If two linear functionals are such that the kernel of one is contained in the kernel of the other, then they are proportional
$\ker T\subset \ker S\Rightarrow S=rT$ when $S$ and $T$ are linear functionals
Print lines between (and excluding) two patterns I'm going to submit form using cURL, where some of the contents is come from other file, selected using sed  If param1 is line matching pattern from other file using sed, below command will works fine:  curl -d param1="$(sed -n '/matchpattern/p' file.txt)" -d param2=value2 http://example.com/submit   Now, go to the problem. I want show only text between 2 matching pattern excluding the matching pattern itself.  Lets say file.txt contains:  Bla bla bla firstmatch It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout. secondmatch The point of using Lorem Ipsum is that it has a more-or-less normal distribution of letters, as opposed to using 'Content here, content here', making it look like readable English.   Currently, lots of "beetween 2 matching pattern" sed command won't remove firstmatch and secondmatch.  I want the result to become:  It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout. How to pad zeroes to a string? Access user fields? $account = \Drupal::currentUser() loads the user object into $account, but how do I access custom fields I've created on the user object (via the admin UI)?  With dpm($account) I can't see any of my custom fields. Entire function bounded by a polynomial is a polynomial Suppose that an entire function $f(z)$ satisfies $\left|f(z)\right|\leq k\left|z\right|^n$ for sufficiently large $\left|z\right|$, where $n\in\mathbb{Z^+}$ and $k&gt;0$ is constant. Show that $f$ is a polynomial of degree at most $n$. Book series with college students finding a way to open portals to other planets I got the storyline of this book series (I believe it was a series) told to me by a colleague at a former workplace but I can't remember the name of the author or of any of the books in the series. The first book is about a couple of college students who find a way to relatively easily open portals to pretty much wherever they want to go. One day, NASA(?) finally succeeds in sending astronauts to Mars(?). When they have just left the spaceship, one of them suddenly gets a tap on the shoulder, and when he/she turns around, these college students stand there in their homemade space suits, chuckling. I believe these students later also start a company that helps other organizations establish themselves on other planets, or perhaps even &quot;conquers&quot; and sells planets to other organizations. A later book in the series also describes a system that lets people upload their minds to the cloud. Some people choose to live solely in the cloud as virtual creatures, only deciding to &quot;descend&quot; into a &quot;flesh&quot; body when they need to perform some task that requires them to be in physical form. Some people also choose to live in physical form but as several entities, or clones, and sync their mind between the clones through this system, basically allowing them to, for example, run a one-man company with several &quot;instances&quot; of the same human who all share their knowledge and all know exactly what all other clones know in the same moment, effectively creating a super-efficient team of workers. Creating or referencing variables dynamically in Sass If two gravitational waves came in contact with each other what would happen? In another question entirely, what happens when a higher gravitational field interacts with a weaker one. What is the term for replacing a name or brand with a funny pejorative / sardonicism? What is the term for when one replaces a well-known name [(Proper) noun, company, brand, etc.] with one that tries to be funny yet pejoratively descriptive, different but similar enough that one's audience can likely understand the replacement?  For example: Whole Foods ===> Whole Paycheck; Comcast ==> Scumcast; Starbucks ==> Charbucks; Kinko's == Stinko's; eBay ==> Evil Bay  I tend to use sobriquet don't believe this explicitly implies funny as well as insulting. Moniker again is close but not specific to the above description.  There is a similar question which proposes tortonym and malapropsim, but it does not seem to settle the argument definitively:   Another answer here proposes dysphemism, but to me it isn't a full fit:  because it doesn't cover the humor aspect. Could someone please explain the role of the transistor in this circuit? I have a feeling it has to do with the LC circuit but I'm not sure and don't understand completely. The following is an image of the circuit (the transistor is n-type. It is used in lots of sensors to detect and generate ultrasonic waves. Compute $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$ Compute   $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$ Programmatically create a user and assign a role Cartoon with a young unicorn and a demon In the late 80s or early 90s I remember watching an animated series that followed a young unicorn and a demon.   In one episode the unicorn gave the demon his horn, and the unicorn almost died.   In another episode there was a man who was able to turn people into human shaped building blocks and built a huge tower from them.   Those are the two scenes I remember with any clarity.   Does anyone have any idea? Is it possible to redirect a command's output to cd? For example, I searched for a directory using locate and got the path to it. Now, instead of writing a cd path, can I redirect the locate output to cd?  I tried this:  $ locate Descargas | grep Descargas$ /home/oliver/Descargas $ locate Descargas | grep Descargas$ | cd $ locate Descargas | grep Descargas$ &gt; cd $ locate Descargas | grep Descargas$ &lt; cd /home/oliver/Descargas $    No luck. This probably isn't particularly useful, but I'm curious. Tax considerations for selling a property below appraised value to family? I own a property that recently appraised for $350,000 in the state of Maryland that I purchased for $300,000 7 years ago. I wish to sell this property for a value of $240,000. Here are my questions:   Is this legal? The state of Maryland has a transfer/recordation tax of 1.5% for each, the buyer and seller. Would this be computed on the appraised or sale value? Will this pose any problem if the buyer needs financing? Would I be able to deduct a capital loss on my tax return?     From comments: I should have mentioned - the buyer is a sibling. How to show that $x^4+1$ is irreducible in $\mathbb Z[x]$ but it is reducible modulo every prime $p$?   For example I know that $x^4+1=(x+1)^4\bmod 2$. Also $\bmod 3$ we have that $0,1,2$ are not solutions of $x^4+1=0$ then if it is reducible the factors are of degree $2$. This gives that $x^4+1=(x^2+ax+b)(x^2+cx+d)$ and solving this system of equations $\bmod 3$  gives that $x^4+1=(x^2+x+2) (x^2+2x+2) \pmod 3$. But is there a simpler method to factor $x^4+1$ modulo a prime $p$? How is a second measured? And why is it measured that way? The earth's rotation around itself (one rotation around Earth's own axis) doesn't take exactly 24 hours. It off by some seconds which becomes somewhere around 6 hours per year and 1 day in 4 years(leap year), which brings the question why didn't we modify the measurement of 1 second ever so slightly so as to avoid leap years altogether.   Well how is 1 second measured exactly?  says      the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. []   Well, why is it measured that way? Is there any technical reason like it is easy to measure and can be standardized easily? Or is it really possible to modify the measurement of time? Significant figures vs. absolute error On , $N_A = 6.022\;141\;29 \times 10^{23} \text{ mol}^{-1}$ has 9 significant figures and a standard uncertainty of $0.000\;000\;27 \times 10^{23} \text{ mol}^{-1}$.  First, can it be written as the following?  $$ N_A = 6.022\;141\;29 \times 10^{23} \pm 0.000\;000\;27 \times 10^{23} \text{ mol}^{-1} $$ If yes, consider the following quote from  (emphasis added):     Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m. To record this measurement as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many significant figures as are consistent with the estimated error. The quantity 0.428 m is said to have three significant figures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement in centimeters would be 42.8 cm and still be a three significant figure number. The accepted convention is that only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m.   and the following quote from  (emphasis added):     The absolute error places bounds telling you that the actual value is expected to fall between x - D x and x + D x. The absolute error is an easy way to report the error and makes it easy to check that you are not reporting too many significant figures. For example, suppose you had a measurement that was reported to be 10.02 ± 0.3 m. Because the reported value is uncertain in the tenths place, it is wrong to report it to the hundredths place. It should be reported to the same decimal place as the absolute error: 10.0 ± 0.3 m. Another point is that the absolute error and the reported value must have the same units.   If there is such a convention (cf. Rice's lab guide) and it is wrong to report more significant figures than is warranted by the absolute error (cf. the joint project's guidelines), and NIST should have adhered to such convention and striven to be correct, is it true that NIST adheres and is correct because the standard uncertainty has two least significant digits (i.e., $27$)?  Had the standard uncertainty been $0.000\;000\;2\text{ mol}^{-1}$, would NIST have reported Avogadro's Number as $N_A = 6.022\;141\;3\times 10^{23}$ with 8 significant figures? can I use same functions with the different type of argument inputs When I'm editing a stack snippet, I often want to copy code from the original question into the snippet. But while the snippet editor is on display, there's no way to access the question, other than opening another tab/window. What I often do instead is copy all the code in the question to the clipboard, open the snippet editor, then paste it all in and revise it to what I want. But when the original code is poorly designed, that ends up being more work than just copying the bits and pieces that I want.  There could be a "View Question" button that pops up the question over the snippet editor and allows copying. Or maybe the Snippet Editor could be draggable and resizable, so you can reveal the question and copy from it; but this would require that it not be purely modal. A question here on meta for instance may stick around for quite a while. A feature-request  maybe even for months. Then the status (tags) gets changed to  or  or whatever and the OP does not get notified.  On a normal post-edit we get a notification but retagging does not count for that. Please add retagging to the edit notifications.