which one to use mysqli_fetch_assoc OR mysqli_fetch_array from performance point of view?
mysql_fetch_array, mysql_fetch_assoc, mysql_fetch_object
I'm trying to do something similar to this epsilon-delta graph I've found.  Specifically, I'd like to copy the placements and arrows, like the L+e and L-e coming out of L. Same thing with the x0 + d and x0-d coming out of the x0. Can someone help me with this? This is what I have so far.    \begin{tikzpicture} \begin{axis}[ ,         legend pos=north east,         axis x line=middle,         axis y line=middle,         x tick label style={/pgf/number format/fixed,                             /pgf/number format/fixed zerofill,                             /pgf/number format/precision=1},         y tick label style={/pgf/number format/fixed,                             /pgf/number format/fixed zerofill,                             /pgf/number format/precision=1},         grid = major,         width=8cm,           height=6cm,         grid style={dashed, gray!30},         xmin=0   ,     % start the diagram at this x-coordinate         xmax= 4,    % end   the diagram at this x-coordinate         ymin= 0,     % start the diagram at this y-coordinate         ymax= 11,   % end   the diagram at this y-coordinate %axis background/.style={fill=white},         xlabel=$x$,         ylabel=$f(x)$,         tick align=outside,         enlargelimits=false] % plot the stirling-formulae %\addplot[domain=0:200, red, ultra thick,samples=100] {K/(1 +    ((K-X0)/X0) * exp(r*x))    }; \addplot[domain=0:200, red, ultra thick,samples=100] {3*x-1 };  \addplot[line width=1pt, dashed, mark=none, black] coordinates {(0,8) (3,8)}; \addplot[line width=1pt, dashed, mark=none, black] coordinates {(3,0) (3,8)}; \addplot[line width=1pt, dashed, mark=none, blue] coordinates {(3.33,0) (3.333,9)}; \addplot[line width=1pt, dashed, mark=none, blue] coordinates {(2.666,7) (2.666,0)}; \addplot[line width=1pt, dashed, mark=none, blue] coordinates {(2.666,7) (0,7)}; \addplot[line width=1pt, solid, mark=none, blue] coordinates {(3.333,9) (0,9)}; \addplot[holdot] coordinates{(60,8.66)};  % 1\addlegendentry{$f(x) = 10 \sin (x)$}  \end{axis}   \end{tikzpicture}   which gives Showing group with $p^2$ elements is Abelian I have a group $G$ with $p^2$ elements, where $p$ is a prime number. Some (potentially) useful preliminary information I have is that there are exactly $p+1$ subgroups with $p$ elements, and with that I was able to show $G$ has a normal subgroup $N$ with $p$ elements.   My problem is showing that $G$ is abelian, and I would be glad if someone could show me how.   I had two potential approaches in mind and I would prefer if one of these were used (especially the second one).   First: The center $Z(G)$ is a normal subgroup of $G$ so by Langrange's theorem, if $Z(G)$ has anything other than the identity, it's size is either $p$ or $p^2$. If $p^2$ then $Z(G)=G$ and we are done. If $Z(G)=p$ then the quotient group of $G$ factored out by $Z(G)$ has $p$ elements, so it is cylic and I can prove from there that this implies $G$ is abelian. So can we show theres something other than the identity in the center of $G$?  Second: I list out the elements of some other subgroup $H$ with $p$ elements such that the intersection of $H$ and $N$ is only the identity (if any more, due to prime order the intersected elements would generate the entire subgroups). Let $N$ be generated by $a$ and $H$ be generated by $b$. We can show $NK= G$, i.e every element in G can be wrriten like $a^k b^l $. So for this method, we just need to show $ab=ba$ (remember, these are not general elements in the set, but the generators of $N$ and $H$).   Do any of these methods seem viable? I understand one can give very strong theorems using Sylow theorems and related facts, but I am looking for an elementary solution (no Sylow theorems, facts about p-groups, centrailzers) but definitions of centres and normalizers is fine. C++ map access discards qualifiers (const) The following code says that passing the map as const into the operator[] method discards qualifiers: #include &lt;iostream&gt; #include &lt;map&gt; #include &lt;string&gt;  using namespace std;  class MapWrapper { public:     const int &amp;get_value(const int &amp;key) const {         return _map[key];     }  private:     map&lt;int, int&gt; _map; };  int main() {     MapWrapper mw;     cout &lt;&lt; mw.get_value(42) &lt;&lt; endl;     return 0; }  Is this because of the possible allocation that occurs on the map access? Can no functions with map accesses be declared const? MapWrapper.cpp:10: error: passing const std::map&lt;int, int, std::less&lt;int&gt;, std::allocator&lt;std::pair&lt;const int, int&gt; &gt; &gt; as this argument of  _Tp&amp; std::map&lt;_Key, _Tp, _Compare, _Alloc&gt;::operator[](const _Key&amp;)  [with _Key = int, _Tp = int, _Compare = std::less&lt;int&gt;,  _Alloc = std::allocator&lt;std::pair&lt;const int, int&gt; &gt;] discards qualifiers NSString instance reports its class as NSCFString My objective here is really simple -- I'm trying to set an NSString to some test data, then return the class, which should be NSString. Here's my code:  NSString* stringer = [NSString stringWithFormat: @"Test"]; NSLog(@"%@", [stringer class]);   The log says that the class is NSCFString, not NSString. What's going on here? Does the Black Panther suit give extra speed? So in Civil War, the Black Panther suit seems to give the suit holder some extra speed, because the guy was running as fast as Bucky and Captain America.  So does it give extra speed? If so, how does that work? $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $ = -$  2.887270... $  The function has no antiderivate and there's no symmetry here to help, if you solve this I would be thankful if you would for a highschooler ^^ I am totally stumped for what to do here, any help would be appreciated.   1) What happens if you apply the method of steepest descent to $f(x)=x_1^2+x_2^2+x_3^2$?  2)Lagrange multipliers method- Find the dimensions of the rectangular box open at the top of greatest internal volume, given the surface area of the five faces is $108 \, \mathbb{cm}^2$.  Thanks I have setup a project of 250 frames with a flag and a wind force field. It works fine until I change the length of the project to 520 frames, then the flag is frozen after frame 250. There must be a simple way to change this. Thanks for any help. Regards, Daniel. I want to update ubuntu 11.04 throught apt-get. So I added the following lines in apt.conf  export http_proxy=http://username:password@proxyserver.net:port/ export ftp_proxy=http://username:password@proxyserver.netport/  export http_proxy=http://deepak:Deepak@123@12.1.1.1:3128   My question is: how do I insert special characters to a username or password?  For instance: my password for proxy is Deepak@123 and it is getting an error. 'find' utility does not output all files when using wildcards Running:  $find . -name *.exe   gives:  ./MakeItSo_1.2.2/MakeItSo_1.2.2/MakeItSo.exe ./MakeItSo.exe   but those are not the only exe files in the directory. For example, running  $find . -name ATLTester.exe   gives:  ./Debug/ATLDmoVexaTester.exe Do badges get calculated in real time, or do they get calculated by an external service? How long does it take for a badge to be awarded, once its requirements are met?  Does Stack Overflow use any external services to do things, like maintenance, e-mailing or badge calculation? Compare two dates with JavaScript Prove that the normalisation of $A=k[X,Y]/(Y^2-X^2-X^3)$ is $k[t]$ where $t=Y/X$ (Reid, Exercise 4.5) This is a problem about finding the normalisation of a quotient polynomial ring. So I have to find the integral closure of the ring in its field of fractions. The problem statement is as follows:     Let $A=k[X,Y]/(Y^2-X^2-X^3)$. Prove that the normalisation of $A$ is $k[t]$ where $t=Y/X$.   Can I do this by showing that the field of fractions $\text{Frac} A$ of $A$ is equal to $k[t]$, and subsequently showing that the field of fractions is normal? (This could be done by showing that $k[t]$ is a UFD?)  I am lost at calculating/determining $\text{Frac}A$, or similarly proving that $k[t]=\text{Frac}A$. Also, how do I show that it is normal?  I hope you can help! Usually, the equality $\mathfrak{m}^\mathfrak{m} = 2^\mathfrak{m}$ for infinite cardinal $\mathfrak{m}$ is proved like that: $$ 2^\mathfrak{m} \leqslant \mathfrak{m}^\mathfrak{m} \leqslant (2^\mathfrak{m})^\mathfrak{m} = 2^{\mathfrak{m} \cdot \mathfrak{m}} = 2^\mathfrak{m} $$ The last step relies much on the axiom of choice, because the fact $\mathfrak{m}\cdot\mathfrak{m} = \mathfrak{m}$ does. Moreover,  states that in $\sf{ZF}$ this fact is equivalent to $\sf{AC}$.  Note, by a cardinal I mean an equipollence class of an arbitrary set, not necessarily admitting a well-ordering.  That has motivated my question: what can we say about relationship of the initial equality and the axiom of choice in pure $\sf{ZF}$?    To avoid question about definition of cardinals without $\sf{AC}$, we may consider the following statement instead:     For any infinite set $X$ exists a bijection $\; F \, \colon X^X \rightarrow 2^X$   where $X^X$ is the set of all functions from $X$ to $X$, $\; 2^X = \mathcal P(X)$ is the power set, and an infinite set is such that cannot be bijectively mapped onto a finite ordinal. $\bigcup \emptyset$ is defined but $\bigcap \emptyset$ is not. Why? Why does $\bigcup \emptyset = \emptyset$ but $\bigcap \emptyset$ is not defined?    If I had to guess, I'd say it's also equal to $\emptyset$. Getting "'file' is different from the same file on the system" when I attempt to update through synaptic Encountered an error while updating through Synaptic Manager. Subsequent updates gave the error at the bottom of the output. I'm a noob so any help is appreciated.  al@al:~$ sudo apt-get -f upgrade Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following NEW packages will be installed:   libjack-jackd2-0:i386 The following packages have been kept back:   linux-headers-generic skype 0 upgraded, 1 newly installed, 0 to remove and 2 not upgraded. Need to get 0 B/202 kB of archives. After this operation, 493 kB of additional disk space will be used. Do you want to continue [Y/n]? y (Reading database ... 310056 files and directories currently installed.) Unpacking libjack-jackd2-0:i386 (from .../libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb) ... dpkg: error processing /var/cache/apt/archives/libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb (--unpack):  './usr/share/doc/libjack-jackd2-0/buildinfo.gz' is different from the same file on the system dpkg-deb: error: subprocess paste was killed by signal (Broken pipe) Errors were encountered while processing:  /var/cache/apt/archives/libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb E: Sub-process /usr/bin/dpkg returned an error code (1) "Planar" graphs on Möbius strips My "network reputation" graph does not accurately reflect my accounts Different font color for question status => closed <= When I stared at  () and I even thought [question refined] as offical status of the post.    &lt;somebody  it now, So, I've edited this question to get same effect>  How about official status [closed] as   different font color or  different font size or put the text [closed] outside the question link   Or   put a special tag as suggested in the    to clarify from those? shell: keep trailing newlines ('\n') in command substitution I want to be able to capture the exact output of a command substitution, including the trailing new line characters.  I realise that they are stripped by default, so some manipulation may be required to keep them, and I want to keep the original exit code.  For example, given a command with a variable number of trailing newlines and exit code:  f(){ for i in $(seq "$((RANDOM % 3))"); do echo; done; return $((RANDOM % 256));} export -f f   I want to run something like:  exact_output f   And have the output be:  Output: $'\n\n' Exit: 5   I'm interested in both bash and POSIX sh.