Parse empty string to int
How do I compare strings in Java?
Prove $$\int _0^\infty f^2(x) dx \leq \frac{2}{3}\cdot  \max_{x \in \mathbb R^+} f(x) \cdot  \int _0^\infty f(x) dx$$ for $f(x) \geq 0$ and convex.   I know via Holder's we can get without the constant $\frac{2}{3}$ but that should also be true for $f$ not convex. I tried some approaches using convexity but didn't get the desired result.   A hint or reference would also help. Also, it would be interesting to know when equality holds. If I took a picture of a windmill on the horizon — given that I know the sensor size and the focal length of the lens and other factors to do with the shot — could I calculate how far away an object is from the photographer? SOQL query for Multiselect picklist i would like to know how to prove that if $a^2+b^2=c^2$ then   a) $3|a$ or $3|b$  b) $5|a$ or $5|b$ or $5|c$  c) $4|a$ or $4|b$   Also that $a^2+b^2+c^2+1$ can't be divisible by 8  Thank you very much! Why have  on every line I've seen this convention pretty much everywhere, and, at times, it comes close to driving me nuts:  &lt;?php //The loop ?&gt; &lt;?php while ( have_posts() ) : the_post(); ?&gt;     &lt;?php the_content(); ?&gt; &lt;?php endwhile; // end of the loop. ?&gt;   Where the &lt;?php and closing ?&gt; are on every single line, even if there is no intervening HTML code.    My question is: Why?  Why include all these extra tags?      To me, it seems this convention adds a significant amount of clutter to code, is annoying to follow in the first place, and adds that many more places to accidentally leave out an opening or closing tag.  NOTE  This is code pulled from the Twenty-Twelve theme, the example given by WordPress. My wife was just issued a multiple entry visa by France, which is good for one year.  Our first trip will be to France, the issuing country.  My question is: after we leave the EU and return, must future trips also start in France? Or may we go directly to (say) Greece from the US on a later visit? Inverting direction of mouse scroll wheel Is there a way to make a mouse scroll wheel invert its direction? I'd like to scroll upwards and have that action scroll downwards and vice-versa. There is no setting on the Mouse control panel that makes this possible.   Any pointers to a hack or a particular mouse model that has such a setting would be appreciated. I am using Windows 7. Bibliography error: "Use of \blx@bbl@verbadd@i doesn't match its definition. \verb" Currently having problems with compiling my Master's thesis after downloading the newest version of TeXStudio and MiKTeX. The error message is as follows:  Use of \blx@bbl@verbadd@i doesn't match its definition. \verb   The only other place I found a similar question regarding this error message was found here:   I am not sure how this applies to my problem, but from what I understand this is due to some problem in an external file. If you need the bibliography-entry, I can provide you with that on short notice, though it is rather long (which is why I didn't include it here in the first place).  I am using Mendeley Desktop v1.16.1 to automatically generate my BibTeX database.   I am using biblatex as follows:  \usepackage[backend = bibtex,         style = numeric-comp,         sorting = none,         natbib = true,         doi = false,         isbn = true,         hyperref = true]{biblatex}   I also have some code to change how the bibliography output, but I doubt it is causing the problem, as commenting it out did not help.  Hope anyone knows what causes my problem and how to fix it.  Thanks. sudo: /etc/sudoers is owned by uid 501, should be 0 To run programs as sudo without password, I edited /etc/sudoers with wrong content.   Then I re-edited it with Mac's default text editor(course sudo cannot be used when /etc/sudoers is wrong).  I tried to run sudo agin, and get this error:   sudo: /etc/sudoers is owned by uid 501, should be 0 sudo: no valid sudoers sources found, quitting   What should I do? I cannot remember the root password (maybe I haven't ever set root password before). Group of order $8p$ is solvable, for any prime $p$ Consider the following question:     Show that a group $G$ of order $8p$ is solvable, for any prime $p$.   I am kind of stuck, but here are my first attempts:  I chose the series of subroups $G&gt;H_8&gt;H_4&gt;H_2&gt;H_1=\{e\}$ where $H_k$ has order $k$. All of these subgroups exist due to Sylow's Theorems. We have the quotients $H_8/H_4\cong H_4/H_2 \cong H_2/H_1 \cong \mathbb Z/2\mathbb Z$, so $G&gt;H_8\rhd H_4\rhd H_2\rhd H_1=\{e\}$. Only the factor $G/H_8 \cong \mathbb Z/p\mathbb Z$ is causing me a headache, because although its of prime order (and hence abelian) I don't know whether $H_8$ is normal in $G$ (unless $p=2$).  If $p\ne 2$, then the number $k$ of Sylow $2$-subgroups is $1$ mod $2$. Since $k$ divides $|G|$ we might have $k=1$ or $k=p$. If we had $k=1$ then $H_8$ would be the only Sylow $2$-subgroup (and hence normal in $G$). But how could we show this?  Or is there even an easier way to approach this problem?  $\ $  edit: I am going to try a different approach: The case $p=2$ is clear. When $p=3$ or $p=7$ the group has order 24 or 56 and since the smallest simple non-abelian group has order 60, the group must also be solvable in these exceptional cases (as Mariano pointed out).  In any other case we get a Sylow $p$-subgroup $H_p$ of order $p$, which is is normal in $G$. The quotient $G/H_p$ has order $8=2^3$; and prime power order implies solvable. So $G/H_p$ is solvable and $H_p$ is also solvable. And since the composition factors of $G$ are those of $H_p$ together with those of $G/H_p$, we conclude that $G$ is solvable iff $H_p$ and $G/H_p$ are solvable, which is the case. Hence $G$ is solvable if $|G|=8p$. "every" vs "each"? "There is a plethora..." or "There are a plethora..."? Is there a way to disable certain Windows 7 keyboard shortcuts?  Specifically, in this case, I want to disable Alt+Space and WinKey+Space. How fast is Earth moving through the universe? As the galaxy is moving and the solar system orbiting the galaxy and the Earth orbiting the sun. So how fast is each object moving and what is the fastest we move at?  Do we even know how fast the galaxy is moving that is not relative to another galaxy (although I guess velocity has to be measured relative to something). How to output string completions to stdout? I was making this recipe: , which was from the old Lincoln Del, one of my mom's favourite places. I mistakenly doubled the sugar, putting in 1/2 a cup instead of a 1/4 of a cup. Given the 2/3 of a cup ketchup, which was Heinz, the soup turned out way, way too sweet.   Is there any way I can rescue this? Shining a laser onto a mirror Theoretically, if I shined a laser at a mirror at an angle of 0 degrees so that the light was perfectly reflected back to the light source, then I should not be able to see the light because it is not reflected to my eyes.  | |  me | |============ laser | | |   However this is evidently not the case, as I am able to see the laser point on the mirror. Why is this the case? My initial assumption is that it is due to diffuse reflection on the imperfect mirror's surface, but I am not sure. Trouble enabling Cube surfer addon Every time I have tried to enable the Cube Surfer addon but this error message comes up. FYI I have the correct versions of everything.  I have had this problem with some other add ons as well. Sometimes it's when I have tried to click a button in an addon (after 'successfully' installing) Change password on root user and user account If I change the password for the root user is that going to automatically change the password for the user account?   I found this link for root:    How do I change the user account password? Why didn't the Ministry use Veritaserum to question criminals? The truth potion (Veritaserum) is one of the most powerful potions that forces the drinker to speak truth. Then why didn't Ministry used it in any criminal cases instead of long discussions and proceedings? I know there are antidotes to the potion (Dumbledore tells Harry in the 6th book , "Slughorn might have been carrying antidote to veritaserum ever since I asked him about the memory"), but why don't keep criminals in custody until the effect of the antidote wears out and then make them drink veritaserum. Won't that result in perfect judgement?