How to prove if $X_n$ converges in probability to $X$ then there exists at least one subsequences converge almost surely to $X$? I have no idea how to proceed.
Convergence in probability implies convergence on a subsequence almost surely.  But this means we fix a subsequence, such that $X_{n_k}$ converges for almost every $\omega$, right? The subsequence we pick does not depend on the $\omega$ right?
How to change color of the text in TextView on hover like in css? Biblatex: Don't show n.d. when no year is given I am using biblatex/biber with several bibliographies for my book, and the misc-type, which is also a single bibliography (as a chapter), for legal documents. These documents often do not have a proper date or rather the date is part of the title. However, Latex gives me a "n.d." output, and I am wondering what I can do for it to not give a "n.d." when there is no year given?    To make clear, the reason for why I don't want to use the "year" field is that I deal with very different kinds of documents, which may either have no date or the date is in the title, because of which I prefer to simply "hard-copy" the whole thing in the "howpublished"-section and need to suppress the year, if none is provided.  MWE:  \usepackage[autocite=footnote, language=german, style=authoryear-ibid, sorting=nyt, backend=biber]{biblatex} \usepackage[bottom]{footmisc} \bibliography{lit.bib} \makeindex \begin{document}  Test\autocite[2]{draftnotice}.  \printbibliography[title={EU Legal Documents}, type=misc1]  \end{document}   My lit.bib is as follows:  @misc1{draftnotice,     Author = {{COMMUNICATION FROM THE COMMISSION}},     Howpublished = {Draft Commission Notice of 2014 on the notion of State aid pursuant to Article 107 (1) TFEU}}   Check out my MWE on overleaf CMake & CTest : make test doesn't build tests Recently, the titles to some questions have been displaying as "undefined":    "undefined" is replaced with the question's true title upon refreshing the page. Is this a bug? Is either "can" or "could" more polite? Does the condition $\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}=1$ imply that $a_n$ convergent?  When I say convergent I mean to $L\in \mathbb{R}$ or to $\infty$ or to $-\infty$  I have a gut feeling this statement is false, just can't find a series which contradicts it.  Thanks a lot Binomial Distribution Problem - Airline Overbooking How to list available shells for use by command-line? Mac asking for password for some files when deleting This happens not for all files. When I move or delete some of the files on my external drive Finder will ask for password. Is it due to permission set on these files ? Can I use something like Sudo when running Finder to prevent these pop ups ? The reason I'm asking is that sometimes I leave the mac running to move some files from one disk to another, just to find it on the password prompt a few hours later. Thank you. Uk Visa Refused need guidelines etc,,, What is the most efficient way given to raise an integer to the power of another integer in C?  // 2^3 pow(2,3) == 8  // 5^5 pow(5,5) == 3125 Can $\frac{\sqrt{3}}{\sin20^{\circ}}-\frac{1}{\cos20^{\circ}}$ have two values? What 70s (60s?) TV show / TV movie had a generation ship whose inhabitants did not know they were on a spaceship? I have the vaguest memory of a TV show (maybe a BBC import?) in which the protagonists were moving through the sections of a massive generation ship whose inhabitants had forgotten that they were on a spaceship... I know there was an RPG with the same plot (which, after all, is a pretty great blank slate) but I definitely feel I saw this on a static-filled 13" B&amp;W TV back in the day... Are $_SESSION variables stored on the client or the server? Merge files based on matching of first column I have two files: File1  ARS-BFGL-BAC-10975 0.9303 688423261 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-11025 0.9092 688423261 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-11044 0.9626 688423261 2 01/04/2015 0.9983763305 ARS-BFGL-BAC-11193 0.9544 688423261 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-10975 0.9303 688423263 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-11025 0.9092 688423263 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-11044 0.9626 688423263 2 01/04/2015 0.9983763305 ARS-BFGL-BAC-11193 0.9544 688423263 1 01/04/2015 0.9983763305   File2:  ARS-BFGL-BAC-10975 10 21225382 ARS-BFGL-BAC-11025 10 84516867 ARS-BFGL-BAC-11193 1 29303546   Desired output  ARS-BFGL-BAC-10975 0.9303 688423261 1 01/04/2015 0.9983763305 10 21225382 ARS-BFGL-BAC-11025 0.9092 688423261 1 01/04/2015 0.9983763305 10 84516867 ARS-BFGL-BAC-11193 0.9544 688423261 1 01/04/2015 0.9983763305 1 29303546 ARS-BFGL-BAC-10975 0.9303 688423263 1 01/04/2015 0.9983763305 10 21225382 ARS-BFGL-BAC-11025 0.9092 688423263 1 01/04/2015 0.9983763305 10 84516867 ARS-BFGL-BAC-11193 0.9544 688423263 1 01/04/2015 0.9983763305 1 29303546   So file 1 has many more rows than file 2. I only want to keep rows in the output that are in file 2 based on column1.   I have tried join but I cant get it to work right-it will tell me my files are not sorted  join -j 1 -o 1.1,1.2,1.3,1.4,1.5,1.6,2.2,2.3 &lt;(sort -k1 file1) &lt;(sort -k1 file2)   Preferably I would prefer an awk command. File 1 will be very large. I have tried   awk 'FNR==NR{a[$1]=$2 FS $3;next}{ print $0, a[$1]}' file2 file1 &gt; output   Any help would be much appreciated. Thanks  Sorry I cant comment below but just to clarify file not all rows in column1 in file 1 will be in file2.  The awk command  awk 'FNR==NR{a[$1]=$2 FS $3;next} $1 in a {print $0, a[$1]}'    will only keep the amount of rows there is in file 2. But ideally what I want is were for expample ARS-BFGL-10975 is repeated twice (realistically way more) to appear twice in my output.  Thanks for the help so far Multiplexing UART I'd like to interface my main microcontroller's hardware serial port to more than one device at the same time. My understanding is that UART on my microcontrollers is based on an active-low 5V TTL.  (I know what I'm explaining here can be technically achieved by using more suited protocols, such as SPI and I2C, but my project requires to be only implemented using UART.)  Here's a pseudo-schematics chart of what I'm trying to achieve:         &ndash; Schematic created using   Please note that:   I don't want to use a second UART interface on the master, or any of the slaves. Only one slave at a time is going to transmit or send data on the line to the master. (e.g. If the slave 1 is transmitting data, slave 2 and 3 should remain idle.) Whatever the master is transmitting can, and should be received by all of the slaves. All of the slaves should be hot-pluggable, meaning they could be removed or inserted at any time. The RX and TX wires to the master are parallel between each slave, so no daisy chaining.   So, my questions are as follows:   Assuming the correct impedance is considered, I shouldn't need an additional circuit to transmit data from the master's TX line to any of the slave's RX line simultaneously. Is this correct? I understand that without current limiting resistors between slaves' TX line and the master's RX line, if any of the devices begin to broadcast data, the line between the devices will short circuit and I risk damaging them. Is this correct? Assuming the items 1 and 2 are correct:  a) Would just some current limiting resistors be enough to use?  b) Can I use 74-series logic gates instead of resistors? Between options a and b above, what route should I choose? For a reliable 115200 baud rate connection, will the switching frequency of a 74HC08 AND gate suffice to be incorporated?   EDIT: I'm well aware of other well-suited protocols such as SPI and I2C. There's a reason I'm using UART, and that's because the optiboot bootloader that is used on the master's mcu communicates over UART, albeit UART's obvious limitations.  Also, while daisy-chaining is definitely a clever approach, due to breaking the 4th requirement, it also breaks bootloader functionality.  The devices could also be USB-to-Serial chips, and using SPI-to-USB or I2C-to-USB would not be feasible in this project.  So, I'd appreciate if you could focus on the 6 questions listed here instead, and share your UART knowledge. Sending an E-mail to all addresses of all contacts in a contact group in Gmail I'm trying to send an E-mail message using Gmail to a contact group where some of the contacts have more than one E-mail address and I want to send the mail to all of them.   Is there a way for me to do that? ON an American street, but IN a British one. Do the twain ever meet? In the United States, we say that someone lives on a street, whereas I've noticed that British people say in. For instance:     Bubba lives on Washington Street.   Colin lives in Cavendish Avenue.   I believe we both would use at when a number is given. For instance:     Bubba lives at 16 Washington Street.   Colin lives at 7 Cavendish Avenue.   I don't think it matters if it's a road, avenue, street, circle, or lane — as far as I know, in America, we always live on a street. Does it vary in British English, or is it always in? If it varies, what are the rules? Create ArrayList from array I have an array that is initialized like:  Element[] array = {new Element(1), new Element(2), new Element(3)};   I would like to convert this array into an object of the  class.  ArrayList&lt;Element&gt; arraylist = ???; How to grep a specific line _and_ the first line of a file?