Make an examples $f:\Bbb{C}\to\Bbb{C}$ holomorph (If it exists) with the property:(Justify your answer)  $Re f(z)&gt;0$ for all $z\in\Bbb{C}$ and $f$ is not constant.  My attemp: I find a question in Conway that is discussed in    But my question is difference. Because we have not the hypothesis   $Re f(z)\geq 0$ and the domain is $\Bbb{C}$ instead of $D$.  So we can not use the open mapping theorem and I think there is not such function!
Suppose that $f$ is holomorphic on $\mathbb C$ and that $\Re(f(z))\ge 0$ for all $z$. Show that $f$ is constant. [Hint: consider $e^{−f(z)}$.]   My thoughts: If $\Re(f(z))\ge 0 $ holds, then $e^{−f(z)}$ is a bounded holomorphic function (do I need to prove this or is it obvious?) So then by Liouville's Theorem $e^{−f(z)}$ is constant.   But then I'm not sure how to rigorously go from this $\exp(−f(z))$ back to $f(z)$.   Could anyone help me piece this together please?  Thanks
Traveling to the US with new passport, visa on the old one I have a valid B1/B2 US visa expiring about a year from now. The passport it's in expired a few years ago, and I recently got a new one.   The passport number does not match, but the national ID number, mentioned in both, does (it used to be the same as your national ID, but not anymore)  Can I travel to the US carrying both passports? Or is it asking for trouble? (I read a few years ago that it was possible, but that might have changed)  Should I just get a new visa to avoid potential complications? I have had several business loans and understand that this is not by any means typical.  I noticed that for a year my payments were not decreasing the principal on the loan. When I asked the bank why, I found out that at some point my payments were getting applied to principal only. Now I am paying interest off that was not paid for 6 months or so.  My banker states that he can change all the interest payments to principal payments. I am confused to why this would be. If I make all my principal payments first then would the bank lose a substantial amount of interest?  This has happened on 2 of the 3 loans I have looked at so far.  If they are willing to change all the payments to principal only, would this be beneficial to paying less interest ultimately? I assume there would be an interest account accruing somewhere that would need to be paid off at the end of the loan.  I understand that typically you have a loan balance that would include interest and principal. My balance owed did not change when I continued to make same payment? It gets applied to interest. The balance on the statement must not be a true balance. There must be interest owed above the balance showed but why would they do this to start with? They applied full payments to principle only first in order for interest to get to be more than several payments What is the reason Men play 5 sets & Women play 3 sets in a Grand Slam in Tennis? In the ATP &amp; WTA events, both Men &amp; Women tennis players play best of 3 sets. But when it comes to Grand Slams, the Men play 5 sets. At the risk of sounding a misogynist, I always believe the reason to be strength &amp; endurance. After all, a 5 set EPIC match lasts 5 hours while a 3 set EPIC last 3 hours.    Is that the only reason. Or am I a naive misogynist? Also was that the case since the history of Grand Slams or did Men play 3 sets before? Can I use extra wire from two separate cables to add a washing machine in a garage? Remove entire row in a file if first column is repeated What does “the lowest common denominator” mean in the context other than math? In the  (May 31) article under the title, “Stephen Hawking angers Trump supporters with baffling array of long words,” Andy Borowitz wrote;     “Speaking to a television interviewer in London, the theoretical   physicist, Hawking called Trump “a demagogue who seems to appeal to   the lowest common denominator. --- “For a so-called genius, this was an   epic fail,” Trump’s campaign manager, Corey Lewandowski, said. “If   Professor Hawking wants to do some damage, maybe he should try talking   in English next time.”        Later in the day, Hawking attempted to clarify his remark about the presumptive Republican Presidential nominee, telling a reporter, “Trump bad man. Real bad man.”   From the context of Professor Hawking’s remark, I take “the lowest common denominator” as referring to the  “social segment of low educated, unsophisticated people,” but I’m not sure.   I thought  "common denominator" is a simple mathematic term. What does it mean in the context of the above quote?  Mr. Trump’s campaign manager says Professor Hawking should try to talk in English. Is this a farfetched way of using “common denominator” from math to politics?   Did Professor Hawking misuse "the common denominator"? Or does Mr. Trump's campaign manager not understand the meaning of "common denominator", which some call an "everyday-use" English phrase?  P.S.  I found the following definition of 'common denominator' in Oxford Advanced Learners English Dictionary;   2) an idea, attitude or experience that is shared by all the members of group - see also Lowest common denominator.  Readers English Japanese Dictionary at hand, published by Kenkyu-sha, a foreign language, especially English language dictionary specialist publisher in Japan, and rated as the most reliable English Japanese dictionary totally dropped the reference to this paticular meaning.  It was a learning. I told to myself that I should have made more homework on English-to-English dictonaries beforehand. I noticed that my American friends tend to use the past perfect form when they use the verb mention in its past form, almost despite of the context of the sentence. I hear them say  "you had mentioned" a lot more often even in situations where the use of simple past would have been perfectly fine. Have you noticed it too and is it one of those unwritten rules, or is there a more formal explanation to it?  It seems like there was more verbs like that, but I am having a hard time remembering it now. If I do, I will edit the post and likely change the title to accommodate other verbs. TikZ Angle Label - Help it "fit" better? I have the following drawn with TikZ    using the code  \documentclass{article} \usepackage{tikz} \usepackage{tkz-euclide} \usetkzobj{all} \begin{document} \begin{tikzpicture} \coordinate (O) at (0,0); \draw (O) circle (3); \coordinate[label = above left:$M$] (M) at (130:3); \coordinate[label = above:$N$] (N) at (80:3); \coordinate[label = below:$A$] (A) at (240:3); \coordinate[label =below right:$B$] (B) at (300:3); \draw (A) -- (M) -- (B); \draw (A) -- (N) -- (B); \tkzMarkAngle[draw = black, fill = white, opacity=1](A,M,B) \tkzLabelAngle[pos = 0.8](A,M,B){$x$} \tkzMarkAngle[pos = 0.2,draw = black, fill = white, opacity=1](A,N,B) \tkzLabelAngle [pos=0.8](A,N,B){$27 ^{\circ}$} \end{tikzpicture} \end{document}   Notice however, tht the 27 degrees does not fit in very nicely. How can I adapt the code to try and move the 27 a bit "lower" so that it fits in better, as well as the angle mark?  Also, how can I get two "double arrows" in the middle of lines AM and BN, to indicate that they are 'parallel'? Error - SqlDateTime overflow. Must be between 1/1/1753 12:00:00 AM and 12/31/9999 11:59:59 PM Show that if $g \circ f$ is injective, then so is $f$. The Problem:  Let $X, Y, Z$ be sets and $f: X \to Y, g:Y \to Z$ be functions.  (a) Show that if $g \circ f$ is injective, then so is $f$.  (b) If $g \circ f$ is surjective, must $g$ be surjective?  Where I Am:  So, I really have trouble with these, for some reason. I can draw pictures and make sense of the problems, but writing down proofs is very difficult for me.   Basically, for (a), I ended up with some complicated statement involving an implication implying another implication and then tried to derive a contradiction. It just got so convoluted that I couldn't make sense of it anymore, and I know there's a quick, elegant way to show it.  For (b), I know that $g$ need not be surjective. Once again, though, proving it directly from definitions has given me a bit of a headache.  Any help here would be appreciated. Thanks in advance.  The Proofs!  Ok, I did it. Thanks for the help, everyone! Let me know if there's anything wrong with these proofs, or if they could bet any better.  (a) Suppose $f$ is not injective. Then $$ f(x_1)=f(x_2) \implies x_1 \ne x_2 \text{        }(*).$$ Let $f(x_1)=y_0=f(x_2)$ and let $g(y_0)=z_0$. Then $$ (g \circ f)(x_1) = (g \circ f)(x_2) = g(y_0) = z_0. $$ Since $g \circ f$ is injective, $$ (g \circ f)(x_1) = (g \circ f_2) \implies x_1 = x_2. $$ However, this contradicts $(*)$. Therefore, $f$ must be injective.  (b) Suppose $g$ is not surjective. Then  $$ \forall y \in Y, \exists z \in Z \text{ such that } g(y) \ne z \text{         }(**).$$  Since, $g \circ f$ is surjective,  $$ \forall z \in Z, \exists x \in X \text{ such that } g(f(x)) = z \text{       } (***). $$  Let $f(x) = y$. Then,  $$ g(f(x)) = g(y) = z. $$  Because of $(***)$, this is true for all $z \in Z$, which contradicts $(**)$. Therefore, $g$ must be surjective. How to make Arduino (Snap) access serial port /dev/ttyUSB0 (or /dev/ttyACM0)? I have Ubuntu 18.04 LTS installed.  I installed Arduino IDE v1.8.5 as a snap with  snap install arduino-mhall119   I have added my user to dial-out group and rebooted:  sudo usermod -a -G dialout $USER  $ groups  username adm dialout cdrom sudo dip plugdev lpadmin sambashare   I connected my Arduino Nano to the laptop, it is detected on port /dev/ttyUSB0 (ch341-uart).  $ ls /dev/ttyUSB0 -al crw-rw---- 1 root dialout 188, 0 авг 13 11:59 /dev/ttyUSB0   I tried to upload the simpliest Blink sketch and get the following errors in the terminal:  $ arduino-mhall119.arduino    avrdude: ser_open(): can't open device "/dev/ttyUSB0": Permission denied   Problem uploading to board.  See http://www.arduino.cc/en/Guide/Troubleshooting#upload for suggestions.**   Also I have installed arduino 1.8.5 with umake - it can access serial port in usual way.  Note: we already have  here, but the solution was to use , not fix for the Snap.  So my question is: How to make Arduino (Snap) access serial port /dev/ttyUSB0 (or /dev/ttyACM0)?  Update: connecting serial-port to the snap fails with the following message  $ snap connect arduino-mhall119:serial-port  error: snap "core" has no "serial-port" interface slots   Current interfaces are:  $ snap interfaces | grep arduino :home                            arduino-mhall119,gedit,organize-my-files,vlc :network                         arduino-mhall119,gedit,organize-my-files,pulsemixer,vlc :unity7                          arduino-mhall119,gedit,organize-my-files,vlc :x11                             arduino-mhall119,organize-my-files,pulsemixer,vlc -                                arduino-mhall119:serial-port   Changing permissions of serial port to 777 with sudo chmod 777 /dev/ttyUSB0 does not help.  The following do not work too (because of syntax errors):  $ sudo snap connect arduino-mhall119:arduino error: snap "arduino-mhall119" has no plug named "arduino"  $ snap connect arduino-mhall119:/dev/ttyUSB0 error: snap "arduino-mhall119" has no plug named "/dev/ttyUSB0"  $ snap connect arduino-mhall119 error: cannot resolve connection, plug snap name is empty   Information about YAML-manifest:  $ ls -l /snap/arduino-mhall119/current/meta/snap.yaml -rw-r--r-- 1 root root 353 июл 28 00:20 /snap/arduino-mhall119/current/meta/snap.yaml  $ cat /snap/arduino-mhall119/current/meta/snap.yaml |grep -A 12 slots  $ cat /snap/arduino-mhall119/current/meta/snap.yaml |grep -A 5 plug     plugs:     - x11     - unity7     - home     - network     - serial-port How can I revert a config file back to the originally installed version after I have edited it? Casting nines and elevens in other bases (radix) and doing check sums for binary Are there ways to determine if a wall is load bearing? Other than looking up blue prints, which many homeowners may not have, are there ways to determine if a wall is load bearing?  Methods I can think of might include:   Going up in the attic to check if ceiling trusses run perpendicular to the wall If the wall is an exterior wall   Any others? How to convince airport security that I am not dangerous when having metallic parts in my body? I had an operation some time ago and now I have small screws in my shoulder which will not be removed anymore. When I decided to fly for vacation, I supposed that these will may bring me into trouble at the airport when going through the metal detector.  So I asked my doctor and at the hospital if there is any kind of "passport" or something similar which confirms the screws in my shoulder so that I do not get into many problems. Unfortunately, they told me such things do only exist if you get a new knee or something, not if you just have a few screws in your body.  When I flew from Vienna to Amsterdam and back, my fears were confirmed: The security staff inspected me very precise, and I had to explain them my story. Thank god I have some scars left so they believed me!  However this is not a permanent solution for the future. Is there any international "passport" which my doctor and hospital do not know about? If not, what else are my possibilities?  I am not that afraid when travelling within the EU, however I fear that this situation might get quite dangerous when I'm in other countries... Seems like this is the most powerful weapon of all: transport your enemy into a bulkhead, planet, etc. Transport your enemy's ship inside a planet, etc.  Is there some technical reason that it can not be used this way? Can you determine a formula for this problem? Toggle Switch to swap the connections of two buttons I am trying to mod my arcade stick so I can switch two commonly swapped buttons on the controller.  Essentially they are simple 2 terminal momentary switches connected directly to the controller PCB. I would like to switch their responsibilities, so in my case the Back button and the LB button on the XBox pcb I would like to swap so the Back actuates the LB button on the PCB and the LB actuates the Back button.  My assumption is that I would need a switch with 8 terminals, 4 in 4 out.  What type of switch am I looking for? comma delineation of consecutive endnotes Consecutive footnotes can be separated by commas by invocation of the multiple option of the  package:    \documentclass{article} \usepackage[multiple]{footmisc} \begin{document} Comma delineation of consecutive footnotes fails upon conversion to endnotes% \footnote{First note.}% \footnote{Second note.}.% \end{document}   This comma delineation fails, however, if footnotes are converted to endnotes using the  package:    \documentclass{article} \usepackage{endnotes} \let\footnote=\endnote \usepackage[multiple]{footmisc} \begin{document} Comma delineation of consecutive footnotes fails upon conversion to endnotes% \footnote{First note.}% \footnote{Second note.}.% \theendnotes \end{document}   How can one preserve automated comma delineation of consecutive endnotes? Should I put myself last? "me and my friends" vs. "my friends and me" or "my friends and I" I've always been taught to put myself last when referring to myself in the same sentence as others but the usage of "me and..." seems to be everywhere these days. The misuse of the word "me" instead of "I" aside, is there some new rule I haven't heard of? Shouldn't we put ourselves last regardless of the "me"/"I" usage?  Examples of "correct" usage:      My friends and I went for some ice   cream. Did you see my friends and me   at the ice cream stand?   Examples of "incorrect" usage:     Me and my friends went for some ice   cream. Did you see me and my friends   at the ice cream stand?   Note: I was also taught that the only person who could put themselves first was the queen.