is definitely one of the most amazing phenomenon that I have heard in a while.  Some examples:   The pressure from the  can perturb the motion of artificial satellites as the momentum is exchanged creating a perturbing force. The  in Australia intend to use high powered lasers to perturb the orbit of space debris, sending space junk in to our atmosphere with the intention that it will burn up!   Question  It has most certainly happened to everyone in the community where you've gone to bed only to realise that you've forgot to close the door. On a much smaller scale, yet equally as annoying as space debris.    What would be the magnitude of photon pressure required to cause a force big enough to close a bedroom door?
Photons have no mass but they can push things, as evidenced by .   Can photons push the source which is emitting them? If yes, will a more intense flashlight accelerate me more? Does the wavelength of the light matter? Is this practical for space propulsion? Doesn't it defy the law of momentum conservation?  Note: As John Rennie mentioned, all in all the wavelength doesn't matter, but for a more accurate answer regarding that, see the comments in  .  Related Wikipedia articles: ,
What should be in the sources.list for Kali Rolling Linux? This is exact content from my sources.list:  #  # deb cdrom:[Debian GNU/Linux 2016.1 _Kali-rolling_ - Official Snapshot amd64 LIVE/INSTALL Binary 20160830-11:29]/ kali-rolling contrib main non-free #deb cdrom:[Debian GNU/Linux 2016.1 _Kali-rolling_ - Official Snapshot amd64 LIVE/INSTALL Binary 20160830-11:29]/ kali-rolling contrib main non-free   I couldn't install the Synaptic package manager and was told to modify sources.list.  I googled a lot and added some repos into it and ran update and upgrade command only to see Kali crash... I had to recover it.  Please mention the exact content that should be there to ensure that Kali Linux works. Can TikZ create pixel art images? Can you create images like this:    when you have something like  0 = green (#54ff00) 1 = white (#ffffff) 2 = red   (#ff0000) 3 = blue  (#0048ff)  Image (Python list of integers defined above): [[2,0,0,0,0,0,0],  [0,3,0,0,0,0,0],  [0,3,2,1,1,0,0],  [0,3,2,2,2,1,1],  [0,3,2,0,0,1,0],  [0,0,0,0,0,1,0],  [0,0,0,0,0,1,0]]   with TikZ?  How far I got  The following MWE defines all colors, produces a grid of the correct size (though the size is determined by hand):  \documentclass[varwidth=true, border=2pt]{standalone} \usepackage{tikz} \usepackage{xcolor}  \begin{document}     \newcommand\n{7}     \definecolor{green}{HTML}{54FF00}     \definecolor{wite}{HTML}{FFFFFF}     \definecolor{red}{HTML}{FF0000}     \definecolor{blue}{HTML}{0048FF}     \begin{tikzpicture}         \foreach \x in {1,...,\n}{             \foreach \y in {1,...,\n}{                 \begin{scope}[shift={(\x,\y)}]                   \draw [fill=green] (0,0) rectangle (1,1);                 \end{scope}             }         }     \end{tikzpicture} \end{document}   Of course, I could simpy make a lot of adjusted                   \begin{scope}[shift={(\x,\y)}]                   \draw [fill=green] (0,0) rectangle (1,1);                 \end{scope}   but I've wondered if this can (with reasonable effort) be done in TikZ / LaTeX.  My problem is giving TikZ the color array. I don't have any idea how to do this. I only know two types of looks in TikZ:  \foreach \x in {0,1,2,3,4,5}{...} \foreach \number in {1,...,\n}{...}   I have never seen a nested over a 2D-array. All I have seen so far were 1D-Arrays of tuples (with fixed tuple size). Parentheses around more than one paragraph Does English allow one to put parentheses around more than one paragraph? Example:     Paragraph 1.      (Paragraph 2.      Paragraph 3.)      Paragraph 4.   (Of course, this is just a simple example. In reality, it looks more clean since the paragraphs are more than one line long, and are not separated by an empty line.) Don't heavier objects actually fall faster because they exert their own gravity? The common understanding is that, setting air resistance aside, all objects dropped to Earth fall at the same rate. This is often demonstrated through the thought experiment of cutting a large object in half. The halves clearly can't then fall more slowly just by being sliced in two.  However, I believe the answer is that when two objects fall together, attached or not, they do "fall" faster than an object of less mass alone does. This is because not only does the Earth accelerate the objects toward itself but the objects also accelerate the Earth toward themselves. Considering the formula: $$ F_{\text{g}} = \frac{G m_1 m_2}{d^2} $$  Given $F = ma$ thus $a = F/m$, we note that the mass of the small object doesn't seem to matter as when calculating acceleration the force is divided by the $m$ term, its mass. However, this overlooks that the force is actually applied to both objects, not just to the smaller one. The acceleration on the second, larger object is found by dividing $F$, in turn, by the larger object's mass. The two objects' acceleration vectors are exactly opposite, so closing acceleration is the sum of the two:  $$ a_{\text{closing}} = \frac{F}{m_1} + \frac{F}{m_2} $$  Since the Earth is extremely massive compared to everyday objects, the acceleration imparted on the object by the Earth will radically dominate the equation. As the Earth is $\sim 5.972 \times {10}^{24} \, \mathrm{kg} ,$ a falling object of $5.972 \, \mathrm{kg}$ (just over 13 pounds) would accelerate the Earth about $\frac{1}{{10}^{24}}$ as much, which is one part in a trillion trillion.  Of course in everyday situations, we can for all practical purposes treat objects as falling at the same rate because of this negligible difference—which our instruments probably couldn't even detect. But I'm hoping not for a discussion of practicality or what's measurable or observable, but what we think is actually happening.  Am I right or wrong?  What really clinched this for me was considering dropping a small Moon-massed object close to the Earth and a small Earth-massed object close to the Moon. This made me realize that falling isn't one object moving toward some fixed frame of reference, but that the Earth is just another object, and thus "falling" consists of multiple objects mutually attracting in space. How can I force SQL Server Management Studio to update the IntelliSense cache? IntelliSense in SSMS isn't updating unless I shut it down and restart. I've tried disconnecting from the server and reconnecting while the SSMS session is active, but that isn't working.  Steps to recreate:    Create a table  Select something from that table SSMS displays squiggly red lines under it with the tip "invalid object name" Execute the query   How can I force IntelliSense to update without restarting SSMS? How to dismiss the Windows 8.1 Upgrade banner? More and more I see, especially in activist communities, Spanish-derived words ending in x or @ in order to neuter the gendering inherent in the original language. For example: latinx (or latin@) as opposed to latina and latino. How, though, are these endings pronounced? Please provide evidence of how this orthography is most commonly pronounced. Note 1: I recognize this is in an English Language site, rather than a Spanish language site, but this phenomenon is very much happening in English, albeit with Spanish loan words. Therefore the question is relevant to non-Spanish-speaking English speakers. Note 2: A question like this can lead to politically charged or, at least, sarcastic comments. Please refrain from bringing in your biases for or against. Note 3: This question is not seeking opinions as to how some people pronounce the suffixes. Answers should address evidence of a developing orthodoxy in pronunciation. I'm looking for a more politically correct substitute for the expression "poor man's", meaning an inferior improvised or makeshift substitute. Usage examples:   "Guncotton is the poor man's TNT" "Poor man's oyster" (mussels, or coughed up phlegm)    My hesitance is mainly because it is not as gender neutral as perhaps it once was. The closest I can think of is "pauper's", but I don't know many examples of usage. How does centrifugal force work? Why don't my female dwellers give birth to children? Our DM keeps interrupting our long rests In the latest campaign, we're still around the third level, but every single night we've spend in the wild so far, we were interrupted by hard combat encounters (as in DMG-worded "hard"), forcing us to use our resources (like HP, spell slots, Ki, once-per-day stuff) and not restoring any of those lost the previous days. I feel like the , as it lasts four to six rounds, so we usually say that we'd like to resume our rest but the answer is always "you've been interrupted, your rest is over, you can't restart any until dusk". So the only real long rests we could have always were in town.  We've always used watch-turns, and being interrupted in the first night of the campaign, we now always spend one hour to find a safe place to rest and we make that intent very clear to the DM. But yet, kobolds, goblins, ghouls and gnolls always find us in the middle of the night, but never when we travel for ten hours during the day (which is comparable to "fast travel" in his own word). Once on the second day in the wild, we were faced to a deadly encounter (as in DMG-worded "deadly") which we survived only by fleeing. And we're kind of forced to get back to the deadly encounter, which is more than one day away from the nearest town.  We're five players and I'm the only one with PnP RPG experience... from ten years ago. I don't remember being this resourceless. We asked if it was a survival campaign and the answer was that it was only a normal introduction campaign found on the Internet that he spiced up a bit. We've also asked if we did anything wrong and the answer was that we followed the normal story.  The DM is mastering his second campaign (the first one is still ongoing, but with veteran players). The DM also plays a lot of survival campaigns as a player.  Is this situation normal? If yes, why? If not, what should I say to the DM?  Note that I'm fully aware of the "long rest" rule as written on page 186 of the PHB. This is why I encouraged my team to say that we resume our rest. (thanks Bloodcinder) This question attempts to collect the few pearls among the dozens of bad C++ books that are published every year. Unlike many other programming languages, which are often picked up on the go from tutorials found on the Internet, few are able to quickly pick up C++ without studying a well-written C++ book. It is way too big and complex for doing this. In fact, it is so big and complex, that there are very many very bad C++ books out there. And we are not talking about bad style, but things like sporting glaringly obvious factual errors and promoting abysmally bad programming styles. Please edit the accepted answer to provide quality books and an approximate skill level — preferably after discussing your addition in . (The regulars might mercilessly undo your work if they disagree with a recommendation.) Add a short blurb/description about each book that you have personally read/benefited from. Feel free to debate quality, headings, etc. Books that meet the criteria will be added to the list.  Books that have reviews by the Association of C and C++ Users (ACCU) have links to the review. *Note: FAQs and other resources can be found in the  and under . Work the Spring There's a book that I read several years ago that I'd like to find.  However, I cannot remember enough about it to find it myself.  Neither the title nor author remain in my mind, nor any keyword or phrase that's unique enough for the Grand Google to nail for me.  Hence my desperate plea here.  In the book, there is an interstellar civilization composed of several power blocks.  The entire civilization did not fill the galaxy, but it did span several stellar systems.  Maybe 10s or 100s.  I seem to remember that one of the civilizations was a decentralized group referred to as the Brotherhood and they seemed to have been keen on preserving old learning and political ideals.  A derelict alien spacecraft from outside all of this had been discovered and at least two of the power blocks sent ships to recover it.  I don't recall if they knew at the time about the power the alien ship had, but they must have had some clue since there was some urgency in capturing this ship.  One of the ships sent to capture the Alien craft was commanded by somebody who was rather shaken up, to say the least.  He had had some big trauma in his past (like... the last ship he captained was annihilated with all hands.) so he was kinda bummed out about things and wasn't really putting his heart into getting this done.  He was assisted by the ship's AI who had a lot of soul-to-soul chats with the captain, and at one point almost relieved him of command because he was just not getting the job done.  I think the ship's name was Boaz.  These were the "good guys".  There was at least one other ship sent from the "bad guys."  The alien craft had some remarkable powers.  The interior volume was apparently infinite and the operators could see and manipulate anything in the universe.  There might have been some example given where all the rats somewhere were found and disposed of.  Whoever had control was tempted by the ole absolute power corrupts absolutely problem, but nobody but nobody could stop them because of their power.  They could eat and multiply within the ship and become real bad-asses.  But alas... (or hurray, depending upon which side you're one) everything fails eventually, and whoever controlled the ship would eventually succumb to some horrible end.  Whereupon the ship became derelict again until some other lucky race found it and repeated the cycle.  The ship had an AI that was real interested in taking the power for itself, but there was some mechanical, spring-loaded, mechanism outside of its control that needed to be worked in order to execute power.  The AI apparently never figured out how to "work the spring" and this made him crazy angry.  The ending is equally foggy for me.  I'm pretty sure the good guys got the ship.  They agonized over what to do with it.  Apparently it was indestructable and nobody wanted to taste the temptation of all that power.  In the end they dumped it on the surface of a neutron star.  There it sat forever more, probably with the crazy AI really pissed off about being there.  If you've read this book, you'll recognize it immediately from these clues.  I'm looking forward to finding out the name of this book.  Thanks! I have a char array buffer that I am using to store characters that the user will input one by one.  My code below works but has a few glitches that I can't figure out:   when I execute a printf to see what's in Buffer, it does fill up but I get garbage characters at the end it won't stop at 8 characters despite being declared as char Buffer[8];   Can somebody please explain to me what is going on and perhaps how I could fix this? Thanks.  char Buffer[8]; //holds the byte stream int i=0;  if (/* user input event has occurred */)  {         Buffer[i] = charInput;         i++;          // Display a response to input         printf("Buffer is %s!\n", Buffer);  }   Output:   tagBuffer is 1┬┬w! tagBuffer is 12┬w! tagBuffer is 123w! tagBuffer is 1234! tagBuffer is 12345! tagBuffer is 123456=! tagBuffer is 1234567! tagBuffer is 12345678!  tagBuffer is 123456789! Limits involving factorials $\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$ I am trying to calculate the following limit  $$\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$$ where $k$ can be any number between $0$ and $N$.  I thought of the following:  If I take the logarithm of the expression then I get:  $$\lim_{N\to\infty} \left(\log(N!)-\log((N-k)!)-k\log N\right)$$    Using the Stirling formula this can be approximated as:  $$\lim_{N\to\infty} \left(N\log(N)-(N-k)\log(N-k)-k\log N\right)$$  Now there are two cases: If $k$ is $N$, then the second term vanishes and the remaining terms cancel. If $k$ is smaller than $N$, then I can drop the $k$ inside the second logarithm and all the terms cancel. So the limit $$\lim_{N\to\infty} \log\left(\frac{N!}{(N-k)!N^{k}}\right)=0$$ Which means that: $$\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}=1$$ I don't know if this is mathematically rigorous. Would like some help. Thanks If $H$ has maximum vertex degree at most $3$ and is a minor of $G$, then $H$ is a topological minor of $G$. If  $H$ has maximum vertex degree at most $3$ (so $\Delta(H)\leq 3$) and $H$ is a minor of $G$, then $H$ is a topological minor of $G$.   The converse follows by definition. However, most sources state this proposition without a proof. Any help is greatly appreciated. AttributeError: MapDocObject: Unable to save on mxd.save/saveACopy? I'm trying to use arcpy to save an .mxd and am having an issue.  It doesn't matter if I use mxd.save or mxd.saveACopy I get the same error.  I know it doesn't look like I am doing anything w/ it here, but it's just a portion of my code:  import arcpy import arcpy.mapping as map arcpy.env.overwriteOutput = True  env.workspace = r"C:\MGIS\FinalProject2.gdb     mxd = map.MapDocument(r"C:\MGIS\Finalproject2.mxd") df = map.ListDataFrames(mxd)[0]  for df in map.ListDataFrames(mxd): df.scale = 2000000  #Add layers into map document addLayer = map.Layer(OKXcounties) addLayer1 = map.Layer(contourLabelText) addLayer2 = map.Layer(contoursClipLyr) addLayer3 = map.Layer(clipOKXLyr) map.AddLayer(df, addLayer, "AUTO_ARRANGE") map.AddLayer(df, addLayer1, "AUTO_ARRANGE") map.AddLayer(df, addLayer2, "AUTO_ARRANGE") map.AddLayer(df, addLayer3, "AUTO_ARRANGE")  # Add contour Labels for lyr in map.ListLayers(mxd):     if lyr.name == "contourLabelText":         lyr.showLabels = True     if lyr.name == "Contour Features":         lyr.transparency = 100  mxd.saveACopy(mxd)   I get the following error:   Traceback (most recent call last):   File "C:\Python26\ArcGIS10.0\Lib\site-packages\pythonwin\pywin\framework\scriptutils.py", line 312, in RunScript     exec codeObject in __main__.__dict__   File "C:\MGIS\geog485\FinalProject2\mxdtest.py", line 7, in &lt;module&gt;     mxd.saveACopy(mxd)   File "C:\Program Files\ArcGIS\Desktop10.0\arcpy\arcpy\utils.py", line 181, in fn_     return fn(*args, **kw)   File "C:\Program Files\ArcGIS\Desktop10.0\arcpy\arcpy\_mapping.py", line 668, in saveACopy     self._arc_object.saveACopy(file_name) AttributeError: MapDocObject: Unable to save.  Check to make sure you have write access to the specified file and that there is enough space on the storage device to hold your document.   Space is not the issue, I have 60 GB of free space and I've checked the windows properties of the .mxd file.  Read-only box is unchecked and I've "allowed" all permissions for all groups:    Does anyone have any idea how if this is a bug or how I can fix this?  I'm using ArcInfo 10.0 SP4. According with Mumford the answer is yes, but there are some obscure points in the proof.  We know that there exists a very ample line bundle on $A$ since every abelian variety is projective. Hence, via some corollaries of the Theorem of the Cube, we get an ample line bundle whose restriction to the kernel of $n_A$ is both the trivial bundle and very ample. This should imply that the dimension of $\ker n_A$ is $0$.  Furthermore, Mumford says that the fact that the dimension of the kernel is $0$ implies the surjectivity of $n_A$.  Is anybody able to clarify these two points to me?  Thanks in advance! How to ensure OpenVPN connection uses specific DNS? I'm using OpenVPN through Tunnelblick on MacOS X Lion.  I need to set specific DNS (with local IP, which works only when VPN is up) for the duration of this VPN session only.  I do not have access to the OpenVPN server configuration. Only client config. Also, DNS from the server doesn't work.  So it works like this: I connect to VPN, go the Network preferences and manually set DNS. After VPN is disconnected, I switch back to default. It works, but it needs to be automatic.  After some exploration I found that OpenVPN up- and down- scripts might help me with that. Unfortunately, I haven't found any specific documentation about how exactly it can be done.  How it can or can't be done? Any advice would be appreciated! Change the title size in scrartcl I'd like to use a smaller title. I'm using the scrartcl documentclass from the . I can change it's color font but not it's size.  \setkomafont{title}{\normalfont\bfseries\small}   Everything works exept the size.