What is `${1- hour}`?
Variable with colon dash ${VAR:-}
Does the artificer's Enhanced Weapon stack on top of hexblade's Improved Pact Blade? ATI Radeon HD 7770 no GPU rendering? How do the definitions of "irreducible" and "prime" elements differ? Can I install any iOS version I wish by picking and choosing which firmware to restore? Novel about a dragon lord who has to wear gloves at all times Universe being flat and why we can't see or access the space "behind" our universe plane? I'm a layman, but i watched some intereting videos about big bang on youtube[michio kaku, hawking this kind of things, not some crackpots :)]   I described everything on my picture:     So is there any possibility to see that inner side, for example, by creating wormhole, or entering new dimension? Or i get something wrong, on the way, and my model is totally wrong?  And another question. I heard that even if you would fly a ship across the universe you would eventually end in the place where you started, because we live in a 3d space that is defined on a surface of big sphere. But why a big sphere? Universe might be a big mobius strip, and the same principle of ending at start will apply. Is it possible?  Thanks in advance, and please don't bash me for silly questions. Im just curious, but i don't have any degree in physics. Im also not an english native speaker. I haven't been able to do this exercise:     Let $f: A \rightarrow B$ be any function. $f^{-1}(X)$ is the inverse   image of $X$. Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$ where $X \subseteq B$.   Since $X \subseteq B$, all the elements in $X$ belong to the codomain of $f$.  Since $f$ is surjective, it means that all elements in the codomain $B$ have some preimage in $A$. Given that $X \subseteq B$, all elements in $X$ must also have a preimage in $A$.  Have $\triangle = f^{-1}(X)$, $\triangle$ is now a set containing the preimages of the elements in $X$. Because of this, $\triangle \subseteq A$.  If we evaluate $f(\triangle)$, we...... nope, I don't know what I'm doing now.    What do you think? How to "flatten" a multi-dimensional array to simple one in PHP? Set same icon for all my Forms Is there any way to set the same icon to all my forms without having to change one by one? Something like when you setup GlobalAssemblyInfo for all your projects inside your solution. How can I change the color of a part of a TextView? How do I calculate areas of an area shapefile in square meters (m²) or in acres (ha)? I didn't find that functionality in the Vector Tools. Has anyone successfully deleted the Windows Installer files successfully before? They are taking up 35.1% of my total hard drive space.  Which ones are needed and which ones can be purged?  In order to see this folder, I had to unhide system files by going to Windows Explorer > Organize (dropdown) > Folder and Search Options > view tab > uncheck ==> Hide protected operating system files (Recommended).  I used WinDirStat program to get these percentages. To see the image in full size, open it in a new tab.  I was told by someone that you should not delete these files, but then I found a utility--Windows Installer CleanUp Utility (very old version) that deleted these.  But it doesn't run on Windows 7.  If anyone has a later version that they found works, please let me know the path. I'm one of very few people at my company who does graphic work, and I do quite a lot of it. Headquarters doesn't quite get that graphics work requires different hardware than, for example, sales work, which is pretty much email/Excel/Powerpoint/web browser and that's it. So they give everybody the same low-end rental PCs to work on.  This was tolerable when we were all on XP.  Recently I got "upgraded" to a new computer, which happens every two years or so as leases expire. The catch: the new PC had the same Core 2 Duo processor that the previous one did, less RAM, it runs Windows 7 instead of XP, and all the Creative Suite applications have been upgraded from CS3 to CS5! I am the first in my office to get 7.  So now I am in a situation where I have the slowest machine in the office, yet I have to do the most demanding work. I got them to OK 2 more gigabytes of RAM, and I hoped that would solve the issues, but it just isn't helping that much at all. I actually have to reboot every day after lunch because the machine stops responding after wake if you leave it asleep for too long.  I am currently talking to Information Systems to see if I can get a capable machine, but it does not bode well for me. Can anyone share any performance optimizations for Win7 that I might be able to use?  Thank you very much in advance! SS A Hilbert space is, by definition, a complete inner product space. If $(V,|.|)$ is finite dimensional inner product space of dimension $n$ then it is (topologically) isomorphic to $\mathbb{R}^n$ which is of course complete. My instinct here is to say "and therefore, $V$ is also a Hilbert space". I'm not sure about this step however since completeness depends on the norm and the norm depends on the selected inner product (assuming the induced norm $||x|| = (x | x)^{1/2}$ is used). So, must we place some condition on the inner product or is the topological isomorphism between $\mathbb{R}^n$ enough to guarantee that V is Hilbert? I understand the reasoning behind the fairly narrow textwidth in a default LaTeX article. 60-80 characters per line and all that. However, I am preparing a document that features many lengthy equations, and it seems silly to me to restrict the equations to fit into the same margins as the text when there's all that whitespace going unused on either side.  I'd like to have equations which are wider than the textwidth do the obvious thing, that is, continue to be centered on the page just like all the other equations, and simply extend into both the left and right margin equally. My equations are unnumbered, so there's no concern about where to put equation numbers.  How might I go about implementing this? What are the different ways that a message can be displayed to a bash shell after a user logs in? I have a CentOS 5.7 VPS using bash as its shell that displays a branded greeting immediately after logging in via SSH. I've been trying to modify it, but can't seem to find where it is in the usual places. So far I've looked in the motd file and checked sshd_config for banner file settings. A banner file is not set.  Where else can I look for where the login message might be? Why do we have more male infants born? Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$? Basically does a vector set that is linearly independent in $R^n$ automatically span $R^n$?  My initial thought is yes, but is there some counterexample that can disprove this? I updated the image in my Gravatar but my old picture still shows up.  Is this a cache issue?  Do I need to log out and then log back in? Anonymous user feedback now in testing Anonymous and unregistered users with &lt; 15 reputation (the amount required to earn the upvote privilege) will now see       feedback   on every post in the area that a logged in user would see "add comment":    When the post area is moused over, the area expands to:     Was this post useful to you? [Yes] [No]     once clicked it will say     sending feedback...   and eventually     Thank you for your feedback.   The goal is to offer the 90% of our traffic that is anonymous users a way to provide more meaningful feedback on posts rather than passively incrementing a view counter.  This click data is currently being evaluated to see what we can do with it. Ideas welcome!