For example, let's say I'm copying instructions by hand. The original instructions say:        Multiply the first by the second   Integrate the third with the fourth   Integrate the third with the fifth      And on a page I write:        Multiply the first by the second   Integrate the third with the fourth   "" with the fifth      I know this example is silly, but hopefully it's clear what I mean.  What is this called?
I've sometimes seen this construct, used to avoid repetitive handwriting, but I don't even know if it's proper English.  If it is, what is the name of this construct? I have no idea what to search for when looking it up...        Don't forget to buy eggs.   &emsp;"&emsp;&emsp;      "&emsp;&emsp;"&emsp;"&emsp;yogurt.   &emsp;"&emsp;&emsp;      "&emsp;&emsp;"&emsp;"&emsp;milk.
Is there any way to set a MacBook Pro to not sleep when you close the lid? find the number of injections/surjections I've been banging my head on this problem for some time now, and could really use help. Bear in mind I'm not very good at this sort of thing and am struggling to get by in class.  Problem:     Given $ \alpha : A \to B       \;\;\;\;\;   |A|=p \;\;\;\;|B|=q $      Find:         Number of Injections: $A \to B$   Number of Surjections: $ A \to B$    Prove that ∃ a bijection $A \to B$       $\Rightarrow$ p = q   find number of bijections: $A \to B$         I apologize for dropping such a big problem on you all, but I just can't get anywhere with this. Help?  EDIT: These answers are really helpful and I believe I've got down the number of Injections, but  we haven't gone through permutations or combinatorics in class so my understanding of it is really hamstrung. I'm unclear on the Stirling theorem as discussed here: , specifically the part where inclusion-exclusion comes into play. I'm not sure how to apply that, since right now I'm letting p = 4 and q = 3, so I don't know where inclusion-exclusion would be used (if at all!) since I don't know how elements would be missing. Is "funnest" a word? We seem to be stuck at an impasse on this issue.  Is funnest a word or not?  If so, does it mean "most fun"? How would I import/export Blender's preferences? I constantly stay up to date with each new release of Blender, but this means my preferences are wiped clean each time. How do I export/import these preferences to avoid loosing my carefully crafted set up each time? How to perform the modular reduce of Rijndael's finite field I am trying to understand how to calculate the modular reduction of Rijndael's finite field.  The example on  page says that {53} • {CA} = {01}, because (11111101111110 mod 100011011) = {3F7E mod 11B} = {01} = 1.  I am able to get to the point where I have 3F7E mod 11B, but cant seem to figure out how the reduction works.        11111101111110 (mod) 100011011      ^100011011             1110000011110       ^100011011             110110101110        ^100011011             10101110110         ^100011011             0100011010            ^100011011 &lt;-- here, right shifted two places?             00000001   From this example, why does it right shift two places at one point?  I also found an example that 0x1b*0xaa equals 0x8c. Trying to solve this myself I get to the point: 0xE0E mod 0x11B   111000001110 ^100011011   11011010110  ^100011011    1010111010   ^100011011     010001100    ^100011011      10010111   This makes it 0x97 Error while running Quickly Transparency/Masking : See through an Outer Sphere and see Inner Sphere in true colours Summary  I want to be able to look through an outer sphere - BlueSphere, and see another sphere inside - RedSphere  This is the target goal I'm trying to get to:    Issues  Here is what I have tried, and the problems I'm having:  1)  If I set the spheres transparency alpha values to 0.75    - then the inner RedSphere does not take on its "true" colour and shows as blue instead of red.    2)  If I set the spheres transparency alpha to lower values of 0.5   the spheres lose their crispness which I don't want and the inner RedSphere still does not take on its "true" colour   { can't paste a 3rd sample - need more reputation points }   Background  I am animating two spheres, one inside the other, superimposed about a common origin.   At the start:   the outer BlueSphere is at full radius the inner RedSphere is at zero radius  As time progresses:   the outer BlueSphere shrinks the inner RedSphere expands    So what happens is the expanding inner RedSphere "bursts through" the contracting outer BlueSphere.  So the effect I am looking for is to see the RedSphere appearing as Red as it expands inside the BlueSphere.  Thinking/Logic  So I figure that transparency is not the way to go.  The transparency settings are behaving correctly - as one would expect, in a "real world" situation - the inner sphere (Red) takes on the colour of the outer sphere (Blue) seeing as we are looking through a (transparent) Blue material.  Any ideas on what approach to take ?  It's almost as if I should be "removing" the part of the BlueSphere that the RedSphere "occupies" so that we see the RedSphere directly without any BlueSphere between us and the RedSphere.  Some sort of masking ??  Advice, comments, suggestions welcome. Thanks.  [requested edit]  Using internal render.  [ My End Solution - Thanks for the guidance ]  Right, so here is the way I got to my final result:  1) I created python drivers for each sphere   I used the frame_current scene property for input Passed that to a scripted expression which used sin() as the scaling factor Used some if / elif conditionals against frame_current to make the spheres visible only when I needed them   2) I created 3 layers   On Layer-1 - background   I put RedSphere AND BlueSphere with drivers driver_Outer_RedSphere() &amp; driver_Outer_BlueSphere() limiting the display of each sphere to show only where each radius > halfway  On Layer-2 - foreground-1   I put RedSphere ONLY with driver driver_Inner_RedSphere() limiting the display of RedSphere to show only where its radius &lt;= halfway  On Layer-3 - foreground-2   I put BlueSphere ONLY with driver driver_Inner_BlueSphere() limiting the display of BlueSphere to show only where its radius &lt;= halfway    3) I rendered each layer to .PNG sequence [RGBA] (alpha channel for transparency)   Render Layer-1 - background   background : [sky]  Render Layer-2 - foreground-1   background : [transparent]  Render Layer-3 - foreground-2   background : [transparent]    4) I brought all 3 sequences into the Video Sequence Editor   Strip-1 - background   blend [cross] opacity [1.00]  Strip-2 - foreground-1   blend [alpha-over] opacity [0.50]  Strip-3 - foreground-2   blend [alpha-over] opacity [0.50]    5) Rendered the 3 layer final sequence to H.264  So the "aha moment" struck me right at the end when I was in the Video Sequence Editor:   "Don't try to make the Outer Spheres transparent, and see through to the Inner Spheres" "Instead overlay the Inner Spheres over the Outer Spheres, and limit the opacity of the Inner Sphere overlay"     So now I see my Inner Spheres in their true colours, but the colours are muted due to the .75 opacity - and hence it gives the visual impression that the Inner Spheres are in fact inside the Outer Spheres.  Thanks all for the input - it got me going in the right direction. Format timedelta to string How do I convert the coordinates of a click to a tilemap position? How do you turn a tilemap (produced by TileD) for cocos2d where I can click on individual items and get a callback?  Is it just a case of converting captured touch and finding out where it is on the tilemap and then converting that to pixels  -- but that doesn't say what item was clicked on.  I have a tilemap of a city with buildings on it, and I'd like to be able to click or press on a specific building, get a callback.  What would be the best way to accomplish this? What is the best introductory Bayesian statistics textbook? Which is the best introductory textbook for Bayesian statistics?  One book per answer, please. I was surprised to only recently notice that      An object of any density can be large enough to fall within its own   Schwarzschild radius.   Of course! It turns out that supermassive black holes at galactic centers can have an average density of less than water's.  Somehow I always operated under the assumption that black holes of any size had to be superdense objects by everyday standards.  Compare the Earth to collapsing into a mere 9mm marble retaining the same mass, in order for the escape velocity at the surface to finally reach that of light.  Or Mt. Everest packed into one nanometer.  Reading on about this , it increases proportionally with total mass.  Assuming matter is accumulated at a steady density into a spherical volume, the volume's radius will only "grow" at a cube root of the total volume and be quickly outpaced by its own gravitational radius.  Question: For an object the , what would have to be its diameter for it to qualify as a black hole (from an external point of view)?  Would this not imply by definition that:   The Earth, Solar system and Milky Way are conceivably inside this black hole? Black holes can be nested/be contained within larger ones? Whether something is a black hole or not is actually a matter of perspective/where the observer is, inside or outside? Backup of clients' directory to Windows Server 2008 We have a machine running Windows Server 2008, and we need to take backup of folder from a desktop on LAN. This folder is not shared.   Is there any tool or software to do this, or can a scheduled task be made which should automatically take the backup of that folder date-wise &amp; make a copy on server? Ie can we do it through Schedule Tasks option ?  Desktop systems have Windows Vista/Windows 7. Allowing all/different file type uploads Why is XOR preferred over XNOR? The XOR operator seems to be a frequently used building block inside many cryptographic primitives.  As far as I can see, its most desirable properties seem be that for the XOR of two bits $a\oplus b=c$:   The information is preserved.  Either $a$ or $b$ can be recovered from $c$ and the other bit. The information is hidden.  An adversary can not learn anything about $a$ or $b$ from $c$ alone.   Neither AND nor OR has these properties but XNOR does.  It seems like any cryptographic application using XOR could be constructed equivalently with XNOR, without incurring any loss in security.  One possible reason to prefer XOR might be that XOR is equivalent to addition modulo 2, whereas XNOR would be addition plus 1 modulo 2, but this seems to be entirely mathematical, and I'm not sure if it actually results in any additional hardware complexity in practice.  Is the choice of XOR then an arbitrary one, made for historical reasons, or is there any tangible underlying motivation for using it over XNOR? WPF DataGrid : CanContentScroll property causing odd behavior How do you determine the size of a file in C? How can I figure out the size of a file, in bytes?  #include &lt;stdio.h&gt;  unsigned int fsize(char* file){   //what goes here? } Who should own files shared by a group and where should they go Trouble creating 3TB ext4 partition due to msdos-partition-table-imposed error Bounty-like facility for rewarding excellent questions Amongst the reasons for starting a bounty, one can select:     Reward existing answer      One or more of the answers is exemplary and worthy of an additional bounty.   Why not enable one to reward excellent questions in a similar manner? Show that every group of prime order is cyclic