If the bounded operators $X\to Y$ form a Banach space in the operator norm, is $Y$ necessarily Banach?
If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)
In the magical world (in Harry Potter) can ghosts use magic?  Can magic be used on ghosts?  Or, once they become ghosts, can they interact with magic at all? What to do when you discover a mistake in the archived copy of your PhD thesis? I've just defended my PhD in mathematics and started a postdoc. While working  on an improvement of one of the results of my thesis, I realized that there are several minor mistakes and a big bug in a proof that invalids a minor result in the thesis (about 3-4 pages out of 110). Unfortunately neither I nor my advisor or referees figured it out the mistake. Though the result is minor, it is announced in the introduction and the manuscript is on-line on an ArXiv-like server, so that I could publish a new version but not cancel the one on-line.   What is the best thing to do? Upload an errata? Upload a "revised" version of the thesis?  Publish a "revised version" of the thesis on my web-page?  Can this damage my future career, making me look not "reliable" as a researcher? Could you tell me how to prove that if two series $ \sum_{n=0} ^{\infty}x_n, \sum_{n=0} ^{\infty} y_n$ are convergent, then $\sum_{n=0} ^{\infty}(\alpha \cdot x_n + \beta \cdot y_n)$ is also convergent and its sum equals $\alpha \cdot \sum_{n=0} ^{\infty} x_n + \beta \cdot \sum_{n=0} ^{\infty} y_n$? zsh: excluding files from a pattern Say I have the following files:   |-- bar `-- foo     |-- type_A_1     |-- type_A_2     |-- type_B_1     |-- type_B_2     |-- type_B_xx     |-- type_B_xx     `-- something_else    I thought the following command  print -l foo/*~{type_B*}   would print everything under foo except things that start with type_B but it doesn't, instead it prints everything under foo:  foo/type_A_1 foo/type_A_2 foo/type_B_1 foo/type_B_2 foo/type_B_xx foo/something_else   I also tried print -l foo/*~type_B and got the same thing.  How does the exception wildcard ~ work in zsh? spectral radius in normed space is subadditive. I am reading the book "characterizations of c*-algebras" by Doran and Belfi. On the page 299, the book reads "It can also be shown that if $xy=yx$, then $\nu(x+y)\le\nu(x)+\nu(y)$." The definition of $\nu$ is as follows: in normed algebra,  $$\nu(x)=\limsup_{n\to\infty}\|x^n\|^{\frac1n}$$  Note that the algebra is not assumed to be complete and is also not assumed to be complex scalar(we can have real scalars)  This is my trial: I just tried to mimic the proof of the Minkowski inequality, but failed.  Thank you How do Horcruxes work? A few questions regarding the Horcruxes.   Had Voldemort actually succeeded in using a Horcrux, would he come back the same age (biologically and/or aesthetically) he was when he made the Horcrux, or the age he would biologically be if he had never died (half died)? If Harry was a Horcrux, then in the graveyard, when Wormtail added Harry's blood to the potion to bring Voldemort back, didn't that technically use up the Horcrux inside of Harry? So in Deathly Hallows when Voldemort kills Harry, shouldn't Harry have actually died rather than just have the Horcrux inside him destroyed, seeing as it was technically used in the Goblet of Fire? For the recently reported production (January 2017) of metallic hydrogen in the laboratory - what is the evidence exactly? My google news page has burst forth the news that metallic hydrogen has been produced in a laboratory using a diamond anvil cell. Only  mentions (at this particular moment) that it has been called into question at - at least - premature. That can be read about in Nature:   Here I only want to ask about the evidence. Is it only the sudden change in visual appearance change as recorded in a camera on top of the microscope, at a specific temperature and pressure? That it "looks shiny?" Or is there actually more direct data than that?  note: I am not asking if the data is sufficient or not, nor if it is convincing, or metallic or not. Just a narrowly defined question about the extent of the observations that have lead to the proposal that a metallic state was achieved.     above: potentially three states of hydrogen as viewed in a diamond anvil cell, from . I know there is a method for a Python list to return the first index of something:  &gt;&gt;&gt; l = [1, 2, 3] &gt;&gt;&gt; l.index(2) 1   Is there something like that for NumPy arrays? Common lines between two files I have the following code that I run on my Terminal.  LC_ALL=C &amp;&amp; grep -F -f  genename2.txt hg38.hgnc.bed &gt; hg38.hgnc.goi.bed   This doesn't give me the common lines between the two files. What am I missing there? I took a look at  but my question is not the same.  I have unique keys encrypting each plaintext (in CBC mode, AES-256) and I do not use a key to encrypt more than one plaintext. Is it insecure to use null IVs in this case? If it is insecure, why? Is it possible to only allow specific packages updates from a PPA Let us say I have added a PPA that has X package that I want but it also has Y package that I do not want to use or receive updates from. How can I, from the same PPA, receive updates for a specific package but deny updates from the same PPA for other packages.  A step by step example would be good since this has happened to me in several PPAs that have a particular package I want but also add a whole bunch of others that I do not yet want to update. How to find a point on a line at a given distance from a given point on the same line (given the equation of the line)? You are given a point P(x,y) on a line of equation ax + by + c = 0. I want another point, Q(a,b) on the same line which is at a distance d from P. There will be two points. I want to find both and know which side of P each one lies.  There are related questions in this forum, but I didn't get what I am exactly looking for. Sorry for beating around the bush, and thanks for any help... Please give me an elaborate explanation. Thanks once again!!! I'm having trouble getting basic APA bibliographies to work. The same thing works with nejm style, but changing the style to apa gives errors:  ! Undefined control sequence. &lt;argument&gt; \mkbibdateapalongextra  {year}{month}{day}\iffieldundef {endyear}{...  Package biblatex Warning: Macro 'name:apa:last-first' undefined. (biblatex)                Using \newbibmacro.  Package biblatex Warning: Macro 'name:apa:first-last' undefined. (biblatex)                Using \newbibmacro.   I'm using texlive 2012, as you can see I'm using biber, yes, I reran biber, and also tried delting the .bbl file and rerunning tools. My source markup is:  \documentclass[12pt]{article}  \usepackage[hidelinks]{hyperref} \usepackage[backend=biber,style=apa]{biblatex}  \addbibresource{BibResource.bib}  \begin{document}  test\parencite{ormrod2004human}  \clearpage  \printbibliography  \end{document} While working in a Java app, I recently needed to assemble a comma-delimited list of values to pass to another web service without knowing how many elements there would be in advance. The best I could come up with off the top of my head was something like this:  public String appendWithDelimiter( String original, String addition, String delimiter ) {     if ( original.equals( "" ) ) {         return addition;     } else {         return original + delimiter + addition;     } }  String parameterString = ""; if ( condition ) parameterString = appendWithDelimiter( parameterString, "elementName", "," ); if ( anotherCondition ) parameterString = appendWithDelimiter( parameterString, "anotherElementName", "," );   I realize this isn't particularly efficient, since there are strings being created all over the place, but I was going for clarity more than optimization.  In Ruby, I can do something like this instead, which feels much more elegant:  parameterArray = []; parameterArray &lt;&lt; "elementName" if condition; parameterArray &lt;&lt; "anotherElementName" if anotherCondition; parameterString = parameterArray.join(",");   But since Java lacks a join command, I couldn't figure out anything equivalent.  So, what's the best way to do this in Java? Should an image carousel on a mobile site automatically rotate? How does the Girl-Genius web-comic relate to the Agatha H. books? After spending some time reading  I was convinced to buy the book.  I've ordered what I think is the  in my local bookstore (yay local) and it seems to relate to the first one or two years of of web content, but I can't be sure.  My question is: "how does the book series line up with the Web comic?"  Does it contain specific episodes/adventures, relate to strips from a specific time-span or is it simply an assortment of episodes?  UPDATE: They are amazing.  It is interplanetary war in the introduction!!!!  Yes! ODBC and ADO connection to SQL Server: What protocol is used when connecting to \? Converting Linux into a Router- Traffic from eth0:0 to eth0 So I have been trying to convert my linux box which is running Mint into an router. eth0 has a public address that has 71.xx.xx.xx for an IP addr. I created an eth0:0 and set it an IP address , 10.0.0.100. I started a DHCP server that is on eth0 ( because it wont use eth0:0) and that's giving out addresses between 10.0.0.101 and 10.0.0.200. I can ping between eth0 and eth0:0 on the same machine. I have a another laptop connected to the linux via a switch and its able to receive an ip addr via the DHCP server. Problem is how do I route traffic from and to eth0:0 to eth0 and vice versa so that computers on the private network that is 10.0.0.x can access internet via the static IP on eth0. $\operatorname{Ext}$ and injectives, respectively projectives While rendering a mesh with smooth shading on, I get a dark region/shadow on certain faces. The effect is more evident when smooth shading is applied to a mesh containing ngons, with the ngons turning black when rendered.   The blackening effect is visible in the viewport too.  How can I solve this problem?