Difference between classical spin and quantum spin
What is spin as it relates to subatomic particles?
When trying to restore a backup to a SQL Server Express 2008 database I got the following error:  Restore failed for Server '...\SQLEXPRESS'.  (Microsoft.SqlServer.SmoExtended) System.Data.SqlClient.SqlError: The database was backed up on a server running version 10.50.1600.  That version is incompatible with this server, which is running version 10.00.2531.  Either restore the database on a server that supports the backup, or use a backup  that is compatible with this server. (Microsoft.SqlServer.Smo)   Is there a way to get a backup which is compatible with the older (in my case 10.00.2531) version from the newer (in my case 10.50.1600) version of SQL Server Express? The third formula on the  states that $$\varphi (mn) = \varphi (m) \varphi (n) \cdot \dfrac{d}{\varphi (d)} $$ where $d = \gcd(m,n)$.  How is this claim justified?  Would we have to use the Chinese Remainder Theorem, as they suggest for proving that $\varphi$ is multiplicative? What invisible flicker do different types of light bulbs have? What waveform does the light coming off different types of artificial light sources have and (of course) what are the underlying physical reason for them?    I was inspired to ask this question because of several things I have been hearing lately.  Firstly, there was a recent TED talk about how .  Researchers have been working on the problem for a little while now and they've made a fairly impressive product, but it was only recently made possible by the LED technology, which has such a fast response that it can easily compare to the transfer rates of electric information condiuits that we normally use.  My understanding is that incandescent bulbs flicker because they have 60 Hz AC power being pulsed through them.  In fact, I think 60 Hz was chosen in the first place because it was a threshold that was unnoticeable to humans.  Looking at a  demonstrates that it has a very significant lag time responding to both the normal electrical phasor and being turned off.  In other words, it flickers but it doesn't go dark at any point in the AC waveform.  Looking for more information, however, I was a little disappointed, since nothing seemed to give a graph of lumens emitted over time for all different kinds of bulbs.  Of course, there isn't just one relevant time scale.  A light could flicker with 60 Hz and also flicker with 2000 Hz (I just made that up).  I'm interested in the complete picture of what lights exhibit what patterns. From time to time I lose all edits because of undo in Object Mode. If I enter immediately after Undo in Edit Mode I can't redo, and switching again in Object results in losing all edit history.  How can I resolve this? Separating undo history by mode or linear/unified will both be acceptable.  Edit:I think the most preferable solution will be to disable/skip edit undos when in object mode through an addon. Moving files of specific type/extension from one directory to another? In C++, sizeof('a') == sizeof(char) == 1. This makes intuitive sense, since 'a' is a character literal, and sizeof(char) == 1 as defined by the standard.  In C however, sizeof('a') == sizeof(int). That is, it appears that C character literals are actually integers. Does anyone know why? I can find plenty of mentions of this C quirk but no explanation for why it exists. Java: Detect duplicates in ArrayList? How does Cantor's diagonal argument work? I'm having trouble understanding Cantor's diagonal argument.  Specifically, I do not understand how it proves that something is "uncountable".  My understanding of the argument is that it takes the following form (modified slightly from the  article, assuming base 2, where the numbers must be from the set $ \lbrace 0,1 \rbrace $):  \begin{align} s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In this case, the diagonal number is the bold diagonal numbers $(0, 1, 1)$, which when "flipped" is $(1,0,0)$, neither of which is $s_1$, $s_2$, or $s_3$.  My question, or misunderstanding, is: When there exists the possibility that more $s_n$ exist, as is the case in the example above, how does this "prove" anything?  For example:  \begin{align} s_0 &amp;= (1,0,0,\mathbf{0},\dots)\ \ \textrm{ (...the wikipedia flipped diagonal)}\\ s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ s_4 &amp;= (0,1,1,\mathbf{1},\dots)\\ s_4 &amp;= (1,0,0,\mathbf{1},\dots)\ \ \textrm{ (...alternate, flipped } s_4\textrm{)}\\ s_5 &amp;= (1,0,0,0,\dots)\\ s_6 &amp;= (1,0,0,1,\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In other words, as long as there is a $\dots \text{ continues}$ at the end, the very next number could be the "impossible diagonal number", with the caveat that it's not strictly identical to the "impossible diagonal number" as the wikipedia article defines it:     For each $m$ and $n$ let $s_{n,m}$ be the $m^{th}$ element of the $n^{th}$ sequence on the list; so for each $n$,      $$s_n = (s_{n,1}, s_{n,2}, s_{n,3}, s_{n,4}, \dots).$$      ...snip...      Otherwise, it would be possible by the above process to construct a sequence $s_0$ which would both be in $T$ (because it is a sequence of 0s and 1s which is by the definition of $T$ in $T$) and at the same time not in $T$ (because we can deliberately construct it not to be in the list). $T$, containing all such sequences, must contain $s_0$, which is just such a sequence. But since $s_0$ does not appear anywhere on the list, $T$ cannot contain $s_0$.      Therefore $T$ cannot be placed in one-to-one correspondence with the natural numbers. In other words, it is uncountable.   I'm not sure this definition is correct, because if we assume that $m = (1, \dots)$, then this definition says that "$s_n$ is equal to itself"&mdadsh;there is no "diagonalization" in this particular description of the argument, nor does it incorporate the "flipping" part of the argument, never mind the fact that we have very clearly constructed just such an impossible $T$ list above.  An attempt to correct the "diagonalization" and "flipping" problem:  $$s_n = (\lnot s_{m,m}, \lnot s_{m,m}, \dots) \quad \text{where $m$ is the element index and} \quad\begin{equation}\lnot s_{m,m} = \begin{cases}0 &amp; \mathrm{if\ } s_{m,m} = 1\\1 &amp; \mathrm{if\ } s_{m,m} = 0\end{cases}\end{equation}$$  This definition doesn't quite work either, as we immediately run in to problems with just $s_1 = (0),$ which is impossible because by definition $s_1$ must be $ = (1)$ if $s_1 = (0)$, which would also be impossible because...   Or more generally, with the revised definition there is a contradiction whenever $n = m$, which would seem to invalidate the revised formulation of the argument / proof.  Nothing about this argument / proof makes any sense to me, nor why it only applies to real numbers and makes them "uncountable". As near as I can tell it would seem to apply equal well to natural numbers, which are "countable".  What am I missing? 90s (or earlier) movie with experimental, invisible, teleporting, time-traveling ship Do I need an airport transit visa through Switzerland (Schengen) if I have no Schengen visa? Do I need an airport transit visa through Switzerland if I have no Schengen visa? Am traveling from Cairo to Moscow via Swiss Air How can I make things link url references, my index, table of contents, and cross references clickable links in documents produced by LaTeX? I generally use pdflatex to produce my documents. Should you include press interviews and articles about your work in your CV? Is it appropriate to include interviews (published online or in print magazines) in an academic CV?   What about articles/news published about your works? I mean brief (one paragraph) news that professional magazines publish about significant research articles.  If yes, how do you do this to avoid exaggeration? Proving an inequality involving the logarithm function: $\frac{1}{n+1} \leq \ln \left(1+\frac 1n\right) \leq \frac 1n$ The question is to prove the inequality $$\frac{1}{n+1} \leq \ln \left(1+\frac 1n\right) \leq \frac 1n\\\forall n \geq 1, n\in \mathbb N$$  I tried using Taylor expansion but couldn't figure out anything. Any ideas? Thanks. 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? How does the lens diameter influence photo quality? I have tested two different 50mm lenses in my camera. One was a Nikkor 50mm ∅52mm. The other one was a Sigma 50mm ∅72mm. I took some pictures with both lenses using the same setup for aperture and shutter speed, but couldn't notice significant differences in the quality of the pictures.   So, how does the diameter affects the photo quality, if it does? What advantages would the ∅72mm lens have over the ∅52mm one? How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$? Given a string file path such as /foo/fizzbuzz.bar, how would I use bash to extract just the fizzbuzz portion of said string? How can a single slit diffraction produce an interference pattern? How can a light passed though a single slit produce a similar interference pattern to the double-slit experiment? How does the diffracted wave produce the points of cancellation and reinforcement, if there is only one wave? Kind of a strange question, but say something has spoiled, i.e. smells bad, tastes bad, etc.  Will it actually always make you sick? Like for instance spoiled dressing, let's say it tastes sour, smells nasty and you eat it, will it make you sick?  If so what actually makes you sick? The toxins/bacteria? or it just being unappetizing?  I ask because I tried a TINY bit of ranch and while it tasted mostly fine (it was a bit tangy) it smelled quite tangy but looked fine. I also saw . Reprojecting MODIS-Sphere ESRI GRID file to WGS84 using QGIS/GDAL I have an ESRI GRID file projected in MODIS-Sphere (here's the dataset ) that I need to convert to a WGS84 GeoTIFF.  I tried Raster > Projections > Warp (Reproject) and got this nonsense:   I then thought I'd use the MODIS reprojection tool or HEG to convert it, but they only accept HDF files and using QGIS' warp or translate functions to convert this file to HDF throwns an error. This guy was trying to do the same thing in Arc, no joy:   I looked for clues in the metadata, and the file seems a little goofy; gdalinfo yields:  Driver: AIG/Arc/Info Binary Grid Files: seto_uf        seto_uf.aux        seto_uf/.aux.xml        seto_uf/.DS_Store        seto_uf/dblbnd.adf        seto_uf/hdr.adf        seto_uf/log        seto_uf/metadata.xml        seto_uf/sta.adf        seto_uf/vat.adf        seto_uf/w001001.adf        seto_uf/w001001.tif        seto_uf/w001001.tif.aux.xml        seto_uf/w001001x.adf Size is 7468, 2911 Coordinate System is `' Origin = (-17345341.010356999933720,8423784.764957003295422) Pixel Size = (5000.000000000000000,-5000.000000000000000) Corner Coordinates: Upper Left  (-17345341.010, 8423784.765)  Lower Left  (-17345341.010,-6131215.235)  Upper Right (19994658.990, 8423784.765)  Lower Right (19994658.990,-6131215.235)  Center      ( 1324658.990, 1146284.765)  Band 1 Block=256x4 Type=Byte, ColorInterp=Undefined   Description = Seto_UF   Min=0.000 Max=101.000    NoData Value=255   So it can't determine the coordinate system.  There's a .tif included in the directory, but gdalinfo on that shows:  Driver: GTiff/GeoTIFF Files: w001001.tif        w001001.tif.aux.xml Size is 7468, 2911 Coordinate System is: GEOGCS["Unspecified datum based upon the GRS 1980 Authalic Sphere",     DATUM["unknown",         SPHEROID["unnamed",6371007,1]],     PRIMEM["Greenwich",0],     UNIT["degree",0.0174532925199433],     AUTHORITY["EPSG","4047"]] Origin = (-17345341.010356999933720,8423784.764957003295422) Pixel Size = (5000.000000000000000,-5000.000000000000000) Metadata:   AREA_OR_POINT=Area Image Structure Metadata:   INTERLEAVE=BAND Corner Coordinates: Upper Left  (-17345341.010, 8423784.765)  Lower Left  (-17345341.010,-6131215.235)  Upper Right (19994658.990, 8423784.765)  Lower Right (19994658.990,-6131215.235)  Center      ( 1324658.990, 1146284.765)    So it says the units are degrees but those huge corner coordinates and origin values don't agree.  Any ideas?  My setup: OSX 10.9.4 QGIS 2.6.1 Brighton GDAL 1.11.2 (apparently there are newer versions but this is the latest you can get on OSX without having to compile it yourself)