Adding huge packages into new projects (Eclipse)
Adding a reference between Eclipse Java projects
Change font of formula number in DisplayFormulaNumbered How do I parse a string to a float or int? In Python, how can I parse a numeric string like "545.2222" to its corresponding float value, 545.2222? Or parse the string "31" to an integer, 31?  I just want to know how to parse a float str to a float, and (separately) an int str to an int. Plural or singular verb for collective term Test for the convergence of the sequence $S_n =\frac1n \left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$ I am trying to show $$\lim_{n\rightarrow \infty} \int_{[0,1]^n} \frac{|x|}{\sqrt{n}}dx=\frac{1}{\sqrt{3}}$$ where $[0,1]^n$ is the unit cube in $\mathbb{R}^n$. I would appreciate any hint. How can I show that the sum   $$ \sum_{k = 0}^n 2^k \binom{n}{k}$$  is equal to $3^n$? Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$ I've been wrestling with this problem (available  ):  Evaluate the integral of $f(z) = \sqrt{z^2-1}$ around the circle $\{z: |z| = 2\}$, where the branch of the square root function is chosen so that $\sqrt{2^2-1} &gt; 0$.  I came up with the answer $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = \pi i$$ using the following argument, which seems a little like voodoo to me.  You notice that there are two points, at $z \pm 1$, where you might have to pick a branch of $log()$ to define the square root. Then, I convinced myself that as long as you exclude from your domain the real interval $-1 \le x \le 1$, the function $f(z)$ can be continuously defined (maybe the two branches somehow cancel?), and so is analytic on its domain.  Therefore you can shrink the contour of integration continuously using the Cauchy Closed Curve Integral Theorem, so that you wind up reducing it to the real integral $$2\int_{-1}^1 \sqrt{x^2-1} dx = \pi i$$  I'm not really sure the answer is correct, and I'm even less certain about the way I got it. I had a hard time convincing myself that $\sqrt{z^2-1}$ was not multi-valued on the domain. To try to get at that I tried $\sqrt{z^2-1} = \sqrt{z+1} \sqrt{z-1}$ and reasoned that the product makes the discontinuity disappear, using $$e^{\frac{\pi}{2}i}\cdot e^{\frac{\pi}{2}i} = -1 = e^{-\frac{\pi}{2}i}\cdot e^{-\frac{\pi}{2}i} $$ for the different branches of $log()$ you can choose.  I'd appreciate any input that would help me get a a better way to look at this.  Thanks!    EDIT  An attempt to use the Residue at infinity:  By substituting $z = 1/w$ you get \begin{eqnarray} \int\limits_{|z| = 2} \sqrt{z^2-1} dz &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1}{w^2}-1} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1-w^2}{w^2}} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^3}\sqrt{1-w^2} dw \end{eqnarray} The integrand is analytic in $|w| \le 1/2$ except at $w = 0$, so we can apply the Residue Theorem. Near $w = 0$, $\sqrt{1-w^2} = 1 - \frac{1}{2}w^2 + \dots$, so the residue of $\frac{1}{w^3}\sqrt{1-w^2} $ at $w = 0$ is $-\frac{1}{2}$. Then the integral is $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = 2\pi i \cdot (-1/2) = -\pi i$$ How to find the smallest $n$ such that $n^a\equiv 1 \pmod p$ Given a prime $p$ and number $a$, how do I find the smallest $n$ such that $n^a\equiv 1 \pmod p$? Is there a non trial-and-error method?  Edit: obviously removing $n=1$! I read news on the BBC (on its website) this morning. When I was reading the news I noticed the definite article the was missing in a sentence. As per my opinion, the reporter missed the article the. But I also thought that the reporter also had some point as he did not use the article there. So I just wanted to confirm so landed here to get some help on it.     On the website:      It also proclaimed the group's leader, XYZ  (name), as caliph and   "leader for Muslims everywhere".      As per my opinion it should have been:      It also proclaimed the group's leader, XYZ  (name), as the caliph and   "leader for Muslims everywhere".   Source link: Nautilus 3.6 doesn't have a status bar? In 12.04, Nautilus showed the amount of remaining space in the status bar , but as of 13.04 the status bar is gone.  gsettings set org.gnome.nautilus.window-state start-with-status-bar true   turned out "no such key".  Is there any way to bring back the status bar? how to run the dialog command with proccess Please look on my code – ( bash script )  I want to display both dialogs on the screen on the same time,   one dialog display the:  tail –f from - /var/log/proccess1.log  ,   and the second dialog display the:  tail –f from the file - /var/log/proccess2.log     but the sad fact is that I can display only one dialog and not both dialogs ( because when I run the first dialog , the second dialog will activate only if the first dialog will killed )   So I create process on the second dialog ( ….. ) &amp;    , in order to display both dialogs    But …. the second dialog create process number but not create the second dialog GUI , ( seems that when we create dialog with process , the process not send the dialog to standard output )  So how to  run the second dialog with process but send the dialog GUI to screen ? , or other solution in order to display both dialogs on screen  My code       #!/bin/bash       # this dialog will locate the tail box on the top of the screen      dialog --begin 15 10  --tailbox   /var/log/proccess1.log  13 125         # this dialog will locate the tail box down in the screen      ( dialog --begin 37 10  --tailbox   /var/log/proccess2.log    13 125 ) &amp; Content Assist for JSF2 + CDI (weld) beans + Eclipse Helios $$y'=x^2+y^2$$ I know, that this is a kind of Riccati equation, but is it possible to solve it with only simple methods? Thank you How to create two partitions? Is there a single word for a "friend of a friend"? I am looking for a word that I could use instead of "friend of a friend". On certain occasions, it happens that you may want to talk about a friend of a friend with someone else.   In such cases how would you refer to this friend? Why does observation collapse the wave function? In one of the first lectures on QM we are always taught about Young's experiment and how particles behave either as waves or as particles depending on whether or not they are being observed. I want to know what about observation causes this change? How can I create my own Action using Photoshop? Can anyone guide me with a simple example? A map $f:S^n\rightarrow S^n$ satisfying $f(x)=f(-x)$ for all $x\in S^n$ is said to be an even map. Show that if $f:S^n\rightarrow S^n$ is an even map, then $\deg f=0$ when $n$ is even and $\deg f$ is even when $n$ is odd. Moreover show that when $n$ is odd, there exist even maps of any given even degree.   My Try:  So $f=(-I)\circ f$. Then $\deg f=\deg (-I)\times \deg f$. If $n$ is even $\deg (-I)=-1$. Hence, $2\deg f=0$, so $\deg f=0$. But how do I show the results when $n$ is odd. No clue at all. This problem is in Hatchers book (A very complicated text). There is a hint but I do not understand it. Can somebody help me to proceed? Click Answer your own question Check community wiki A dialog box     Are you sure you want to make this post Community Wiki?   will appear, Click OK or Cancel; The same dialog will appear again.   Google Chrome 44.0.2403.107 / Windows8.1 / site rev 2015.7.25.3609 Capitalization of names that begin lowercased, at the beginning of a sentence