If the set of test function corresponding to the kernel of distribution f coincides with the kernel of distribution g, then the distribution f is a constant multiple of g.
I would like some help with this exercise.  Suppose that $f_1,\ f_2 \in V^*$ and that $\text{Ker} f_1 = \text{Ker} f_2$. Show that $f_1 = k f_2$ for some scalar $k$.  I expect your suggestions.  Thanks!
I saw this movie a while back. I don't remember how it starts, but from where I remember watching it, it may have not been too far from the start. Apparently, Earth has been conquered by some alien empire or something and humanity are basically cavemen being used as slaves. From what I remember, the main antagonist alien is seen taking one of the slaves to a room where a machine is used on him to make him smart; this is apparently a big no-no so the main antagonist and his sidekick have to keep it quiet. The idea was that by making one of the slaves smart, it could increase the work output of the others. Apparently the antagonist is using the slaves on Earth to gather gold bullion  which is apparently still very valuable to the aliens but he's doing it illegally (not the slave labor; that's apparently ok). The protagonist who had the machine used on him becomes the intermediary between the slaves and the aliens and begins teaching the other slaves. I remember him teaching them mathematics and I remember him saying that it was universally accepted (I think he may have been referring to algebra or trigonometry). At some point he becomes aware that they are slaves and organizes a plan to free not only his fellow slaves but the Earth. Some escape and find an old museum which has old flight simulators, and shows that humanity wasn't always a slave race and that it may have been modern times in which Earth was invaded (i.e. no lasers or starships). I think they also find Fort Knox as there is a huge collection of gold bricks and weapons. The protagonist comes up with a plan to destroy some sort of teleporter the aliens use to transport stuff to and from Earth, however that alone wont be enough as they could fight back, which will be bad for humanity, which is still undeveloped. So the plan also includes using the teleporter before destroying it to to transport and detonate a nuclear warhead on the alien home world which apparently cripples any attempt to immediately send a fleet but also as a show of strength. After executing their plan, the main antagonist is captured by the humans and as an insult is locked in a cage surrounded by the gold he sought. If I recall correctly the place is set to detonate as to destroy the precocious gold and that will be used against the aliens should they mobilize a fleet in the future (i.e. attack us and we destroy Earth's supply of gold). The antagonist's side kick for some reason I remember as a big black man from whom the antagonist had removed his hand at some point and also apparently the antagonist was cruel to him. After the antagonist is locked up, he is trying to appeal to his sidekick's loyalty, however the sidekick takes the humans' side, I'm also getting an image that apart from treating him kindly the sidekick's missing hand was restored. Getting MAC Address I need a cross platform method of determining the MAC address of a computer at run time.  For windows the 'wmi' module can be used and the only method under Linux I could find was to run ifconfig and run a regex across its output.  I don't like using a package that only works on one OS, and parsing the output of another program doesn't seem very elegant not to mention error prone.   Does anyone know a cross platform method (windows and linux) method to get the MAC address?    If not, does anyone know any more elegant methods then those I listed above? Where to find my Favorites in Google Chrome? Draw a vertical line over the entries of a column in an array The bevel depth (the radius of the tube) is set to 9cm but it actually isn't when compared to the background grid. This is is confirmed by importing it into sketchup and scaling it to the proper units it turns out the radius is only around 2.286cm. This problem only shows up on certain projects. What's wrong and how do I fix it?  (sorry that I can't upload the file, it's a long story) I got my dad a Logitech LS21 system for Christmas. It's a 2.1 system, but it's recognized in Windows 8 as a 2.0 system (it says there is no subwoofer connected).    How would I go about getting the sub recognized?  It plays some sound now, but it's so quiet you can't hear it without putting your ear right next to it. In an integral domain every non-zero prime ideal is invertible implies every non-zero proper ideal is invertible. Why is $1 in a function not printing the script's first argument? Why doesn't echo $1 print $1 in this simple bash script?    #!/bin/bash # function.sh print_something () { echo $1 } print_something  $ ./function.sh 123  -&gt; why doesn't it print '123' as a result? How Do I Allow A Standard User to Install Programs? Yes, I realize that defeats the purpose of standard user. But here is the situation. A friend of mine wants to set up time limits for his home schooled son, and his son needs to be a standard user in order to use Family Safety. But at the same time, his son (who I personally think is way too old to have time limits), needs to be able to update and install some of his games on his computer. So I guess it's just sort of "light" parental control (just something to help him focus and not get distracted with hours of gaming).  It is the basic version of Windows 8.1, so there is no Group Policy editor (gpedit.msc). However, I'm fairly good with computers and I figured out how to install it. But it doesn't have a lot of the features that the "real" gpedit seems to have. Here is an example of what is in my gpedit: UK visit visa: What documents prove genuine relationship with the visitor? Could gravity accelerate light? Display the full URL of the home page? Is it possible to display the full, absolute URL of the home page in Drupal 7, like  www.example.com/The-best-example-possible ?  I'd like to display the full URL of the home page, not just the hostname. I accidentally posted a question without being logged in. Is there a way to associate that question with my account?   For more information, visit &quot;&quot; in the .   a.k.a. How can you link a registered account to a cookie-based account? a.k.a. How do I merge an unregistered account with a registered account a.k.a. Merging users a.k.a. How do I associate anonymous questions I’ve asked with my registered account? a.k.a. Is there a way to claim an unregistered user? (in case anyone searches with those terms) Understanding central limit theorem What is wrong with the following sentence:      The Central Limit Theorem  implies that, as the sample size grows, the error distribution approaches normality.   Am I correct by saying that it should in stead state the MEAN of the sample error approaches zero as sample size grows? Isomorphism between complex numbers minus zero and unit circle How do we show that $\mathbb{C}^{\times}$ and $S^{1}$ are isomorphic as groups? How is Starkiller Base's beam visible from Takodana in The Force Awakens? On Takodana,      the main characters and various bar patrons can see the planet Hosnian Prime being destroyed by Starkiller Base with their (respective) naked eyes. How did they see this? Is the Hosnian system close enough to see? If it's not very close and they could just see the explosion, how did the light from it reach them so quickly? dd aplied to dev USB before connect corrupt /dev/sdX and dont work Very basic question: how do I write a short literal in C++?  I know the following:   2 is an int 2U is an unsigned int 2L is a long 2LL is a long long 2.0f is a float 2.0 is a double '\2' is a char.   But how would I write a short literal?  I tried 2S but that gives a compiler warning. URLs: Should I use hyphens, underscores or plus symbols? Which is better for search engines?   example.com/my_cool_page.html example.com/my-cool-page.html  example.com/my+cool+page.html In an Econometrics - Time Series textbook (Hamilton), I saw the claim, without proof: Consider the sequence $ \psi_j $, then, for $ x &gt; j $, $ \frac1j &gt; \frac1x $, and therefore: $$  \frac1j &gt; \int_{j}^{j+1} \frac1x dx $$ for $x$ &gt; $j$. When I plug in numbers for $j$, I see that this is indeed satisfied. But I'd like to know the intuition behind this or a proof.