Say I have a holomrphic function $f(z)$ in domain $D$, say $|z|&gt;4$ and my function is not holomorphic for $|z|\le4$ - it has some poles there. Does it mean there is necessarily an antiderivative for $f(z)$? I know I can use  and calculate all the residues inside $|z|\le4$ and check if their sum is zero. However what seemed more intuitive to me is to prove that since $\int_{\gamma}f(z)dz$ for every $\mathbb{\gamma}$ contained in $D$, depends only on the start and end points, there exists an antiderivative for $f(z)$. Is my prof correct? Can I conclude that in general, a holomorphic function in a domain $D$ not only has infinitely many derivatives in $D$, but it has also infinitely many antiderivatives there?
I have read that a holomorphic function in an open disc has a primitive in that disc. Does this mean that for any holomorphic function $f$ in any open set $U,$ that $f$ has a primitive? I say this because I can take a large enough open disc to cover the open set $U$ and find its primitive there. Is this a correct way of thinking?
Does infinity exist in physical systems? Sometimes people fail at asking a question by being too broad, unclear like . So I'll take a stab at what I believe to be the same question, but more concise and clearly stated:     Does infinity exist in either terms of structure, parameters, or   measurement in any physical systems?   Can infinity have any real connection with reality?  Or is infinity purely a mathematical concept just used by physicists as a convenient way to describe the very large, an approximation?  I have heard that if you model a physical system (), and you run into infinity as a solution, then you have either made an error in your calculations or your model is wrong. I am rebuilding an old server.  Only one of the five old sites need to go live and all five of the old sites point to the same IP address.  Unfortunately any time a request is made for one of the old sites via their own unique domain names they are passed the pages from the one site that I'm trying to make live.  I would just like the old sites to display a 404 instead of the one site that I'm actually trying to make live.  As an example:   Site 1 (192.168.0.1) [www.first.com] Site 2 (192.168.0.1) [www.second.com] Site 3 (192.168.0.1) [www.third.com]   I want to move site 1 live again.  So I turned on apache on the machine with the IP address of 192.168.0.1, with all of site 1's files in the /var/www directory.  When I browse to 192.168.0.1 or www.first.com I correctly see site 1. When I browse to www.second.com and www.third.com I also receive site 1 which is the problem.  Is there a way I can 404 any request which comes in without www.first.com?  Here is my sites-available:  NameVirtualHost *:80  LogFormat "%h %l %u %t \"%r\" %&gt;s %b" common  &lt;Files ~ "^\.ht"&gt;     Order allow,deny     Deny from all     Satisfy All &lt;/Files&gt;  &lt;Directory /&gt;   Order Deny,Allow   Deny from all   Options None   AllowOverride None   Options None &lt;/Directory&gt;  &lt;Directory /var/www&gt;   Order Allow,Deny   Allow from all &lt;/Directory&gt;  &lt;VirtualHost *:80&gt;         ServerName first.com         ServerAlias www.first.com         DocumentRoot /var/www         ErrorLog /var/log/first.com.err         CustomLog /var/log/first.com.log common &lt;/VirtualHost&gt;  &lt;VirtualHost _default_:*&gt;         ServerName unknown         DocumentRoot /var/www_404 &lt;/VirtualHost&gt; Caption makes Table move in statsoc class Where can I find information about upcoming special issues in a field of study? How can I find information about upcoming special issues related to a special field of study? There are good websites for upcoming conferences but I could not find any place to search for special issues. My Wi-Fi connection seems to be very weak and the range is very low. It drops by two bars if I just move to the next room and by two if just step outside.  The speed is also not fast as compared to what I get from the router on my desktop .  My laptop is a HP laptop with RTL8723de module. Can anyone help me in bumping up my Wi-Fi speed?  Result of lspci -nnk | grep 0280 -A3:  03:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. Device [10ec:d723] Subsystem: Hewlett-Packard Company Device [103c:8319] Kernel driver in use: rtl8723de Kernel modules: rtl8723de At what point does a caster define the target of a spell? The new School of Invention tradition for Wizards () while still in playtesting (and indeed a bit silly in my opinion, more of a "chaos wizard"), got me thinking about its reckless casting ability. This allows the caster to cast magic they do not have prepared and get a random result. The random spells have different targeting criteria (Wall of Stone, Fireball, Feign Death , Mass Cure Wounds) and so it is not possible to decide the target of the spell until it has been cast, as you don't know what you are going to get until it is cast.  This suggests that the designer of the subclass has made the assumption that you don't actually target until you have cast the spell and release it, which makes sense from one point of view, strongly supported by the way a prepared action casting works, PHB p.193 where you cast the spell and hold the energy until the condition is met for the readied action at which point you target the spell.  While the Unearthed Arcana is not RAW or finalized and released, my question is not about this subclass, but about the official rules as a whole.  Is there was any direct RAW, or other supporting or opposing RAW, that states at what point a caster defines the target of a spell?  As a sub-question: are there any circumstances where it actually matters, other than the already defined Readied Action spell casting, in the official rules? Repeatedly rolling a six sided die four times and summing the highest three results gives you a distribution with what mean and standard deviation? Repeatedly rolling a six sided die four times and summing the highest three results gives you a distribution with what mean and standard deviation?  I've only taken AP statistics, but I would like to learn how to do this. dollar-terminated strings In my assembly language class, our first assignment was to write a program to print out a simple dollar-terminated string in DOS.  It looked something like this:  BITS 32     global _main  section .data     msg db "Hello, world!", 13, 10, ’$’  section .text _main: mov ah, 9 mov edx, msg int 21h ret   As I understand it, the $ sign serves to terminate the sting like null does in C.  But what do I do if I want to put a dollar sign in the string (like I want to print out "it costs $30")?  This seems like a simple question, but my professor didn't know the answer and I don't seem to find it using a google search. Chromatic Number The smallest number of colors needed to color a graph $G$ is called its chromatic number, and is often denoted $\chi(G)$.  Show that if graph $G$ is simple, then $$ \chi \ge \frac{V^2}{V^2 - 2E}. $$ Subdivision surface modifier issue I'm following . After using Boolean I cleaned up the extra vertices. Edge flow looks fine on my mesh.   However, when I apply a Subdivision Surface modifier my mesh becomes really messy as if something is wrong with the edge flow.   Can you guys help spot the problem?  Mesh topology:    Subdivision issue: Windows 7 USB install error I am trying to install Windows 7 Professional x64 from a bootable USB stick. I have used the Windows 7 USB DVD Download Tool to create the media from an ISO.  The machine boots from USB fine, and enters the Windows installation wizard but then I get an error stating:     A required CD/DVD drive device driver is missing. If you have a driver floppy disk, CD, DVD, or USB flash drive, please insert it now.   I have tried setting the SATA controller in the BIOS to both AHCI and ATA but neither appear make any difference.  I've also tried both the USB 3 and USB 2 ports with no difference.  I've also tried to use the files from an official Dell recovery CD as this is a Dell laptop but again, no dice.  All this because there's no optical drive in the machine!  Dell Vostro V131 / i5-2450M / BIOS A04  Can anyone offer any advice please? What is a "Swap Area"? So I noticed this question has not been asked directly;  What is this "Swap Area" people keep referring to when it comes to installing Ubuntu? Set active image node with python There's any way to change it directly by Python, or there's any way to set by Python what node image is the active to display in viewport (Textured) and bake? Does the series $\sum \limits _{n=0}^{\infty} \cos(n\pi)$ converge or diverge? Does the series $\sum \limits _{n=0}^{\infty} \cos(n\pi)$ converge or diverge?   On substituting values I get alternate $1$ and $-1$.    So taking sum of infinite GP, I get $\dfrac 1 2$. So it looks like it converges. I want to burn Ubuntu Minimal CD ISO to an old, 1 GB USB thumbdrive. Regular ISO doesn't fit. I already tried Startup Disk Creator and Unetbootin but both failed. I tried installing GRUB and pointing it to boot like this:  insmod part_msdos linux /linux initrd /initrd.gz   but it doesn't work. I also tried dd but I ended up with not bootable drive.  Rufus worked on Windows with the same thumbdrive but I no longer use Windows.  What else can I do? This has come up    : migrating old questions causes problems.   The most popular solution to this to date has been to . This is do-able, but frankly it feels like treating a symptom, and doing so in a way that penalizes folks who answer what are by all appearances valid, on-topic questions.   Migration works best as a way to salvage good but off-topic questions and give them new life on a site where they can thrive. But shuffling old, answered, on-topic questions around for the hell of it is a waste of everyone's time.   Therefore, I think the real solution is much simpler: just disable the migration of old questions. They're rarely welcomed or heavily improved post-migration, often overtly disliked by folks on the destination site, and can end up causing a rather bad experience for folks who were participating in good faith on the original.   I suggest that questions older than 601 days should not be eligible for migration, either by normal user close-votes or by moderators. In extreme cases, we can perhaps provide an alternate means of moving old questions, but under normal circumstances these should be done quickly or not at all.   1 60 days is actually based on a  introduced this past spring: migrated and then rejected questions older than 60 days cause the authors to suddenly gain (permanent) reputation on the destination. What we've gelost — why doesn't English use the prefix "ge-"? The Germanic languages that I'm familiar with all use a prefix similar to ge- on past participles:  German: Ich habe mir den Fuß gebrochen. Dutch: Ik heb mijn voet gebroken.  But English doesn't do this at all:  English: I've broken my foot.  Where did this prefix come from? Did English ever have the ge- past participle prefix? If so, why was it lost? Capitalization of "Theorem 1" in mathematics papers In many mathematics papers, I read sentences like:     With an appeal to Theorem 4.5 we get …   Is the capitalization of theorem in this case correct? If it is correct why do we capitalize the word? Recommended books for advanced undergraduate electrodynamics What books are recommended for an advanced undergraduate course in electrodynamics? SF short story ID, written 40s—60s, primitive aliens who are much smarter than us I'm looking for a story that was probably written somewhere from the 1940s to the 1960s. I think I read it in an anthology, possibly in the 1970s.  A group of human explorers landed on a planet with primitive aliens, living in hunter-gatherer villages. They hoped to make a profit from trading our goods for—well, I'm not clear on what they wanted from the aliens.  The native people learned the human language before the explorers could learn theirs. Then the natives suddenly started producing technological innovations far beyond what they originally used. I remember that wooden sailing ships suddenly replaced their canoes. All the natives had to do was hear a story once from the explorers before copying the technology in the story.  Finally, the explorers realized that the natives were much, much smarter than us and that Earth faced a serious problem.  I'm fairly certain that it wasn't a Heinlein story, but I remember that it had some qualities similar to his work.