Consider the set $F=\{f:\mathbb C\to\mathbb C\mid f\text{ is an entire function, }|f'(z)|\leq|f(z)|\text{ for all }z\in\mathbb C\}$. Then which of the following are true?  $F$ is a finite set  $F$ is an infinite set  $F=\{\beta e^{\alpha z}\mid\beta\in\mathbb C,\;\alpha\in\mathbb C\}$  $F=\{\beta e^{\alpha z}\mid\beta\in\mathbb C,\;|\alpha|\leq1\}$    My attempt: I take $f(z)=2$ then option $2$ is discarded and when I take $f(z)=\exp(z)$ then option $1$ is also discarded. But I'm not know how to solve it by a general method. Please help me.
Could someone advise me on how to determine all entire functions $f$ such that $|f'(z)| \leq |f(z)|, \forall z\ ?$  Hints will suffice, thank you.
Explanation of terminal objects using limits I understand terminal objects, but I falter when trying to achieve them using the approach of diagrams, the category of constant diagrams $\mathcal{C}^{\mathcal{J}}$ and limits.  I have the empty category 0, now I have a diagram $D: \mathcal{J} \to \mathcal{C}$. However this diagrams image should be empty, because there are no objects or morphisms to map. At this point, I'm confused, because I can't get to the universal property $\forall c \in \mathcal{C}. \exists! f: c \to T$ anymore, because I'm missing T. (EDIT: I get that this is how it is supposed to be)  But continuing with the category of constant diagrams, even if I have a constant diagram mapping everything to one object / morphism, there is nothing to map, so the functors image is still empty. So now I'm missing both $T$, and any kind of $c$.  EDIT: It seems to me, have I chosen 1, instead of 0, I would have come up with that is considered the definition of the terminal category. What am I missing? Are configurations written and read directly to/from .yaml files or still to the database? Background  Drupal 7 and previous versions have attracted criticism for Drupal web site admin configuration being stored in the MySQL database, the criticism being that being in a database means that it cannot be directly managed in git together with the PHP code based development for a Drupal site (custom modules, themes etc.).   Secondly with configuration being in the database along with content, transporting configuration between development, test, staging and live servers as part of development activity is complicated, though Features module (and related) can help.  Reading through:   ...I'm getting the impression that, in Drupal 8, the database is still used to store the config, when for example a site builder creates a new content type, rather than this being written to a .yaml file which is used directly.  So actually it seems that the role of the yaml file(s) is a much more purer (than Features) vehicle for the configuration. Whereas with Features it was PHP code which was harder to read what the configuration was, including if doing diffs between commits where config had been updated resulting in a new version of the Features-based config export. By that I mean not that PHP itself is hard to read, as I'm familiar enough with it, having written custom modules, hooks, themes. What I mean is that to express a configuration in PHP is perhaps not the most legible way to do it. So I can see the rationale of using yaml. The difference is that yaml will be read by a parser to apply a config. The complexity of applying the config is in the parser, which most folks need not concern themselves with most of the time, so the yaml can more cleanly describe the config. whereas in Features, there is no parser / yaml (or other script) separation. The descripton of the config and the means to apply it are necessarily in the same place as PHP code which is executed directly, so it's bound to be a bit harder to read the config, particularly if doing git commit diffs.  So there's the rationale for yaml, a Declarative Programming approach to storing configuration management in Git, contrasted with Features which is an Imperative Programming approach. And next what I need to know is this the case that Drupal 8 does still store config in the database does still and yaml files are the means for transporting config (replacing what Features did in D7 and before)?  (By the way I am a big fan of Drupal and spend most of my time at work, working with it for the sites that my organisation produces and maintained and am also involved in the community. So this question is not a stealth campaign against Drupal in favour of other platforms. It is a genuine question to try to dispel the apparent mystique around Drupal 8 and the new config management system)  Update @Berdir's answer (accepted) is a great definitive summary as to the state of Drupal 8 regarding configuration management.  I recently discovered that using yaml for config in Drupal 8 is a concept that has been developed for Drupal 7 with the  module, also read a  on it which includes comparing features.   Update   Is a definitive answer about making config active from DB storage, which corroborates with @Berdir's answer. How to convert milliseconds into human readable form? what is the C++/CLI syntax to subscribe for events? I'm updating some old Managed C++ code with lines like this:  instanceOfEventSource-&gt;add_OnMyEvent(      new EventSource::MyEventHandlerDelegate(this, MyEventHandlerMethod) );   where   EventSource is the class that publishes events instanceOfEventSource is an instance of that class EventSource::MyEventHandlerDelegate is the delegate type for the event MyEventHandlerMethod is a (non-static) method within the current class (of which "this" is an instance) with the signature matching EventSource::MyEventHandlerDelegate   What is the right syntax for this in C++/CLI? It is not unusual for an Ubuntu (or other distro with apt package management) user to encounter the error: user@box ~ $ sudo apt install x [sudo] password for user:  Reading package lists... Done Building dependency tree        Reading state information... Done Package x is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'x' has no installation candidate  There have been several questions asked concerning this on various StackExchange sites,for example  on AskUbuntu, but these are generally about how to obtain the specific package despite the error. I have found no package that is not found simply (though not always easily) by determining if it is still distributed, and under which repository if so, and ensuring that repository is in apt.sources, or the worst comes to the worst downloading a .deb or source to compile. So my question is more general, and although I am guessing it has a rather simple and therefore non-exciting answer I cannot think how to find it by conventional search engine methods, so I turn to AskUbuntu: Is there a command or option I can use to determine what package / which packages reference the missing package? Windows vs Linux Local Time? In Hitchcock's Vertigo, there is one part of the film that has never made sense to me and I believe that it was a cheap ploy to mislead the audience until the ultimate reveal (I won't spoil it here).    In this scene Jimmy Stewart watches Kim Novak enter a rooming house and afterwards sees her standing by the window on the 2nd floor.  When he enters the house and talks to the inn-keeper, she tells him that Kim Novaks's character positively never came in and even shows him her room key that is still behind the front desk.  They go up to the room and find it empty.   This scene seems to imply that the Kim Novak character may have had a ghost like quality. But given the reveal at the end she clearly does not and there was no way for her to enter the room without a key and without being seen by the inn-keeper.  If this was done by some other director I probably wouldn't have given this much thought but Hitchcock was a perfectionist (especially for this film) so I never understood the significance of this scene other than to mislead the audience (with a cheap ploy IMO).  Does anyone who is familiar with this film have a different explanation/perspective about this scene in an otherwise brilliant movie. I am on Ubuntu and I have forgotten the password for my Gnome Keyring (yes, stupid me, I know). Any way I can get it back? I have already looked at , but it says it's not possible if my home directory is encrypted and unfortunately my home directory is encrypted. Err http://archive.canonical.com natty InRelease     Err http://security.ubuntu.com oneiric-security InRelease                Err http://extras.ubuntu.com natty InRelease                             Err http://security.ubuntu.com oneiric-security Release.gpg   Temporary failure resolving ‘security.ubuntu.com’ Err http://archive.canonical.com natty Release.gpg   Temporary failure resolving ‘archive.canonical.com’ Err http://extras.ubuntu.com natty Release.gpg   Temporary failure resolving ‘extras.ubuntu.com’ Err http://gb.archive.ubuntu.com oneiric InRelease Err http://gb.archive.ubuntu.com oneiric-updates InRelease Err http://gb.archive.ubuntu.com natty-backports InRelease Err http://gb.archive.ubuntu.com oneiric Release.gpg   Temporary failure resolving ‘gb.archive.ubuntu.com’ Err http://gb.archive.ubuntu.com oneiric-updates Release.gpg   Temporary failure resolving ‘gb.archive.ubuntu.com’ Err http://gb.archive.ubuntu.com natty-backports Release.gpg   Temporary failure resolving ‘gb.archive.ubuntu.com’  Reading package lists... Done W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/oneiric/InRelease       W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/oneiric-updates/InRelease   W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/natty-backports/InRelease   W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/oneiric-security/InRelease   W: Failed to fetch http://archive.canonical.com/ubuntu/dists/natty/InRelease   W: Failed to fetch http://extras.ubuntu.com/ubuntu/dists/natty/InRelease   W: Failed to fetch http://archive.canonical.com/ubuntu/dists/natty/Release.gpg  Temporary failure resolving ‘archive.canonical.com’ W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/oneiric-security/Release.gpg  Temporary failure resolving ‘security.ubuntu.com’ W: Failed to fetch http://extras.ubuntu.com/ubuntu/dists/natty/Release.gpg  Temporary failure resolving ‘extras.ubuntu.com’ W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/oneiric/Release.gpg  Temporary failure resolving ‘gb.archive.ubuntu.com’ W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/oneiric-updates/Release.gpg  Temporary failure resolving ‘gb.archive.ubuntu.com’ W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/natty-backports/Release.gpg  Temporary failure resolving ‘gb.archive.ubuntu.com’ W: Some index files failed to download. They have been ignored, or old ones used instead.   This is what I'm seeing when I try to run sudo apt-get update. I did an update on my instance yesterday and am now experiencing this. How to prevent system applications (like the Software Center) from asking for password? What does the '!!!' syntax mean in javascript? Where does Drupal store its content? I have been currently learning Drupal while trying to duplicate a Drupal application into CakePHP.  I have been looking at the  database tables to know where data is being stored so I can safely migrate any data or study how it is working.  I have researched and have come across questions like:     So far, I have only seen the title in my Drupal (7) installation.  What I have seen in my node revisions table for a recipe content type, which includes fields like, field_ingredients, field_instructions, field_description, field_preptime, field_cookingtime, just the title of the recipe. This is a sample record on my node_revision table.  nid   |  vid  |  title         |  log   | timestamp  | status | comment | promote  | sticky ------------------------------------------------------------------------------------------- 1     |  1    |  Awesome Sauce |        | 1369998600 | 1      | 2       | 1        | 0   As you can see I can only see the title. Where are the other field contents? What EXACTLY happens when I ask to delete my account? Problem from Herstein on group theory The problem is:  If $G$ is a finite group with order not divisible by 3, and $(ab)^3=a^3b^3$ for all $a,b\in G$, then show that $G$ is abelian.  I have been trying this for a long time but not been able to make any progress. The only thing that I can think of is: $$ab\cdot ab\cdot ab=aaa\cdot bbb\implies(ba)^2=a^2b^2=aabb=(\text{TPT})abba.$$ Now, how can I prove the last equality? If I write $aabb=abb^{-1}abb$, then in order for the hypothesis to be correct, $b^{-1}abb=ba\implies ab^2=b^2a$. Where am I going wrong? What should I do? I have 4 copies of the Hot Questions widgets.  Sometimes, possibly after they reload on their own, I can only tap to open the last widget I added. If I tap on the question of any others nothing happens.  If I refresh each one then tapping works on the one I refreshed. Install suspension forks on non-suspension bike I have a 1990s Saracen PowerTrax. Is there a way I can install a suspension fork, or will that muck up the bike somehow? I'm actually interested in ways to raise the bars with respect to the seat, so that wouldn't be a problem. My toes rubbing in the wheel, in the other hand, would definitely be a problem. Is this true?  If $A$ and $B$ are sets, then $A=\emptyset $ if and only if $B = A \bigtriangleup B$.  If $A=\emptyset$ then $B=\emptyset$ too?  Could someone help me please? Generalised rule for verb usage in simple present tense using participle What are the requirements to use iMac screen as a second monitor - Target Display Mode? I have a Surface Pro 4 and an iMac (late 2019). I would like to connect my Surface Pro to the iMac to use the iMac screen as a second monitor.  Is that possible?  What are the requirements to use an iMac as a second screen? I want to use Windows 7 or 8 but I don't know to install a software like VirtualBox which we have to do with the use of terminal. I don't want to use Windows as a main OS so I want to use it in VirtualBox. Can you tell me how to install downloaded files in Ubuntu. I once installed java runtime but don't know the meaning of the lines which I have written in terminal, I just did as the blog posted by a man says.