Is the expansion accelerating or decelerating?
Dark Energy / Accelerating universe: naive question
Can I run OSX applications? Context: I prepare my scientific documents using LaTeX and compile to a PDF. I often need to seek comments on drafts from collaborators who do not use LaTeX. Most of these collaborators use Windows OS. Assume also that the collaborator does not need to edit the document.  They only need to be able to add comments to the document. Most would be familiar with the commenting system in MS Word, for example. I'd like to be able to give the collaborator some clear instructions about what software and system they should use to comment on the draft.  This should involve free software and an easy to use interface.  Question: What is a good strategy for getting comments on draft documents when the collaborator does not know LaTeX?  Initial thoughts: I know Adobe professional allows you to add comments to a PDF.  However, some collaborators don't have this software and it costs money.  I could send the raw LaTeX to the collaborator. However, given all the markup, the collaborator may find LaTeX source a bit mysterious.  UPDATE: After posting I noticed  to a similar question. Along with a number of other good tips (such as printing and getting paper comments), he mentions jarnal, xournal, and gournal as free cross-platform PDF annotators. I'd be curious to know whether experts have found them adequate for the above mentioned purpose and whether any of them are to be preferred. Others mention FoXIt. And yet others discuss the option of exporting to MS Word or Open Office and using the reviewing system within these programs. Can i prevent/restrict standard user from installing/uninstalling software in Ubuntu 12.04 desktop? I'm trying to solve the following equation:  $$x^3-y^3=xy+61$$  I got:  $$(x-y)(x^2+xy+y^2)=xy+61$$  But I can't go any further. I am looking for a solution in integers.  I need some hints to proceed, please! In Dummit and Foote, Exercise 15.18 (p. 727 3rd edition) one is asked to prove that for a commutative ring with unity $R$, and $f$ a non-nilpotent element of $R$, that the localization $R_f$ is isomorphic to $R[x]/(xf - 1)$.  I have done this, using the strategy outlined in the problem, using the universal property of $R_f$ proved in Theorem 36. The problem I have is this:  If $R_f \cong R[x]/(xf - 1)$ and $\phi:R[x] \to R_f$ is a surjective homomorphism, it stands to reason that $\text{ker}(\phi)$ should be $(xf - 1)$. I cannot show this directly. The surjective homomorphism I have in mind is, for:  $p(x) = a_0 + a_1x + \cdots + a_mx^m$  $\phi(p) = \dfrac{a_0}{1} + \dfrac{a_1}{f} + \cdots + \dfrac{a_m}{f^m}$  It is clear to me that $\phi$ annihilates $(xf - 1)$, so that ideal is contained in the kernel. What I cannot show is the other containment, or equivalently:  If $\phi(g) = 0_{R_f}$ then $g(x) \in (xf - 1)$. The trouble I am running into is that $R$ might be a "bad" ring, containing a lot of zero-divisors, $f$ might even be a zero-divisor (being non-nilpotent is a considerably weaker property), so the usual polynomial tricks of the division algorithm or using the irreducibility of $xf - 1$ aren't much use, here.  I feel I am missing something obvious....what is it? What is the maximum RAM supported by the desktop and server editions? I have just downloaded "ubuntu-14.04.1-desktop-amd64.iso" and "ubuntu-14.04.1-server-amd64.iso" through "".   Please can someone confirm the maximum RAM that is supported.  According to many sites, Maximum RAM supported by the OS  ubuntu-14.04.1-desktop : " 2^64 bytes " -- Kindly confirm  ubuntu-14.04.1-server : " 2^64 bytes " -- Kindly confirm I'm trying to use Python to place a camera. I know the camera's location, and the forward and up vectors for the camera (i.e. the direction it's pointing and its orientation). How do I do this?  I know that it's possible to calculate a raw world matrix from the above information, which I can then apply to the camera, but I was rather hoping not to have to. Is there an easier way? Cannot find Background Images feature to add in a photo in Blender 2.8  Where is it? How do I install Ubuntu to a USB key? (without using Startup Disk Creator) If you are hurrying to reply, System → Administration → StartUp Disk Creator -- no, that's not what I'm talking about.   I want to try Ubuntu 11.04's Unity without touching my existing Ubuntu install.  To do this, I need to install the nVidia drivers first (sigh).  To do this, I need changes to persist a reboot.  To do this, I need to really install Ubuntu on a USB key.  How do you do that?    What I tried   I tried to make a USB key from , then boot from it, then choose "Install Ubuntu." The installer refused to install to the installation media itself. I tried, from my installed copy of Ubuntu:  sudo kvm /dev/sdb --cdrom .cache/testdrive/iso/ubuntu_natty-desktop-i386.iso   ...but the installer didn't detect the disk properly. After my lie down, I posted  on SO. As I suspected would happen, it got moved to programmers. Unfortunately, the kind of people I'm interested in getting answers from (litb,skeet et al - the top SO programmers in their respective disciplines) don't frequent Programmers much. So my question is, where to ask somewhat non-specific questions of high-powered users? I am trying to show that: \begin{equation} \frac{n}{\phi(n)} = \sum_{d \mid n} \frac{\mu^2(d)}{\phi(d)} \end{equation} where $\phi(n)$ is  and $\mu$ is the .  The identity clearly holds for $n=1$, so if we write $n=p_1^{a_1} \cdots p_k^{a_k}$ for the prime decomposition of $n$, the left-hand side becomes: \begin{eqnarray*} \frac{n}{\phi(n)} &amp; = &amp; \frac{p_1^{a_1} \cdots p_k^{a_k}}{\phi(p_1^{a_1}) \cdots \phi(p_k^{a_k})} \\ &amp; = &amp; \frac{p_1^{a_1} \cdots p_k^{a_k}}{(p_1^{a_1-1})(p_1-1) \cdots (p_k^{a_k})(p_k-1)} \\ &amp; = &amp; \frac{p_1 \cdots p_k}{(p_1-1)\cdots (p_k-1)} \end{eqnarray*}   Whereas the right-hand side becomes:  \begin{eqnarray*} \sum_{d \mid n} \frac{\mu^2(d)}{\phi(d)} &amp; = &amp; \sum_{\substack{d \mid n \\ p^2 \nmid d}} \frac{1}{\phi(d)} \\ &amp; = &amp; 1 + \frac{1}{\phi(p_1)} + \dots + \frac{1}{\phi(p_k)} + \frac{1}{\phi(p_1 p_2)} + \dots + \frac{1}{\phi(p_{k-1}p_k)} \\ &amp; + &amp; \dots + \frac{1}{\phi(p_1 \cdots p_k)} \\ &amp; = &amp; 1 + \frac{1}{p_1 - 1} + \dots + \frac{1}{p_k - 1} + \frac{1}{(p_1 - 1)(p_2 - 1)} + \dots + \frac{1}{(p_{k-1}-1)(p_k-1)} \\ &amp; + &amp; \dots + \frac{1}{(p_1 - 1) \cdots (p_k - 1)} \end{eqnarray*}  I am unsure of how to proceed from this point however. Any help would be much appreciated. What makes some laser beams visible and other laser beams invisible? Don't know what could it be but my daughter keeps on crying every night. She's sleeping and suddenly she starts crying. Hungry ? (She drinks her last bottle of milk around 8pm.) Maybe teething? (every night, don't think so) Miss being in mommy's and daddy's bed? (she cries even if she's in our bed) I'm out of ideas, and we are kind of exhausted! Any ideas what might be the reason for her to cry every night? Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed? I'd like to determine the function corresponding to the following power series: $$x + \sum_{n=1}^\infty (-1)^n\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n} \frac{x^{2n+1}}{2n+1}, $$ where $|x|&lt;1$. ModelBuilder not adding output feature class to Table of Contents? I'm trying to create a tool in ModelBuilder that will take a new point from a user, create a feature class for this point and display it on a map.  What I've done is:   I've created a feature class for a point-like feature in ArcCatalog. I've prepared a really simple model in ModelBuilder, that starts with a feature set variable (which takes the feature class as a schema and symbology file). The variable is marked as a parameter. Next I'm using the Copy Features tool that takes the variable as input and saves it as a feature class in my scratch workspace. The output feature class is marked as a parameter with the 'add to display' option.   After the module is run I get a shapefile in my scratch workspace. I can add it manually to TOC and it contains the selected point. However no matter what I do, I can't display it in TOC automatically after the model completes.  There is a known issue described in several places that doesn't allow to display newly created layers in TOC when model finishes with the 'add to display' option. However there's a quick workaround, which is to mark the output layer as parameter. In my case it doesn't work.  I'm using ArcGIS for Desktop 10.1 on Windows 7 x86_64. What should happen if a logo I made is similar to another? Note: This is a canonical post created so that we can close the many similar questions as duplicates as discussed in .   We have created a logo for a client and they love it. We've already started preparing the materials that will feature the new logo.   However, after we had created the logo, we found a logo for another company that looks eerily similar. We did not intentionally create the new logo to look like the one of the other company, in fact we didn't even know it existed beforehand, but it does regardless.  What should we do? Is this plagiarism? Can our client use the logo we have created? Should they? Or do we need to come up with another logo that's more different? How to set up a wi-fi hotspot with an Ubuntu laptop (access point mode)? I've read , and carefully followed the instructions provided. I am sure the wireless card in my laptop supports going into wireless access point mode. But unfortunately, when I use the following command to start hostapd service it throws an error:   $ sudo service hostapd stop  Starting advanced IEEE 802.11 management hostapd                      [fail]    The instructions mentioned above said this could possibly be because my wireless card does not support the g mode, and provided the wiki of hostapd. But what is g mode? I tried to switch to a, or b mode, but it just didn't work.  Can anyone help with this or recommend a tool like connectify in windows ?  ps. I am using Ubuntu 12.04, 32 bit. I have an ADSL wired network, and I want to share it by setting my laptop into a WiFi hotspot with  my windows phone. What is the order when doing $x^{y^z}$ and why? Does $x^{y^z}$ equal $x^{(y^z)}$? If so, why?   Why not simply apply the order of the operation from left to right? Meaning $x^{y^z}$ equals $(x^y)^z$?  I always get confused with this and I don't understand the underlying rule. Any help would be appreciated! Best way to put commas into large numbers I've started a new job and it involves looking at a bunch of big numbers. Is there an easy way to add commas to an int or decimal field to make it readable?  For example, SQL Server outputs the column on the left, but for my own sanity, I need it to look like the one on the right:  2036150 -&gt; 2,036,150     ...or would I have to write some heinous   left(right(vandalized_data),6),3) + ',' + right(left(vandalized_data),6),3)   function?  The perfect thing would be commas in the display grid, then plain integers in the output.