Let $f$ be an entire function and assume f(0) = 1 and $|f(z)| \large \geq\frac{1}{3}\left| {\LARGE e^{z^{3}}}\right|$ for all $z$.   Show $f(z) = {\huge e^{z^{3}}}$ for all $z$.    Can this be shown with the Cauchy integral formula?
Suppose $f$ and $g$ are entire functions with $|f(z)|\leq|g(z)|$ for all $z$.  How can we show that $f=cg$ for some complex constant $c$?  Thanks for any help :)
I'd like to find a Windows batch counterpart to Bash's $@ that holds a list of all arguments passed into a script.   Or I have to bother with shift? Error AL lib: UpdateDeviceParams: Failed to set 44100hz, got 48000hz instead. What can I do? I have Win 10 and when I open Blender I have the error:     AL lib: UpdateDeviceParams: Failed to set 44100hz, got 48000hz instead I've come across quite a few answers that request the asker to, for example: "send the user an email", after which the answerer will provide them with the code or other resources they're looking for.  A few examples:          Should we take action against these questions?  I feel like these answers aren't appropriate (see my answer below).  Update:  Perhaps there are some cases where this is acceptable. I've seen a few questions regarding a particular piece of commercial software where the author/developer of the software answers, telling the asker to contact either them or their organization's in-house support.  I'm on the fence about this case. If I came across a question here describing a similar problem I was having, it would be useful to me to have the support information and know that I could contact it for assistance.  I'm interested in others' opinions on this situation in particular. What is the icon next to Spotlight in menu bar, and how to remove it? What is this icon   in OS X menu bar and how do you remove it? Let $z_1, z_2, z_3,$ ...be a sequence of independent random variables s.t. $P(z_i=1)=P(z_i=-1)=\frac 1 2$. Does this sequence converge almost surely?  My intuition is telling me that the sequence will approach the random variable Z? i.e. $z_n-&gt;Z$ as $n-&gt;\infty$ and Z is just another RV s.t. $P(Z=1)=P(Z=-1)=\frac 1 2$.  Here is my confusion, if a sequence converges almost surely, then $z_i$ should be different for each term s.t. it approaches Z in the end; but in this sequence $z-i$ is the same for every term. So I dont udnersntand. I own a notebook running Ubuntu 16.04 with Unity DE that does not have any keyboard LEDs to indicate NUM-Lock or CAPS-Lock states.  It would be useful for me to see them anyway, ideally through an indicator in Unity's panel.   Please note that I only want to see the states of NUM-Lock, CAPS-Lock and optionally Scroll-Lock. I do not want to see whether any other modifier keys like Shift, Ctrl, Alt, Super etc. are currently pressed. I only want a replacement for my missing LEDs.  Are there any working indicators available?    I already have read , but it does not suit my needs. indicator-xkbmod only displays a wrong icon but does not react on keyboard NUM-/CAPS-Lock status changes, kbstate is for KDE only and key-mon does not show the NUM-/CAPS-Lock states but indicates key presses to modifier keys. I would like site specific magic links. Currently you can write [so] in a comment, and it links like this: . I would like to be able to have site specific ones, so for example: English Language &amp; Usage  [dictionary] would go to http://dictionary.com and shows as   Ubuntu  [launchpad] would go to https://launchpad.net/ubuntu and shows as   [launchpad#bugnum] would go to https://bugs.launchpad.net/bugs/bugnum and shows as   [forums] would go to http://ubuntuforums.org/ and sows as   [discourse] would go to http://discourse.ubuntu.com and shows as   [paste] or [pastebinit] would go to http://paste.ubuntu.com and shows as   [install-d] would go to http://ubuntu.com/download/desktop/install-ubuntu-desktop and shows as   [install-s] would go to http://ubuntu.com/download/server/install-ubuntu-server and shows as   ppa:peterlevi/ppa would go to https://launchpad.net/~peterlevi and shows as   There is    Ask Different  [applesup] would go to http://www.apple.com/support and shows as   Christianity  [bible] would go to http://biblegateway.com and shows as   Currently, they are all the same, for all sites. I would like devs (mods maybe) to be able to add them on a per site basis. This is just a selection of examples. People can comment or answer with ones they would like and I'll edit them into this question. I asked this because  on Ask Ubuntu Meta wasn't possible right now - because it wasn't a feature.  [The devs] said right now it isn't possible because magic links are network wide, and they weren't sure it was high enough priority to really get done anytime soon, but if you want you can post a feature-request on Meta Stack Exchange requesting site specific magic links and see if you can garner more support for the feature and maybe get a dev to champion it.  So that's what I've done! For what longest possible time it was possible to hold light in a closed volume with mirrored walls?   I would be most interested for results with empty volume but results with solid-state volume may be also interesting. How to go with proving this : Let $R$ be a ring and let $I$ be an Ideal of $R$.  Prove that the factor ring $R/I$ is commutative iff $rs-sr \in I$ $\forall r$ and $s$ in $R$  any hint how to go with this... Got a working screen via HDMI, but the DVI won't go past 1360x768 (a PackardBell Maestro monitor). Had no issues in Windows 7.  I've tried all the xrandr tricks, see the output below:   xrandr  Screen 0: minimum 8 x 8, current 3280 x 1080, maximum 16384 x 16384 VGA-0 disconnected (normal left inverted right x axis y axis) DVI-D-0 disconnected (normal left inverted right x axis y axis) HDMI-0 connected primary 1920x1080+1360+0 (normal left inverted right x axis y axis) 510mm x 287mm    1920x1080      60.0*+   59.9     50.0      1680x1050      60.0      1600x900       60.0      1440x900       59.9      1280x1024      75.0     60.0      1280x800       59.8      1280x720       60.0     59.9     50.0      1152x864       75.0      1024x768       75.0     70.1     60.0      800x600        75.0     72.2     60.3     56.2      720x576        50.0      720x480        59.9      640x480        75.0     72.8     59.9   DVI-D-1 connected 1360x768+0+0 (normal left inverted right x axis y axis) 0mm x 0mm    1024x768       60.0 +    1360x768       60.0*    59.8      1152x864       60.0      800x600        72.2     60.3     56.2      680x384        60.0     59.8      640x480        59.9      512x384        60.0      400x300        72.2      320x240        60.1     cvt 1920 1080 # 1920x1080 59.96 Hz (CVT 2.07M9) hsync: 67.16 kHz; pclk: 173.00 MHz Modeline "1920x1080_60.00"  173.00  1920 2048 2248 2576  1080 1083 1088 1120 -hsync +vsync  xrandr --newmode "test" 173.00  1920 2048 2248 2576  1080 1083 1088 1120 -hsync +vsync  xrandr --addmode DVI-D-1 test X Error of failed request:  BadMatch (invalid parameter attributes)   Major opcode of failed request:  140 (RANDR)   Minor opcode of failed request:  18 (RRAddOutputMode)   Serial number of failed request:  37   Current serial number in output stream:  38    I'm using the latest driver from Nvidia (binary, 352.63) because Nouveau would show a black screen on my second monitor.  I got stuck on manually finding/creating a xorg.conf file and adding some monitor hacks, can anyone help me? And when I tried the following commands /etc/hostnames and /etc/hosts, it says:  bash: permission denied. Changing text applied when duplicating file in Finder When duplicating files in the finder, OS X attaches a space followed by 'copy' to the file name. This can lead to some file alphabetizing problems and the copies may appear out of order (not directly subsequent to the original). Is there a way to change the appended text? I would prefer that it says '_1' or _copy. Thanks. I have a scenario where i want to calculate sum of column   SAL|CAL|TAG|VAL 12.11"|"1.1"|"2.1"|"1.1 13.11"|"1.1"|"2.2"|"2.2 14.11"|"1.1"|"2.4"|"2.4   My below code not giving output giving output as 0.00  I need output for this column CAL VAL  awk -F'|' '{T+=$2} END { printf "%.2f\n", T }' demo.txt   output :  6.7 5.7 When should I use velocity versus addForce when dealing with player objects? Mobile SE sites not allowing edits to edits When you have less than 2K rep and your edit goes in a queue, you are usually allowed to revise your edit while it is being reviewed, by clicking the edit button again on the question page. However, when on mobile SE sites, the edit button disappears when you have submitted an edit for review.    Editing  by  into the question: It seems that the cause of this is when the mobile site hides the edit link (when there is a pending edit), it doesn't check who is making the edit, which means that it hides it for your own as well as other's edits. Why are Flash applications so sluggish/crashy? I've noticed that Flash applications tend to be more sluggish under Ubuntu than they do under Windows on the same machine. This is particularly noticeable when watching HD video or playing graphics/physics-heavy games. Are there any ways of improving the performance of Flash under Ubuntu, or is this just an issue with the Linux version that I will have to live with?  Currently I'm just cutting down on the number of tabs open, blocking flash ads, and closing other programs, but I'm looking for ways to affect Flash itself.  Other things I have already been doing include using Youtube's HTML5 feature and playing videos straight from /tmp in VLC. I was wondering if there was some way of streamlining Flash itself though. Perhaps not.  More Specific Question: Is there anything I can do in mms.cfg to boost performance? How to change the snapping increment in different units? I would like to know how to change the increments used for snapping transforms.  This would be useful in a number of situations but my problem now is that when I change the units it does not scale the snapping increments to match.  So when holding down ctrl the cube snaps from here:    To here:    I would like it to snap to the 1 foot grid, or possibly any other amount I find useful.  It would also be nice to be able to change the rotation snap as well. I have Canon lenses and would like to purchase an adapter to use them on the D3200? Is there one available? If so name and model would be appericated. I understand that I will have to shoot on manual mode. Can I delete user directory after deleting user? The reason I ask is because I recently made the mistake of installing Oracle 12c on my sub-performance laptop. Noticing the excessive amount of resources this added up to on startup, I decided to uninstall it.  What I failed to see through, however, was the fact that it created a new Windows user account in order for the initial installation to work out. In my case, it was mandatory because I only had an administrator account and I didn't see the need to use the built-in account. So, after failing to successfully install 12c twice, I wound up creating not just one, but two Windows user accounts. This had to do with something in regards to how Oracle sets up the Oracle Home business and whatnot, but I have no idea what any of that detailed, so I just went ahead and did it.  After uninstalling what I could in regards to Oracle and the database, I decided the next thing to do would be to remove the created users.  Having Windows 10 Home installed, I couldn't use the local users &amp; groups view/tool to delete these from the GUI. SO, I did the next best thing and Googled a solution. In my case, I used the following command:  net user username /DELETE   When I executed the command, the console gave the response of having successfully deleted the account for both accounts specified.  To verify that this had worked, I went to the users directory located in %SYSTEMROOT%/Users/ and came to find that the user directories were still there.  What does this mean and if I should delete them, will anything bad happen?  Can I even delete these directories?  Regards,  --T.R.G I'm bugged by the following that's summarized on p. 109 of .     False theorem: All horses are the same color.      Proof by induction:      $\fbox{$P(n)$ is the statement: In every set of horses of size $n$, all $n$ horses are the same color.}$   $\fbox{Base Case or $P(1)$:}$ One horse is the same color as itself. This is true by inspection.   $\fbox{Induction Step:}$ Assume $P(k)$ for some $k \geq 1$.   $\fbox{Proof of $P(k + 1) :$}$   Since $\{H_1, H_2, ... , H_n\}$ is a set of $n$ horses, the induction hypothesis applies to this set. Thus, all the horses in this set are the same color.   Since $\{H_2, H_3, ... , H_{n+1}\}$ is also a set of $n$ horses, the induction step likewise holds for this set. Thus, all the horses in this set are the same color too.         Therefore, all $n +1$ horses in $\{H_1, H_2, H_3, ... , H_n , H_{n+1}\}$ are the same color. QED.   The issue the instructor was trying to point out is clearly valid. For the case $n = 1$, there is only ${H_1}$. So this case says nothing about possible overlapping elements of each set of $(n + 1)$, for instance $H_2$ in the above proof.    But it was proposed in the class discussion that this was the only problem. Had you been able to prove $P(2)$ true, then a proof of the above format would have been fine.    My interpretation is that yes, you could prove all horses are the same color, if you can prove that any set of two horses will be the same color. But this format would not work.  Why not? The problem I see is that the above proof is for the existence of at least one particular pair of sets of horses of sizes $n$ and $n + 1$, such that in each set, all horses are the same color.  Particularly when the set of size $n$ is a subset of the set of size $n + 1$.  In order to prove the induction step, don't you need to prove that sets of sizes $n$ and $n + 1$, do not necessarily contain the same, overlapping elements?  You could prove that any horse can be added to a set of 2 horses.  Take the last two, and they must be the same color, and so on.  Wwhatever color the first two happen to be, all other horses must thus be the same color.    Am I misinterpreting the example, or am I making a logical error? Thanks in advance.