In AWS EC2, I am using Centos 7, I observe strange behaviour where a binary for Hashicorp Vault CLI (/usr/local/bin/vault) is available during boot to commands I run in user data.  It is also available for users normally.  However, if I run sudo -i it is not available.  If I run sudo su - root, then it is available! Why would a command be available in user data as root, but not if I try to login as root using sudo -i?
When I run sudo, what exactly happens to my environment?  When I run sudo command, it doesn't seem to see my or root's environment. For example, my path for both includes /usr/local/bin, but if I try to run one of the program's without the full path, it fails.  I thought sudo ran as root, and hence got root`s environment. Is there a different way that bash executes under sudo than under root or my normal user?  EDIT:  I have been using sudo -i lately, but recently it has been causing problems because my current working directory gets set to /root. This is as expected (sorta), but I still don't understand why sudo isn't recognizing my executables in /usr/local/bin.  EDIT:  I am running Fedora 15.
Why is this sequence of equicontinuous functions uniformly bounded? Let $\left\{f_{n}\right\}$ be a sequence of equicontinuous functions where $f_n: [0,1] \rightarrow \mathbf{R}$.  If $\{f_n(0)\}$ is bounded, why is $\left\{f_{n}\right\}$ uniformly bounded? In Euclidean geometry texts, it is always mentioned that point is undefined, it can only be described. Consider the following definition: "A point is a mathematical object with no shape and size." I do not understand what is the problem with this definition. Please give the detailed reasons. Thanks in advance! One of the mysteries that my numerics class left me with are "stiff systems". Our prof didn't really manage to explain what they are. Now that the class (and the test) are over, I'm still curious.   The most concise definition about "stiff systems" I've found so far is: "There is no universally accepted definition of stiffness". So, if there is none, I don't expect one.   I'd be thankful about information on both of the following points:   From what kind of (real-world) problems do stiff systems arise? What's so "stiff" about them? What's the good thing - or the bad thing - that I'd worry about when I have to numerically solve such a real-world problem? Looking at the properties for a Windows file I get two attributes, “Size” and “Size on disk,”  and "Size on disk" is always larger.  What do these two metrics mean? $ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $, prove $ab + bc + ca \le 3$ If $a,b,c$ real numbers such that $$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $$,  prove that $ab + bc + ca \le 3$.     Attempt:  Assume that $a,b,c &gt; 0$.   $$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1  $$ $$ \implies  (a^{2} + b^{2} + 1)(b^{2}+c^{2}+1) + (a^{2} + b^{2} + 1)(a^{2}+c^{2}+1) +  (a^{2} + c^{2} + 1)(b^{2}+c^{2}+1) \ge (a^{2} + b^{2} + 1)(b^{2}+c^{2}+1)(c^{2} + a^{2} + 1)$$  $$ \implies  ((ab)^{2} + (ac)^{2} + (bc)^{2} + a^{2} + 2 b^{2} + c^{2} + b^{4} + 1) + ((ab)^{2} + (ac)^{2} + (bc)^{2} + b^{2} + 2 a^{2} + c^{2} + a^{4} + 1) + ((ab)^{2} + (ac)^{2} + (bc)^{2} + a^{2} + 2 c^{2} + b^{2} + c^{4} + 1) \ge (a^{2} + b^{2} + 1)(b^{2}+c^{2}+1)(c^{2} + a^{2} + 1)$$  $$ \implies  3((ab)^{2} + (ac)^{2} + (bc)^{2}) + 4(a^{2} + b^{2} + c^{2}) + (a^{4}+b^{4}+c^{4}) + 3  \ge (a^{2} + b^{2} + 1)(b^{2}+c^{2}+1)(c^{2} + a^{2} + 1)$$  Next, notice  $$(a^{2} + b^{2} + 1)(b^{2}+c^{2}+1)(c^{2} + a^{2} + 1) = ((ab)^{2} + (ac)^{2} + (bc)^{2} + a^{2} + 2 b^{2} + c^{2} + b^{4} + 1)(c^{2} + a^{2} + 1) $$ $$ = (abc)^{2} + a^{2}c^{4} + b^{2}c^{4} + (ac)^{2} + 2(bc)^{2} + c^{4} + b^{4}c^{2} + c^{2} + a^{4} b^{2} + a^{4}c^{2} + (abc)^{2} + a^{4}  + 2(ab)^{2} + (ac)^{2} + b^{4}a^{2} + a^{2} +  (ab)^{2} + (ac)^{2} + (bc)^{2} + a^{2} + 2 b^{2} + c^{2} + b^{4} + 1 $$ $$ = 2(abc)^{2} + 3(ac)^{2} + 3(bc)^{2} + 3(ab)^{2} + c^{4}a^{2} + c^{4} b^{2} + b^{4}a^{2} + b^{4} c^{2} + a^{4}b^{2} + a^{4} c^{2} + a^{4} + b^{4} + c^{4} + 2(a^{2} + b^{2} + c^{2}) + 1  $$  So we have  $$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $$ $$ \implies  2(a^{2} + b^{2} + c^{2}) +  3  \ge 2(abc)^{2}  + c^{4}a^{2} + c^{4} b^{2} + b^{4}a^{2} + b^{4} c^{2} + a^{4}b^{2} + a^{4} c^{2} + 1 $$ Are shell scripts sensitive to encoding and line endings? Renaming user name I made a mistake in the username at the time of installation. So I changed the name of the user after logging in by creating a guest account with SUDO rights. But when I checked the list of users using ls /home command I am not seeing the new name for the user instead Old name is appearing. But I use the new name to login.   Is it like I need to change the name inside Home directory separately? Also , if there is any other changes needs to be done .. ? How do I efficiently filter computed values within a Python list comprehension? The Python list comprehension syntax makes it easy to filter values within a comprehension.  For example:  result = [x**2 for x in mylist if type(x) is int]   Will return a list of the squares of integers in mylist.  However, what if the test involves some (costly) computation and you want to filter on the result?  One option is:  result = [expensive(x) for x in mylist if expensive(x)]   This will result in a list of non-"false" expensive(x) values, however expensive() is called twice for each x.  Is there a comprehension syntax that allows you to do this test while only calling expensive once per x? Assume that $M$ and $N$ are two finitely generated $R$-modules. Then $\operatorname{Hom}_{R}(M,N)$ is a finitely generated $\mathbb Z$-module and/or $R$-module (in this case, assume that $R$ is commutative)?   Note that $R$ is not Noetherian ring. Is there any counterexample (for any cases)? Generic htaccess redirect www to non-www I would like to redirect www.example.com to example.com. The following htaccess code makes this happen:  RewriteCond %{HTTP_HOST} ^www\.example\.com [NC] RewriteRule ^(.*)$ http://example.com/$1 [L,R=301]   But, is there a way to do this in a generic fashion without hardcoding the domain name? How to completely remove desktop? I wanted to switch to Xfce (I had KDE and GNOME installed), and I did this :    sudo apt-get install xubuntu-desktop sudo apt-get remove kubuntu-desktop sudo apt-get remove ubuntu-desktop sudo apt-get autoremove   but to my surprise, I could still pick gnome, kde plasma, etc during the log in.  So, how do I completely remove KDE and GNOME desktops? I have a fairly modern desktop computer, an AMD Athlon II X2 based silent PC, that does not work.  When turned on, it will start physically (all fans are rotating, disks start up...) but not give a signal on any of the graphics ports (DVI, VGA, and HDMI, I tried all three). Also, the reset button does not seem to have any effect.  I have stripped the mainboard bare of all SATA connections, extension cards, and the one 2GB RAM chip to eliminate them as the problem source, but to no avail, so I think it's fair to assume it's either the mainboard or the processor that are at fault.  However, I have neither a replacement mainboard, nor a replacement processor handy to identify which one is broken. The cause of the defect is unknown, so for all I know, it could be both. Therefore, I'm reluctant to buy replacement hardware blindly before knowing more.   Is there any way to further diagnose (or at least get some indication) which component is broken without buying replacement hardware? Pluralizing abbreviations where the noun is not the last word Calculating the number of possible paths through some squares I'm prepping for the GRE.  Would appreciate if someone could explain the right way to solve this problem. It seems simple to me but the site where I found this problem says I'm wrong but doesn't explain their answer. So here is the problem verbatim:    Find the number of paths from x to y moving only right (R) or down (D).  My answer is 6. What am I missing??  Thanks for any help. Why was Gotham City changed from a mostly fictional city to New York City in the Nolan trilogy? In Batman Begins, Gotham City has a futuristic/fictional and run down look: think of Oldtown, the trains built by the Wayne Corporation etc.   In The Dark Knight Rises, Gotham City looks like plain old real world New York City — we don't see the trains anymore. Oldtown is just a standard poor neighborhood. Lots of the locations used in the movie are easily identified as real world NYC locations: the stock exchange or East River bridges for example.   My question is: Why did Nolan change Gotham city from a shady fictional more cartoon-like town to plain old NYC?   Edit: The examples from Batman Begins and The Dark Knight Rises were just for illustration; I didn't intend to limit the question to those two movies.  Edit 2: I specifically want to know why Gotham City was changed from a cartoon-like city in Begins to an almost real-world NYC in The Dark Knight Rises (via not so cartoon-like but not yet real-world like Chicago in The Dark Knight Rises). Why it's NYC or Chicago is not so important for me. But why, e.g., were the trains which featured prominently in Begins gone in The Dark Knight Rises? There was only a very short in-universe time-span between the events of the two movies, yet Gotham changed drastically. Where can I find 32-bit version of Ubuntu? I need to find the 32-bit version, and all I keep finding is the 64-bit. Can anyone provide me with a link? Combining two expressions (Expression>) We have two sequences , $(a_i)_{i=1}^{2n}$ and $(b_i)_{i=1}^{2n}$ such that  $1\leq a_i, b_i\leq n$ for every $i$.  Show that there are two sets of indexes $I, J \subseteq \left \{ 1,2, ... 2n \right \}$ such what $\sum_{i\in I}a_i=\sum_{j\in J}b_j$.  Well, the question didn't say anything about those sets being empty but I believe that's not what they meant. I don't know that to do with questions like these. There are obviously much more subsets that possible sums ($2^{2n}-1$ compared to $2n^2$) but it doesn't really help.  I'd be glad to hear ideas, hints or solutions. Can I get back my saved data? Height/Radius ratio for maximum volume cylinder of given surface area