I am reading the book Development Economics through the Decades: A Critical Look at Thirty Years of the World Development Report by Shahid Yusuf (2008). I struggle to understand the meaning of " functional" in the following sentence:     They are at best functional and at worst weak.   Here is the full context:      The interest of policy makers lies not in whether the state should be large or small or more or less interventionist; the interest is in what specific forms of intervention over a period of time yield the best results under similar external circumstances. The same is true regarding institutions. Everyone can see that market institutions in successful East Asian industrializing countries are at best functional and at worst weak and minimally supportive.   I would be grateful if anyone could explain meaning of the phrase in that last  sentence.
state that "at best" is an idiom. But, what is the grammatical function of "at best" (for example, in the below sentences?)        Their response to the proposal was, at best, cool.   The government's response seems to have been at best confused and at   worst dishonest.   If he drops the course now, at best he’ll get an incomplete, and he could fail.      Thanks
Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet? Of course, we've all heard the colloquialism "If a bunch of monkeys pound on a typewriter, eventually one of them will write Hamlet."  I have a (not very mathematically intelligent) friend who presented it as if it were a mathematical fact, which got me thinking... Is this really true?  Of course, I've learned that dealing with infinity can be tricky, but my intuition says that time is countably infinite while the number of works the monkeys could produce is uncountably infinite.  Therefore, it isn't necessarily given that the monkeys would write Hamlet.  Could someone who's better at this kind of math than me tell me if this is correct?  Or is there more to it than I'm thinking? Boy asks 'How about pie?' I am looking for the title of a 1950s science fiction movie, involving an astronomer trying to decode some extraterrestrial signal, where the juvenile (male) character asks 'how about pi?' which all the adults interpret as a foolish 'how about pie?' question. Why does a 'sudo -i' login shell break a here-doc command string argument? In the sequence of five commands below, all depend on single-quotes to hand off possible variable substitution to the called bash shell rather than the calling shell. The calling user is xx, but the called shell will be run as user yy. The first command substitutes $HOME with the calling shell's value because the called shell is not a login shell. The second command substitutes the value of $HOME loaded by a login shell, so it is the value belonging to user yy. The third command does not rely on a $HOME value and creates a file in the guessed home directory of user yy.  Why does the fourth command fail? The intention is that it writes the same file, but relying on the $HOME variable belonging to user yy to ensure it actually does end up in her home directory. I don't understand why a login shell breaks the behaviour of a here-doc command passed in as a static single-quoted string. The failure of the fifth command verifies that this problem is not about variable substitution.  xx@host ~ $ sudo -u yy bash -c 'echo HOME=$HOME' HOME=/home/xx xx@host ~ $ sudo -iu yy bash -c 'echo HOME=$HOME' HOME=/home/yy xx@host ~ $ sudo -u yy bash -c 'cat &gt; /home/yy/test.sh &lt;&lt; "EOF" &gt; script-content &gt; EOF &gt; ' xx@host ~ $ sudo -iu yy bash -c 'cat &gt; $HOME/test.sh &lt;&lt; "EOF" &gt; script-content &gt; EOF &gt; ' bash: warning: here-document at line 0 delimited by end-of-file (wanted `EOFscript-contentEOF') xx@host ~ $ sudo -iu yy bash -c 'cat &gt; /home/yy/test.sh &lt;&lt; "EOF" &gt; script-content &gt; EOF &gt; ' bash: warning: here-document at line 0 delimited by end-of-file (wanted `EOFscript-contentEOF')   These commands were issued on a Linux Mint 18.3 Cinnamon 64-bit system, which is based on Ubuntu 16.04 (Xenial Xerus).  Update: The here-doc aspect is just clouding the issue. Here's a simplification of the problem:  $ sudo bash -c 'echo 1 &gt; echo 2' 1 2 $ sudo -i bash -c 'echo 1 &gt; echo 2' 1echo 2   Why does the first of those two commands preserve the linebreak and the second does not? sudo is common to both commands, yet seems to be escaping/filtering/interpolating differently depending on nothing but the "-i" option. Ubuntu 20.04 interface font too small after restart, even with high scaling factor I prefer to use bm package to bold math. However, I noticed that when used with eulervm, this gives inconsistent results for ‘&lt;’ and ‘>’ characters.  I wonder what causes it and can the usage bm be fixed to get proper ‘&lt;’.  \documentclass{article}  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc}  %\usepackage{amsmath}  \usepackage[euler-digits,euler-hat-accent]{eulervm}  \usepackage{bm}  \begin{document}      \texttt{\hphantom{mathbold}\llap{bm}}: \quad $ 1 + 1 &lt; 3; \quad \bm{1 + 1 &lt; 3} $      \texttt{mathbold}: \quad $ 1 + 1 &lt; 3; \quad \mathbold{1 + 1 &lt; 3} $  \end{document} Proving that $\sum\limits_{n = 0}^{2013} a_n z^n \neq 0$ if $a_0 > a_1 > \dots > a_{2013} > 0$ and $|z| \leq 1$ I'm going to teach a preparation course for the complex analysis qualifying exam from my university (which basically consists of me doing some problems from past exams) and I'm trying to solve some questions from previous exams. One of the questions is the following:           Prove that $\displaystyle{\sum_{n = 0}^{2013} a_n z^n \neq 0}$ if the coefficients  satisfy $a_0 &gt; a_1 &gt; \dots &gt; a_{2013} &gt; 0$ and $|z| \leq 1$.      I tried to approach the problem by using the reverse triangle inequality to try to isolate the leading term, which I thought should be the constant coefficient, as follows:  \begin{array} . \left|  \sum_{n = 0}^{2013} a_n z^n \right| &amp;= \left| a_0 +  \sum_{n = 1}^{2013} a_n z^n \right| \\ &amp;\geq |a_0| - \left|  \sum_{n = 1}^{2013} a_n z^n \right|\\ &amp;\geq |a_0| -  \sum_{n = 1}^{2013} |a_n z^n|\\ &amp;\geq a_0 -  \sum_{n = 1}^{2013} a_n |z^n|\\ &amp;\geq a_0 -  \sum_{n = 1}^{2013} a_0 |z^n|\\ &amp;= a_0\left( 1  -  \sum_{n = 1}^{2013} |z^n| \right) \end{array}  Then for $|z| &lt; 1$, we have that this last expression is equal to  $$ a_0\left( 1  -  |z| \frac{|z|^{2013} - 1}{|z| - 1} \right) $$  and my hope was to prove that this was always positive, nevertheless, after failing to prove it, I plotted the expression inside the parenthesis as a function of $|z|$, and found out that it changes sign in the interval $(0, 1)$.  Question  Can my approach somehow be made to work? And if not, how can I prove that the sum $\displaystyle{\sum_{n = 0}^{2013} a_n z^n \neq 0}$ under the given conditions?  Thank you very much for any help. Booting from USB and not installing I created a live usb to boot Kubuntu, which has worked well enough. However, when the installation gets to the point of telling me to restart the computer (and it restarts) the installation window pops up again, and the computer is still signed in as a live user. None of the installation or settings appear to have saved.  Any ideas? What made us think that Earth moves around the Sun? What is "anycast" and how is it helpful? I'd never heard of anycast until a few seconds ago when I read "".  The wikipedia "" article on it is quite formal and doesn't really evoke a mental picture of how it would be used.  Can someone explain in a few informal sentences what "anycast" is, how you configure it (just in a general sense), and what its benefits are (what does it make easier)? Cannot install Ubuntu in VirtualBox due to "this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot" error Can you please explain this to me?          Could you please explain this to me?   I am unable to figure out which to use which situation. I did google, and some posts say they are both the same, even if the second one is more formal. Other posts say could is the past tense of can, but in the above example, I don't think could is used as past tense of can.  What is correct way to use these words? How does one install PlayOnLinux? How do I install PlayOnLinux on Ubuntu? why each left ideal of this is minimal? I'm DM'ing a play-by-post campaign and I'm at a point in the adventure where the group all meets for the first time. They've all had something stolen from them at the same time and saw a creature that took something run into a nearby alley (there's three separate parties within the play group currently, as they've only just started, so there's three separate robbers running into alleys in the marketplace).  Ideally, I want the players to have their PCs all give chase so they end up in the same part of town, all looking for the same thing. However, I don't want to railroad my players into doing this. I know I'm not supposed to take away player agency or narrate their actions for them, but the only way I could think of was to tell them that they start giving chase.  So how would you deal with this situation? And more broadly, how can I stop something like this happening again?  If it matters, we're currently playing D&amp;D 5e. How did nobody at Hogwarts (especially Dumbledore) figure out what killed Myrtle? Approximation of real number to the power of irrational Say I have two numbers, $c\in\Bbb R^+\,,q\in\Bbb{R\setminus Q}$.  Is there a way to approximate the value of $c^q$?  This question bugging me because of how simple it sound in compare to how complicated it is. First I want to understand what a power of irrational number is, when talking about $\Bbb R^+$(I use this domain for sake of simplicity) we have very well defined actions for power a rational number, we can even use some theorems to get $c^{a/b}=\sqrt[b]{c^a}$, but when I am dealing with irrational number I can not do this.  I know that we have some definition for this because the solution of the equation $2^x=3$ is irrational.  So what exactly does it mean to take something to a irrational power and is there a way to approximate a numeric value for this? I'm working in C, and I have to concatenate a few things.  Right now I have this:  message = strcat("TEXT ", var);  message2 = strcat(strcat("TEXT ", foo), strcat(" TEXT ", bar));   Now if you have experience in C I'm sure you realize that this gives you a segmentation fault when you try to run it. So how do I work around that? I just bought a new house and I'm looking to run some cables. One of the areas I would like to run it to would require drilling through a 2x10 sistered joist. Realizing that going through the joist should be a last resort, if the hole is 1/4" and in the middle of one of the joists will this weaken the integrity?  I have seen lots of articles about drilling through the depth of a joist, but very few regarding drilling vertically. Is Autopilot Openstack 16.04 available? How do I list the default installed packages?