There is a basic result about commutative semigroups which says     Any commutative semigroup satisfying the cancellation property can be embedded in a group.   However, I read that     Not every semigroup with cancellation can be embedded in a group.   Can someone provide a reference or an example of a (non-commutative) semigroup with cancellation that cannot be embedded in a group?  What else is known about algebraic structures with the cancellation law which may not be subsets of a group?
Under what assumptions can a semigroup $(S,*)$ be embedded into a group?
Drift velocity in Drude model Is it possible to flash a custom ROM without a custom recovery image For an un-rooted device, almost all articles/forum posts I've read say that in order to flash a custom ROM you first need to flash (or boot) a custom recovery image like TWRP.   I'm not sure I understand why. If the bootloader is unlocked shouldn't it be possible to manually flash images that make up the custom ROM to the required partitions with fastboot flash &lt;partition&gt; [ &lt;xxxx.img&gt; ], and leave the stock recovery untouched.  I realize that this may be difficult and that there is no benefit in doing it this way, but I'm curious to know whether or not it is possible, and if not, why? How to disable "time travel" entirely? Does quantum spin contribute to the angular momentum of a black hole? How does deleting work? What can cause a post to be deleted, and what does that actually mean? What are the criteria for deletion? Can I print a custom paper on standsard size in word? What's the difference between using > and >> in shell? This tiny little script deletes all small features in all layers. This works fine but the size of .shp files are not reduced. Please tell me why...  canvas = iface.mapCanvas() expr = QgsExpression("$length&lt;100") for l in canvas.layers():     l.startEditing()     it = l.getFeatures(QgsFeatureRequest(expr))     for ft in it:         l.deleteFeature(ft.id())     l.commitChanges() Every Christmas, Harry receives a mediocre gift from the Dursleys. In Harry Potter and the Chamber of Secrets he gets a toothpick.     At that moment, Hedwig swooped into the room, carrying a very small package in her beak.     “Hello,” said Harry happily as she landed on his bed. “Are you speaking to me again?”     She nibbled his ear in an affectionate sort of way, which was a far better present than the one that    she had brought him, which turned out to be from the Dursleys. They had sent Harry a toothpick    and a note telling him to find out whether he’d be able to stay at Hogwarts for the summer    vacation, too.    They hate owls, but obviously use them to contact Harry at school? Playing a remote movie on the remote computer I have two computers (a desktop and a laptop) running linux connected to my local area network. I like to ssh from my laptop over to my desktop and run programs there, and sometimes listen to music on my desktop, which is connected to my stereo system. Lately, I've been wanting to play movies on the desktop and desktop screen, but cue them from my laptop across the room.   Unfortunately, I cannot play a movie in the current X session running on my Desktop on from my laptop. What is odd about this is that I can listen to the audio coming from the speakers that are hooked up to my desktop, by playing the audio files over ssh! This tells me that there must be a way to send the movie to that Xsession, from the ssh shell that I am connected to.  Does anyone have any ideas about this? I'm using C# on Framework 3.5.  I'm looking to quickly sort a Generic List&lt;T&gt;.  For the sake of this example, let's say I have a List of a Person type with a property of lastname.  How would I sort this List using a lambda expression?  List&lt;Person&gt; people = PopulateList(); people.OrderBy(???? =&gt; ?????) I did setup an easy scene with an area light behind a window. In the glass (simple plane) which is in front the area light is visible - how can I turn this off so that the background is shining throgh? Since I can't find any alternative to Linux'  elevation command, I have the following question:  How to define a PowerShell function which requires elevation? I mean UAC prompt.  Say, such function follows:  function system-check {     SFC /ScanNow }   System:  Windows 8.1 Pro 64-bit  PowerShell:   Major  Minor  Build  Revision -----  -----  -----  -------- 5      0      10586  117    EDIT1:  To be 100% understandable let me rephrase:   I run PowerShell as user I run the aforementioned function system-check I want the function to elevate in order to be able to execute the command; note, that I want the UAC prompt to appear Can I kill the Golem pre-hardmode? Proof of a limit for a recursively-defined sequence I have a sequence defined by $$ a_1=1,\quad a_2=1,\quad a_n=\frac{1}{a_{n-1}}+\frac{1}{a_{n-2}}\text{ for } n\ge2. $$ Now, if $\lim_{n\to \infty}a_n=g$ then $\lim_{n\to \infty}a_n=\lim_{n\to \infty}\Bigl(\frac{1}{a_{n-1}}+\frac{1}{a_{n-2}}\Bigr)=\frac{2}{g}$ so $g=\sqrt{2}$ or $g=-\sqrt{2}$ but $a_n&gt;0$ so $g=\sqrt{2}$.  Now, how do I prove that it has an actual  limit? Also, it can be proven that $1\le a_n\le2$, and it's not monotonic because $a_4 \gt a_5 \lt a_6$. Also, it's not monotonic after some $N\in\mathbb N$ How to remove/install a package that is not fully installed? Best VNC / remote desktop software for assistance Poll on best VNC / remote desktop software for assisting others on Windows/Mac machines from Ubuntu?    I've heard good things about TeamViewer and Fog Creek Copilot, but I'm wondering if the included GNOME Vinaigre VNC client is good enough for this.  To specify, I'm looking for best option based on:   SIMPLEST ease-of-use for client to download/use on their end. See #1. Works cross-platform I am able to control client's mouse and/or keyboard from remote machine. Gravitational wave solutions to the Einstein field equations It is well known that general relativity predicts gravitational waves, but I would like to know how. What solution(s) to the Einstein field equations yield something which can be interpreted as a wave(-like) phenomenon? Understanding Clip Warning 000117 for Polygons? This error makes little sense because 95% of the time this works without any problem, but here is the situation:  I am clipping polygon A by polygons B-H.  While most of the time this works perfectly, occasionally this happens:   All layers are from the same coordinate system, and the processing extent is the same as polygon A when I setup the clip. Polygons C-H clip just fine without any errors, so it is usually polygon B that has the issue; however, most of the time there are no issues whatsoever. The polygons do overlap each other. I have repaired the geometry, but the results are the same.  Given that it isn't a coordinate problem, a processing extent problem, or even a geometry problem, what else could it be causing this error, and what would I have to do to resolve this problem?  UPDATE:  The error happened again with my largest set of Polygon A; however, I then deleted 75% of the Polygon A set and it worked just fine. So my question now is: how limited is the Clip feature when it comes to large areas, and is there a way around this without having to divide the Polygon A shapefile into several segments? What is the difference between $Q=\Delta U+W$ and $\Delta U=Q+W$?