it assumes that I want to install Home Edition:    I am able to get Windows 10 Professional to install if I disable UEFI &amp; use Legacy instead, but I feel that this is stepping around the issue rather than resolving it.  Is it possible to have the Windows 10 installer ignore any serial keys preinstalled in the BIOS/UEFI? If so, how? If not, is using Legacy mode really the only way around this? Allow me to get notifications for new Meta posts, like mods do I'm currently helping out on . One of the most valuable things on new beta sites, especially private/early public betas, is Meta participation - see :  Treat Meta Questions Like Gold It’s not unusual for your meta site to receive significantly less traffic than the main site. The problems begin when you meta starts to get ignored by the community and ignored by the moderators. It is particularly disturbing when users reach out in meta and starts talking about improving the site or asking for help… only to be ignored; No follow-up, only deafening silence  Because of this, Diamond mods get a notification in their inbox for each new question on their Meta, helping ensure that each meta post is addressed. However, wouldn't it be great if Diamond mods weren't the only ones that could do this? The post does say that the community needs to be seeing these questions too. As an involved user, I would really like to be notified of these new questions - it would increase the good I could do the site. How about this?:  Of course, it would be opt-in, not opt-out, and per-site. A feature like this would greatly improve the good that enthusiastic site-builders can do for the site, and would, most likely, increase the overall chances of a site's success. Preserving signatures of decorated functions How can I replace a string in a file(s)? Sum of indepedent random variables and a constant Let $X_1$ and $X_2$ be independent Normal random variables with mean $\mu_1$ and $\mu_2$, and variances $\sigma_1$ and $\sigma_2$. Let $Y = X_2-X_1 + c$, where $c$ is a constant. For notational simplicity, let $Y = X' + c$, where $X' = X_2-X_1$ The moment generating function of a Normal random variable $X_n\sim N(μ_n,σ_n^2)$ is $$M_{X_n } (t)=\text{exp}\Big(μ_n t+\frac{σ_n^2 t^2}{2}\Big)$$ Then, $$M_{X'} (t)=\text{exp}\Big[t(\mu_1+\mu_2)+\frac{t^2}{2}(\sigma^2_1+\sigma^2_2)\Big]$$ Thus, by the uniqueness property of moment generating function, $X'$ is said to follow a Normal distribution with mean $(\mu_1+\mu_2)$ and variance $(\sigma^2_1+\sigma^2_2)$. How do I proceed from here to derive the following:  First, I want to establish that $Y$ is also a Normal random variable using the moment generating function. The constant $c$ bugs me, but I cannot ignore it. As per my understanding, $Y\sim N\big(c+\mu_1+\mu_2,\sigma^2_1+\sigma^2_2\big)$ (and I could be completely wrong). But I don't understand how to apply the moment generating function to prove that.  Secondly, I want to derive $P(Y \leq a)$, where $a$ is a constant. If I am not mistaken, $P(Y \leq a)$ can be written as $$P(Y \leq a)=\Phi\Bigg(\frac{a-X_2-X_1 + c}{\sqrt{2(\sigma^2_1+\sigma^2_2)}}\Bigg).$$ But how do I arrive at that.   Any help is high solicited and appreciated. What is inertia of a body? The definition of  is  "Inertia is the resistance offered by the body whenever its state of motion is changed."   What is inertia of a body? Is inertia actually a force exerted by the body?  If so, then why is there no application of inertia in numerical problems involving application of force on a body? What is the actual application of inertia in theory? Proving an entire, complex function with below bounded modulus is constant. How would I show that an entire function $f$ with the property $|f(z)| \geq 1$ must be constant?    I'm aware of Liouville's theorem, just not sure how to apply it here. Let $B$ be a commutative domain and $A \subseteq B$ a subring. Suppose that the extension $A \to B$ is finite, i.e. $B$ is finitely generated as an $A$-module. If $I \cap A = \lbrace 0 \rbrace$ for some ideal $I$ of $B$, can we conclude that $I = \lbrace 0 \rbrace$?  I know that if $I$ contains a nonzero prime ideal, the statement holds since $A \to B$ is an integral extension, whereby no two comparable prime ideals of $B$ can have the same intersection with $A$. But does the statement still hold if $I$ does not contain a nonzero prime ideal? And what if $A \to B$ is only assumed to be an integral extension?