Let $f(z)$ be an entire function satisfying $|f(z)|\leq k|z|$ for some positive constants $k$ and all $z$. Show that $f(z)=az^2$ for some constant $a$.
Let $f$ be an entire function such that $\mid f(z) \mid \leq A \mid z \mid$ for all $z$, where $A$ is a fixed number. Show that $f(z)=a_1z$, where $a_1$ is a complex constant.
In the book Limit Theorems of Probability Theory by Valentin V. Petrov, I saw a distinction between the definitions of a distribution being &quot;continuous&quot; and &quot;absolutely continuous&quot;, which is stated as follows:  &quot;...The distribution of the random variable $X$ is said to be continuous if $P\left(X \in B\right)=0$ for any finite or countable set $B$ of points of the real line. It is said to be absolutely continuous if $P\left(X \in B\right)=0$ for all Borel sets $B$ of Lebesgue measure zero...&quot;  The concept I am familiar with is:  &quot;If a random variable has a continuous Cumulative Distribution Function, then it is absolutely continuous.&quot;  My questions are: are the two descriptions about &quot;absolute continuity&quot; in (1) and (2) talking about the same thing? If yes, how can I translate one explanation into the other one? Java - Could not find the main class I lost my Italian residence permit abroad, how can I obtain a duplicate so that I can fly back to Italy? Sweden is going to ban me from flying if I can't show them my lost permesso di soggiorno from Italy. It was issued in Florence because my old one expired while I was in school. How do I get a copy? The volume of a cone with height $h$ and radius $r$ is $\frac{1}{3} \pi r^2 h$, which is exactly one third the volume of the smallest cylinder that it fits inside.  This can be proved easily by considering a cone as a , but I would like to know if it can be proved or at least visual demonstrated without using calculus. Correct way of declaring pointer variables in C/C++ I've checked  for acute:  an acute illness is one that has quickly become severe and dangerous Compare:CHRONIC  And for chronic:  lasting for a long time Compare:ACUTE  Can a disease be both &quot;acute&quot; and &quot;chronic&quot; simultaneously? For example it could be the case where a certain illness quickly becomes serious and have long term consequences Are there any &quot;obtuse illnesses&quot; ? Login not redirecting back to page where login link was clicked if account created If you give a user sudo privileges how can I remove the sudo privileges and make the user become just a regular user?  I used:  sudo adduser username sudo   Now I've changed my mind. How do I reverse a list using recursion in Python? Index entries duplicated for captions How to open a PDF form file that says Please wait...? Show sub reasons in close review queue Currently close vote review queue shows the top level close reason in the header, but some close reasons, for instance, off topic have very different sub reasons. For instance, "demonstrate minimal understanding" is different from "This question belongs on a different site in the stack exchange network".  It would be nice if sub close reasons were also shown. Can't understand a proof: Let $a,b,c$ be integers. If $a$ and $b$ divide $c$, then $lcm(a,b)$ also divides $c$  Proof I've been shown:  Since $c$ is a common multiple of $a,b$, it means that $lcm(a,b) \leq c$.  So: $c=q\cdot lcm(a,b)+r$, $q \in \mathbb Z$ and $0\leq r \leq lcm(a,b)$  Since $c$ and $lcm(a,b)$ are common multiples of $a,b$, then so is $r$. But $m$ is the least common divisor, then it means $r=0$.   [Proof taken from: http://www.math.utah.edu/~wood/4400/hw1sol.pdf]  I cannot understand the last step... Why does it imply that $r=0$?   Thank you! in my mariadb i have replication, i tried to change the location of the binlogs by changing the configuration file as so: log-bin = /new/path/mysql-bin I also tried to change the index location as so: log_bin_index = /new/path/mysql-bin.index but every time when I restart I see that the location of the binlog files is /var/lib/mysql... i tried to check with mysqld --verbos --help | grep bin and I saw that the lob-bin parameter is mysql-bin and not what I wrote in the cnf... how to I make the MySQL to take the value of the log-bin from the cnf file? this is the cnf file of the MySQL for sure... Logic soundness and completeness I have to do a number of similar type questions, but I am having trouble grasping the general concepts around soundness and completeness. I have read up on the general definitions and think I understand them, but when asked to show something like the following I come up blank. Thanks for any ideas/help.   Show that the following propositional proof system, PCa, is sound but not complete.  PCa  Connectives (and constants) ∨, ∧, →, ↔, ¬, 0, 1  Axioms All tautologies of the form F→F  Rules of inference Hypothetical Syllogism 13.04 - more than four workspace shortcuts in GNOME Flashback (No effects) I'm using GNOME Flashback (No effects) on Ubuntu 13.04 and I've got six workspaces however when entering System Settings -> Keyboard -> Shortcuts -> Navigation I only see options to address the initial four.  It used to be options up to 12 workspaces there and as I certainly don't need that much, I want to have at least enough for the amount currently active.  How can I restore or add more shotcuts specifically to navigate and move windows to workspace 5 and 6? How can I change Blender's theme? I just downloaded blender and its very bright. I want it darker. How can I change the color of it? Is there a formal spelling for the English letter names? Why won't vertical-align: middle work?  And yet, vertical-align: top does work.   span{   vertical-align: middle; } &lt;div&gt;   &lt;img src="https://via.placeholder.com/30" alt="small img" /&gt;   &lt;span&gt;Doesn't work.&lt;/span&gt; &lt;/div&gt; OS X computer name not matching what shows on terminal My computer name in System Preferences &gt; Sharing is set to &quot;archos&quot;, but is showing as &quot;iphone&quot; on Terminal. It just started doing this after I loaded Xcode for doing iPhone development: Last login: Mon Nov  7 14:46:55 on ttys001 iphone:~ travis$   Any ideas what could be causing this?