I'm from a place where there is no "L" in the language, and it's always been tricky to say.   Well, I did some research and, at least for American-English, there are two types: A "light L" and a "dark L".   Individually, I don't have a problem, but putting the dark L together with another word is sometimes a challenge. For example, I'm uncertain about "all of". Out of habit I use a light L to say it similar to "olive", but from what I read (and correct me if I'm wrong), I think I'm supposed to use a dark L for "all". This is very uncomfortable to say.  What's the proper way to pronounce "all" and "all of"? Is there a difference when put together?  EDIT: I did some more research, and some sources say that the dark L also uses the tip of the tongue as well as raising the back of the tongue. It's possible that "all of" is used in this manner. "All of" and "olive" may be different after all.  The linked post  does have some information, but it doesn't fully answer this question.  Tom says in the question that     Dark "L": is "L" at the end of the word or after a vowel sound.   Example: ball, pull.      Light "L:: is "L" at the beginning or before a vowel sound. Example:   light, love.   Araucaria says in an answer that      The rule for dark /l/ is that we always use dark /l/ when /l/ isn't   followed by a vowel. So in the word falafel the first /l/ is clear, the second is dark.   But neither of these posts seem to say if the rule applies when a word ending in "l," such as "all," is followed by a word starting with a vowel sound, such as "of."
"Dark L" is "L" at the end of the word or after a vowel sound. Example: ball, pull.  "Light L" is "L" at the beginning or before a vowel sound. Example: light, love.  There are 4 explanations of how to pronounce "dark L":   1st explanation: the tongue tip must contact the ridge right behind the upper teeth. 2nd explanation: before the tongue tip must contact the ridge right behind the upper teeth, you must curl the tongue and make sound like /r/ before make the /l/ as in the 1st explanation. 3rd explanation: just put the tongue between upper and lower teeth is enough to make the dark L 4th explanation: the tongue tip must contact the ridge right behind the upper teeth &amp; the back of the tongue raises up (a British teacher teaches that).   see this vid:  and  for more info  So what is the correct way to make the "dark L"?
This is my follow up question. My previous question is here:   Problem:  If I add the image in my table, I get the following output as shown in the image below. Why is the Co-Supervisor going below?   I am using this code:  \begin{tabular}{|l|c|r|} \hline \bf Author: &amp; \hspace{5pt} &amp; \bf Research Supervisor:\\ \hline Mr. X &amp;  \hspace{5pt} &amp; Prof. Dr. Z\\ \hline \includegraphics[width=0.40\textwidth,height=10mm]{Figures/images} &amp;  \hspace{5pt} &amp; \bf Co-Supervisor:\\ \hline &amp;  \hspace{5pt} &amp; Prof. Dr. Y\\ \hline \end{tabular}   What I want is shown below:   PS: Please ignore the table borders, they are for demo only, I won't be using them in my final code.  The final product: that I desire is: How can I disable the “News and Interests” Widget on the Windows 10 Taskbar? On Windows 10 version 1909 and newer releases, Microsoft has added a &quot;News and Interests&quot; widget on the Taskbar (see ):  How can I remove this Widget from the Taskbar? Is there a way to have coloured hyperref hyperlinks in the PDF, but have them print "as if" they were black? I like having my hyperref hyperlinks a different colour, so it's obvious that they are links. But when I print a copy of the PDF, I don't want the links to be coloured, because you can't click them, so it doesn't matter and it's distracting.  Other than just having a separate "for printing" version of the PDF where I turn off the hyperlinks, is there a way to have the printed version come out without the coloured links? Equivalence of the definition of the Subbasis of a Topology I came to know about 2 definitions of a subbasis of a topology. 1. A collection of subsets of X viz. S is said to be a subbasis of a topology T on X if S covers X and the finite intersections of elements of the subbasis form the basis elements (H.L.Royden). 2. If we consider the all the topologies on X containing S, then their intersection is also a topology on X and it is the smallest topology containing S. Then S is said to be a subbasis of the smallest topology, and the topology is said to be generated by S.  Now I want to prove their equivalency, i.e. S is a subbasis of a topology T iff T is generated by S. I have tried in the way: First let T is generated by S. Then by 2nd definition T is a topology containing S. Let B be the set of all finite intersections of elements of S.Then S is a subset of B and B is a subset of T (as T is a topology). LET T1 be the collection of possible unions of elements of B, we will show that T = T1. After this I am not able to proceed. Also I am unable to sketch the converse part. If something is wrong, please let me know, and also I hope to get help. Thank You. Can't modify list elements in a loop How secure would github hosting be for private repositories? Hill cipher, unknown letter value I've been struggling on this problem for a while now : the Hill cipher is well-known to be vulnerable to known-plaintext attack due to its linearity. Given a key matrix $K$ of size $n\times n$, one can retrieve the key with as little as $n^2$ plaintext/cipher text couples.  All examples found on the Internet assume an alphabet where $A=0, B=1 \dots Z=25$, but how could we break the Hill cipher using a know-plaintext attack without any clue over the alphabet permutation nor the key matrix ?  I've tried several things such as  the whole set of equations together, however it requires several divisions in $\bf{Z}_{26}$ which aren't possible (i.e. division by even numbers or 13) How can I use colours to separate texture node treatment? I'm used to doing all my coding in one C file. However, I'm working on a project large enough that it becomes impractical to do so. I've been #including them together but I've run into cases where I'm #including some files multiple times, etc. I've heard of .h files, but I'm not sure what their function is (or why having 2 files is better than 1).  What strategies should I use for organizing my code? Is it possible to separate "public" functions from "private" ones for a particular file?   question precipitated my inquiry. The tea.h file makes no reference to the tea.c file. Does the compiler "know" that every .h file has a corresponding .c file? Print only the Nth line before each line that matches a pattern I'm trying to print only the &lt;N&gt;th line before a search pattern. grep -B&lt;N&gt; prints all the &lt;N&gt; lines before the search pattern. I saw the awk code  that can print only the &lt;N&gt;th line after the search pattern.  awk 'c&amp;&amp;!--c;/pattern/{c=N}' file   How to modify this to print only the &lt;N&gt;th line before each line that matches pattern ? For example, here is my input file  ... ...    0.50007496  0.42473932  0.01527831    0.99997456  0.97033575  0.44364198 Direct configuration=     1    0.16929051  0.16544726  0.16608723    0.16984300  0.16855274  0.50171112 ... ...    0.50089841  0.42608090  0.01499159    0.99982054  0.97154975  0.44403547 Direct configuration=     2    0.16931296  0.16553376  0.16600890    0.16999941  0.16847055  0.50170694   ...   I need a command that can give me back the 2nd line before the search string Direct configuration. I'm trying to run this in SUSE-Linux Time travel film: character with male and female reproductive organs is taken back in time by a barman who turns out to be themselves I have had a friend give me a rough description of a film and I'm curious to find out what it actually is. I don't know very much. I understand this will be difficult, especially since every time my friend explains the tale it's different so this description is likely to contain some inaccuracies.  The film's plot begins with a recounting given by the main character, who had both male and female reproductive organs but had one set removed (not sure which, think male ones were removed). The main character is narrating this tale to the barman in a bar. The barman then takes the main character back in time, where they make love to themselves and produce a child.  The child, once born, is abandoned by the mother in the past - but the barman takes the child to the orphanage and leaves them there, ensuring their survival. Eventually it is revealed that the child was the main character themselves, and so was the barman.  In other words every major character introduced up to that point was the same person who had severely messed with their own timeline. How do I identify which CPU a MacBook uses? I'd like to identify which CPU this notebook is using, in terms of code names such as "Ivy Bridge" and "Haswell". The little Apple logo in the upper left shows some information, but not this. Notation: What does the tilde below of the expectation mean? Is an option missing in the new off-topic reasons? How would one prove that $$\lim_{n\rightarrow \infty} \frac{F_{n+1}}{F_n}=\frac{\sqrt{5}+1}{2}=\varphi$$  where $F_n$ is the nth Fibonacci number and $\varphi$ is the Golden Ratio? In several cases I want to add a toolbar to the top of the iPhone keyboard (as in iPhone Safari when you're navigating form elements, for example).    Currently I am specifying the toolbar's rectangle with constants but because other elements of the interface are in flux - toolbars and nav bars at the top of the screen - every time we make a minor interface change, the toolbar goes out of alignment.  Is there a way to programmatically determine the position of the keyboard in relation to the current view? Citing @inbook with biblatex: how to put authors/editors before book title? I have to move a MongoDB Collection (Size: 1TB+) from Sharded MongoDB Cluster to another[5 shards on both clusters]. During this operation, it is assumed that the accompanying program will be offline, so no need to worry about inconsistent data, but I need to minimize the downtime.  I've tried testing it with mongodump and mongorestore, but looks like that is taking ages to finish.  Please share your experiences for such kind of scenarios.  Note: Cluster has only one collection, so I am open at cluster level sync as well. Tikz shortandoff-on newcommand problem Usually I have no problem with babel and !:, and I don't use shortandoff-on switch. But since I made a command using !#1 parameter, the problem comes up again.  The same synthax used outside the command work fine, but in the command I get the error message :  ! Package tikz Error: + or - expected.  How to solve the problem without using the shortandoff-on switch ?  \documentclass[french,a4paper]{article} \RequirePackage{etex} \RequirePackage[utf8]{inputenc} \RequirePackage[T1]{fontenc} \RequirePackage{fourier}  \RequirePackage{tikz} \usetikzlibrary{calc,intersections}  %%%%%%%%%%%%%%%%%%%%%% %%%% Francisation %%%% %%%%%%%%%%%%%%%%%%%%%%  \RequirePackage{babel}  %%%%%%%%%%%%%%%%%%% ---------------------------------------- %%%% Géométrie %%%% %%%%%%%%%%%%%%%%%%%-----------------------------------------      % #1 option du path     % #2 premier point     % #3 second point     % #4 longueur dans un sens     % #5 longueur dans l'autre     % défini Mil#1#2 \newcommand{\Med}[5][]{%     \path[#1,name path=Med#2#3] ($(#2)!.5!(#3)$) node (Mil#2#3) {}      ($(Mil#2#3)!#4!90:(#3)$) -- ($(Mil#2#3)!#5!270:(#3)$) ; }  \tikzset{small dot/.style={fill=black,circle,scale=0.3}}  \begin{document}  %\shorthandoff{:!} \begin{tikzpicture}  \coordinate[label=below left:$A$] (A) at (0,0) ; \coordinate[label=below right:$B$] (B) at (4,0) ;  \draw (A)--(B) ;  %\Med[draw]{A}{B}{1}{1} ;  \draw($(A)!.5!(B)$) node (MilAB) {}      ($(MilAB)!1!90:(B)$) -- ($(MilAB)!1!270:(B)$) ;   \end{tikzpicture} %\shorthandon{:!}  \end{document} Every subspace of a vector space has a complement I want to see if my proof is true or I thought very trivially?    If $H$ is a subspace of a finite dimensional vector space $V$, show there is a subspace $K$ such that $H\cap K=0$ and $H+K=V$    So far I have tried :    $H\subseteq V$ is a subspace $\Rightarrow\,\exists\;K=(V-H)\subseteq V$ $K$ is a subspace because it's the sum of two subspace $V$ and $(-H)$ Now we should prove that $H\cap K=0$ We assume $H\cap K\neq0\Rightarrow\exists\,\vec u\neq0\,,\,\vec u\in H\cap K$ $\vec u\in H\cap K\Rightarrow \begin{cases}\vec u\in H\\\vec u\in K\,\Rightarrow\vec u\in V-H\Rightarrow\vec u\in V,\,\vec u\notin H\end{cases}$ That's a contradiction so our hypothesis was wrong and $\vec u=0$