How can I show $U^{\bot \bot}\subseteq \overline{U}$?
Double orthogonal complement is equal to topological closure
Get a resource using getResource() How many ways can N elements be partitioned into subsets of size K? Mann-Whitney U test and K-S test with unequal sample sizes Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$ How to Hide sections of InfoPath form based on Group membership I need to Hide "Sections" of InfoPath form using SharePoint or AD group membership (either is fine). How can I achieve this?  InfoPath 2010 in SharePoint 2010 How to rename partitions? I'm new at Ubuntu; I installed Ubuntu 12.10 and the partitions appear like 30 GB volume and like 78EF-2C5E in task bar. I tried to rename it but rename and remove buttons are deactivated so I tried by using disks but it gives me error:  (Error setting label: Command-line `mlabel -i "/dev/sdb8" ::"windows"' exited with non-zero exit status 1: Total number of sectors (18550784) not a multiple of sectors per track (63)! Add mtools_skip_check=1 to your .mtoolsrc file to skip this test  (udisks-error-quark, 0))   and this happen also to any attached usb to my laptop. My wife and I are preparing to sell our home and are discovering some weird things. Our home was built in 1958, so it is older. We found this in a corner that had some furniture in front of it.   We are wondering    What kind of wiring is this?  Is it safe to handle or remove? What and where are the stack and heap? Short story set in the near future where all wars are settled on the moon using automated machines? Plot Details/Summary  Another one where I have only sketchy memories of the tale, I fear.   The setting for this one is the near future (from the writer's perspective, which I think was the 1970s).  Man's reached a point where bloodshed and loss of life are no longer necessary to settle conflicts.  Instead, all disputes are settled through an annual combat held on the surface of the moon, using the best combat machines each nation can come up with.  The protagonist, as I recall, is an engineer for the Americans.  He recollects past conflicts, and the circumstances for this years fracas.  Much of the combat is told from his observers' perspective.  The actual conflict is a rather clever affair, with a description of each team's designs and all the tricks and gee-whiz things they built into them.  The protagonist's team manages to prevail, when they managed to use an attack as a feint, with the real attack being a swarm of microscopic machines (they did not use the term nanites) that destroyed the opposing machine from the inside.  Timeframe/Other Details  I think this one dates from the 1970s.  I don't think it more recent, given my recollections of when I read it, and also the technology descriptions they used in it.  There is an outside chance that the combat is not between rival nations, but rival corporations.  That would change the premise of "man evolving beyond bloodshed", of course.  I think it's nations fighting, though.  I am almost 100% certain this was in a sci-fi magazine, not an anthology. Tool for straightening a bent metal bar of the gate? Someone's car hit our metal bar gate, so one of the rods is bent as shown in the photo. What kind of a tool can I use to bend this back, so it's straight? Thank you! From Berkeley Problems in Mathematics, Spring 1999, .  Let $f(x)\in \mathbb{Q}[x]$ be an irreducible polynomial of degree $n\ge 3$. Let $L$ be the splitting field of $f$, and let $\alpha\in L$ be a zero of $f$. Give that $[L:\mathbb{Q}]=n!$, prove that $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$.   (BELOW IS NONSENSE, SHOULD BE IGNORED)  Following Gerry Myerson's advice, since $L$ is the splitting field of $f$, $L$ must be Galois over $\mathbb{Q}$. Thus the Galois group for $[L:\mathbb{Q}]=S_{n}$. Gerry now asserts that either $\mathbb{Q}(\alpha^{4})$ is of degree 2 over rationals or it must be $\mathbb{Q}$. But assuming this one can rule out the case $\mathbb{Q}$, since this would imply $\alpha$ is the root of a 4th or 2nd degree polynomial over $\mathbb{Q}$. But we know $n\ge 3$. So $\alpha$ must be the root of a 4th degree polynomial. We know $S_{n}$ has normal subgroups $A_{n}$ when $n\not=4$ and $V,A_{4}$ when $n=4$. I do not know how to proceed any further.   Now assuming $\mathbb{Q}(\alpha^{4})$ is a degree 2 abelian extension over $\mathbb{Q}$. We should have a chain of normal extensions $\mathbb{Q}(\alpha)\supset \mathbb{Q}(\alpha^{2})\supset \mathbb{Q}$. This would imply $S_{n}$ has a normal subgroup which has a normal subgroup. But we know $A_{n}$ for $n\ge 5$ are simple. So the only possibility is $\mathbb{Q}(\alpha)$ has a Galois group isomorphic to $V$. In this case $n=4$ as well. I can only proceed to here. LaTeX figures side by side How to fix invisible form fields in Firefox while using Adwaita Dark Theme (or any other dark theme) I have this issue with some form fields in Firefox and using the adwaita-dark theme. In some webpages where the field background is white, you cannot read the text because it is also white.   This question was edited in order to clarify that this kind of wording of the question might help people who are not familiar with what a GTK+ theme. I also thing that the wording will help to get more hits through search engines. If it's still considered a duplicate, I'll accept it. Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$? I have the following question:  Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$?  Note: the symbol $\cong$ denotes a homeomorphism between topological spaces  What I think:  I think that in fact there is a homeomorphism between those spaces, because is possible to express the lexicographic order as union of vertical lines with open extremes, I mean this is a basis for the lexicographic order. If I consider the Identical function I have the homeomorphism. Am I right? What are the practical differences between Bash and Zsh? With the news that , I'm finding lots of results telling me about the switch, and that it may cause problems with shell scripts, but I'm not familiar enough with Zsh to know what those problems might be.  My shell scripts are really not that complicated, but I've only ever used Bash on macOS and Linux - zero experience with Zsh. Can anyone provide a simple practical comparison, or specific stumbling blocks I will need to know, so that I can start working towards being ready for the new shell when Catalina is released? How do I get current date/time on the Windows command line in a suitable format for usage in a file/folder name? Update: Now that it's 2016 I'd use PowerShell for this unless there's a really compelling backwards-compatible reason for it, particularly because of the regional settings issue with using date. See @npocmaka's     What's a Windows command line statement(s) I can use to get the current datetime in a format that I can put into a filename?  I want to have a .bat file that zips up a directory into an archive with the current date and time as part of the name, for example, Code_2008-10-14_2257.zip. Is there any easy way I can do this, independent of the regional settings of the machine?  I don't really mind about the date format, ideally it'd be yyyy-mm-dd, but anything simple is fine.  So far I've got this, which on my machine gives me Tue_10_14_2008_230050_91:  rem Get the datetime in a format that can go in a filename. set _my_datetime=%date%_%time% set _my_datetime=%_my_datetime: =_% set _my_datetime=%_my_datetime::=% set _my_datetime=%_my_datetime:/=_% set _my_datetime=%_my_datetime:.=_%  rem Now use the timestamp by in a new ZIP file name. "d:\Program Files\7-Zip\7z.exe" a -r Code_%_my_datetime%.zip Code   I can live with this, but it seems a bit clunky. Ideally it'd be briefer and have the format mentioned earlier.  I'm using Windows Server 2003 and Windows&nbsp;XP Professional. I don't want to install additional utilities to achieve this (although I realise there are some that will do nice date formatting). Run an exe from C# code Maximum Likelihood Estimate with different parameters Suppose that X and Y are independent Poisson distributed values with means $\theta$ and $2\theta$, respectively. Consider the combined estimator of $\theta$ $$ \tilde{\theta} = k_1 X + k_2 Y $$ where $k_1$ and $k_2$ are arbitrary constants.   Find the condition on $k_1$ and $k_2$ such that $\tilde{\theta}$ is an unbiased estimator of $\theta$. For $\tilde{\theta}$ unbiased, show that the variance of the estimator is minimized by taking $k_1 = 1/3$ and $k_2 = 1/3$. Given observations $x$ and $y$ find the maximum likelihood estimate of $\theta$ and hence show that $\tilde{\theta}$ is also the maximum likelihood estimator.   I have gotten (1) and (2) okay, but it's (3) I am having trouble with, I'd be okay if $X$ and $Y$ had the same parameter but I'm having trouble with $X$ and $Y$ having different parameters, any help would be appreciated.   NOTE   For (1) I got $k_1 = 1 - 2k_2$.   For (2) I found the variance of $\tilde{\theta}$, then differentiated and let equal to zero to minimize - therefore we get (after subbing in $k_2 = 1 - k_1/2 $) $$3k_1-1=0,$$ which when subbing in $1/3$, we see it is minimised.   Thank you. How can I disable the “News and Interests” Widget on the Windows 10 Taskbar? On Windows 10 version 1909 and newer releases, Microsoft has added a &quot;News and Interests&quot; widget on the Taskbar (see ):  How can I remove this Widget from the Taskbar? App crashes, dock icon remains, can't reboot, yet no process in ps aux to kill