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How does one experimentally determine chirality, helicity, spin and angular momentum of a fundamental particle? One of whom destroys the Earth, perhaps accidentally, while fighting another... the plot also involves a human colony ship or planet that loses contact with the Earth; I think a small boy is also involved with the plot, although it's been 20-30 years since I read this story.  Any help would be appreciated!  It's driving my brother and me a bit batty.  Here's the batty brother's take: the main being has created others who are now at war, exploding stars. To escape, the main being accelerates the star of the human colony as a decoy. However, most of the story centers on some guy who winds up living forever, as they keep sticking him in cryogenic sleep and reawakening him. If memory serves me right, they abandon the colony planet for a while and move to asteroids as the star is weakening because it is using it's energy to accelerate. When it decelerates, it is the only star left in the universe. The one "being" was almost reduced to living off the energy of a black hole when it appears, and he sees it and sets off to go there, with a cryptic ending that the humans very well might fight him off. A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$ Let $f_n = \mathbb 1_{[-n,n]}$ for all $n \in \mathbb{N}$   Compute explicitly $f_n \star f_1$ for all $n \in \mathbb{N}$.  Show that $f_n \star f_1$ is the Fourier transform of $g_n = \frac{  \sin{(2\pi x)} \sin{(2 \pi nx)}}{\pi ^2 x^2}$  Show that $\| g_n \|_1 \to \infty$  Deduce that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$    Here, $C_0(\mathbb{R})$ is the space of continuous functions $f : \mathbb{R} \to \mathbb{R}$ that tends to $0$ at $-\infty$ and $+\infty$. I managed to compute 1) and proved 2). But I don't know how to prove 3). Moreover, I don't see how can 1), 2) and 3) prove 4). Can anyone help? Installing 64-bit geoprocessing of ArcGIS for Desktop? I am trying to install 64-bit processing to ArcGIS 10.2, but the ESRI .  One similar question on this exchange  that shows an option to include this, but my setup installation program (which I downloaded) does not show this installation window, but instead goes straight to selecting features to install as shown below.  I can't find any other documentation for running 64-bit geoprocessing on ArcGIS version 10.2.  Can anyone show me how to do this? or is it best to just try to install the service pack 1 version of it? HDMI/Displayport audio control for OS X How can I find the source of a mysterious bad smell? We have recently moved home, and all is fine appart from a mystery smell which I'm unable to track down. It's driving me crazy (actually, my wife thinks I am crazy as she can't smell it).  I'm hoping someone on here could offer some tips on how to track it down, or what it might be.  Here's some info:  Background: The house is a two floor (plus basement) block/concrete construction.  There is a wide hallway on the groundfloor connecting the rooms (including kitchen, toilet/shower room, stairwell).  The stairs are wood-board on concrete.  The floor in the hall and kitchen  is tiles over concrete, the rest woodblock/parquet over concrete.  Location of the smell: I usually smell it when coming down the stairs, seems to be strongest about half way down.  However sometimes it doesn't smell on the stairs at all, but rather in the ground floor hallway.  Seems to move around quite a lot. Occasionally I have felt it upstairs, but assume this is it drifting. The basement smells fine.  The Smell: The best description of the smell I can give is something like old rubbish.  What I've investigated so far:  1) Something died somewhere?  This was my initial thought, and since I usually notice the smell on the stairs I thought I'd try there first.  I've taken up some of the wood on the stairs (not all yet) but not looking promising, as there really isn't much space between the wood boards and the concrete.  Not really sure where else something could have gotten, as everything seems to be tight against the concrete.  2) Smell from kitchen moving into rest of house? I never really detected a bad smell in the kitchen, but thought I'd rule it out anyway. I thought maybe it was the bin under the kitchen sink that might be causing it.  So I moved the bin to a small storage room at the back of the kitchen (and kept the door closed) and thoroughly cleaned inside the cupboard under the sink. No change.  I also looked behind all of the cabinets for a problem, but could not see anything.  3) Gas from drains? The sink doesn't smell in the kitchen, and it's got a P-bend trap on the pipe - so I can't see a problem there.  Cant detect a smell from the plugholes in the bathroom either.  The bathroom sink waste pipe has a bottle-trap on it.   Don't know if there is a trap on the shower as it's a sealed unit, but I'm guessing yes (and can't smell anything).  Can any one think of something I might have missed, or give any advice? Summarizing flatness of county with statistic Elevation variance per square mile I need to classify every county in the US as either hilly, moderately hilly, or flat. Accuracy is not critical, just a rough classification. I used R and followed the advice in  answer to import elevation and counties and calculated the zonal variance. This was inherently biased towards larger counties since they have more surface for hills, so I need to divide by area. If I divide variance by square miles does that reasonably represent hilliness? The preliminary results seem decent, with the highest values being places like Colorado, Hawaii, Montana, etc. Take the function  $$ \begin{cases}f(x,y)=(x^2+y^2)/\sin(\sqrt{x^2+y^2}) &amp; \text{when } 0&lt;\lvert (x,y)\rvert&lt;\pi\\   0 &amp; \text{when } (x,y)=(0,0) \end{cases}$$  I got that this function is differentiable at $(0,0)$. I calculated the partial derivatives at $(0,0)$ of which both were $0$ and trying to show the definition of differentiability is not satisfied but I keep getting that it is. Plz help. 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 .. ? ReadList can't read from file containing high-precision Reals How do you use plural or singular form of an adjective? Looking for a short story about an artist and a forger Back in the late 1970s to early 1980s, I read a short story about an artist and a forger.  Between the two of them, they managed to start a revolution that brought down a corrupt dictatorship.  It was science fiction:   The dictatorship was interplanetary, maybe interstellar.   The artist used some kind of advanced technology to make his art works.   Plot:  The artist is one of the best (if not the best) at what he does.  The dictator wants the artist to make what amounts to a family portrait in whatever medium it is he works in.  Think of it like painting - you create the image manually (not a photograph) but it is much more than just a flat image.    The artist doesn't like the dictator - maybe on general principles, maybe because he knows the dictator personally - and refuses to make the "portrait."  The dictator has the artist arrested, and will only let the artist free again if he makes the portrait.  The artists makes the portrait.  He does the work while in the prison or jail.  That's where the forger comes into things. The forger is also in jail for something or other.  The forger makes copies of art works.  He of course recognizes the artist, and knows what the artist works with.  The forger can somehow see what the artist is working on.  The artist finishes the portrait.  At first the dictator is thrilled.  It looks exactly the way he wanted it.  As time goes by, though, the people looking at the picture see that it represents the vileness and corruption of the dictator.  The more you look at it, the more of the evilness of the dictator you see in it.  That is the genius of the artist, and whatever medium he is using.  Once you notice the hidden levels of the portrait, you can't unsee them and you see more and more of it as you look.  I think the effect carries over into reality as well.  Once you've seen the dictator's corruption in the portrait you also begin to see it in the dictator and his works as well.  This of course seriously pisses off the dictator, who has the artist killed and the portrait destroyed.  While in prison, the forger watched as the artist created his masterpiece, and recognized it for the subversive thing it is.  He also recognized it as the ultimate rebellion from the artist - the artist knows what will be seen, and that he will be killed for it.  All of that inspires the forger to do something more meaningful with his life than make forgeries for the money.  The forger is released from prison.  He saw the completed portrait, and knows how it was made.  He begins making forgeries of the portrait - like, hundreds if not thousands of them.  These are distrubuted throughout the nation/empire.  The people realize what evil is controlling them once they see it in the copies of the portrait, and eventually a revolution rises and brings down the dictatorship.  It was probably older than the 1970s.  I expect earlier than 1960.  Any ideas? Why is it so hard to find the roots of polynomial equations? The question that follows was inspired by  question:  When trying to solve for the roots of a polynomial equation, the quadratic formula is much more simple than the cubic formula and the cubic formula is much more simple than the quartic formula.    That the general solutions to various polynomial equations are so complex and difficult to derive seems to suggest a fundamental limitation in the problem solving capabilities of the mathematical machinery. Does this intuition of mine make any sense? What should I make of it? Why is it that with each successive degree in a polynomial equation, the solution becomes so much more complex? Can I gain some intuition about what makes finding the roots so hard? According to the : "there is no general algebraic solution—that is, solution in radicals— to polynomial equations of degree five or higher." What is so special about the quintic that makes it the cut-off for finding a general algebraic solution? Question is pretty much in the title: is it possible for an alliance to win as one, instead of a single player being the winner?  And if there is such way, is there a difference between classic and disharmony? How to disable SSLv2 or SSLv3? How to proof the the derivative of $x^2$ is $2x$? Servlet returns "HTTP Status 404 The requested resource (/servlet) is not available" On my fully updated Ubuntu 18.04.3 system, audio doesn't work unless I switch between outputs. When I boot my PC, the right output (stereo speakers) is already selected by default, but there is no audio from Chromium, Firefox, VLC or any other program. However, the GNOME speakers test works. I can hear "front left" and "front right" from there, but no audio from other programs. In order to fix that, I can simply switch to another audio output (e.g. HDMI out) and then switch back to the stereo speakers, and the audio will magically work. Any idea why? It's not a big deal because it takes a couple of seconds to switch between outputs, but it's kind of annoying to do that after every reboot. Does $E = mc^2$ apply to photons? What is the remainder of $\,3^{3^{3^{\:\!\phantom{}^{.^{.^.}}}}}\!\!\!$ divided by $46$?  The level of powers is $2020$.  First there is no parenthesis so it means 3 power of 3 which is also power 3 and so on 2020 times  Second I think that we can use Fermat's Little Theorem but I don't know how, and maybe there is a better way.