Perform a LEFT Join on Derived tables failing with aliases
What is the error "Every derived table must have its own alias" in MySQL?
What's the difference between a Long Term Support Release and a Normal Release? What are the differences between an Ubuntu Long Term Support release (LTS) and a normal release? Are there any simple rules for choosing the definite vs. indefinite (vs. none) article? I can’t for the life of me figure out where to use a and where to use the — and where there is no article at all. Is there a simple rule of thumb to memorize?   The standard rule you always hear:     “If a person knows which item you are talking about then use "the"   . . . doesn’t clear things up for me, as I have no idea whether or not they know. Why does gulp.src not like being passed an array of complete paths to files? Getting all the combinations in an array How to remove `t=canonical` from Firefox browser searches made on DuckDuckGo? I read an interesting question here in the forum () and came up with the following doubt: even though its diffraction angle is too small to be detected, if we had the possibility to detect it, what would the diffraction of a soccer ball through a pair of posts look like? I mean, in the case of electrons, there is a screen in which the diffraction pattern can be appreciated. But what about this case? Would we see lots of soccer balls in different places or what? Using the expression "the same" for a previously mentioned item I frequently use &quot;the same&quot; as in the following sentence.  I need the details of XYZ project. Could you please send me the same as soon as possible?  Is this grammatically correct? I have not been corrected till now, but I have not seen the usage from native speakers very much either. Update: Seems like my example sentence was ambiguous. Hope the following sentence is better.  I need the documents for the meeting. Could you please send me the same as soon as possible? A fiber bundle over Euclidean space is trivial. What's the easiest way to see this? The only thing I could think of was to try to patch together trivializations. I couldn't find a way to make that work. Thank you! edit: For the record, here's why I asked about this special case of the more general result about fiber bundles over contractible spaces. In the much beloved book by Bott and Tu, it's claimed that the Leray Hirsch theorem can be proven in the same way the Kunneth theorem is proven:  induct on the size of a finite good cover for the base space, then apply the Mayer Vietoris sequence and the Poincare lemma for the induction step. It's assumed that there exists a finite good cover for the base space, but it's not assumed that this cover is a refinement of the cover of the base space, which gives the local trivializations of the fiber bundle. Therefore, to apply the Poincare lemma in the induction step, it seems that you need to know that the result I asked about is true. Since fiber bundles had just been introduced in the text, I thought there may be a short, elementary proof that the authors had taken for granted. How to delete entry in Auto Complete in Microsoft Edge How do I delete an unwanted entry in AutoComplete in Microsoft Edge?  I have tried everything including highlighting with the down arrows and nothing works. Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated? Let $I$ be any ideal of $\mathbb {Z}[x]$, and $I=\left&lt;{f_1,f_2 , ...}\right&gt;$.  Without loss of generality, $f_1$ has minimal (absolute value) coefficient of constant term (if there exist).  Then, let $g$ be any element of $I$ .  We have for some integer $m$ that $g - mf_1$ is element of $I$ (minimal coefficient and division algorithm).  I guess this process terminate finitely, but I don't know how can I do next step.  ( ex. $g-mf_1, g-mf_1-nf_2, ...$)  Please help me and thanks for in advance. I'm looking for a word which indicates that a person has adopted a quality suggested by their name, e.g. a person named Grace who is indeed graceful, or perhaps someone named Shepherd who has become a shepherd.  I have a strong notion that I once learned such a word, but I have forgotten it and have never re-discovered it. Multiple I2C devices with the same address I have multiple devices with the same address, and only one I2C bus. If I don't want to/can't use an address multiplexer, will the following arrangement work? (sorry for the messy schematic)          &ndash; Schematic created using   SW1 and SW2 are microcontroller I/O, and are pulled low when we don't want to talk to the corresponding IC, and set to high impedance when we do want to talk to that IC. Can anyone see any problems with this, apart from with clock stretching? Assuming you choose diodes with a small voltage drop, like a schottky.  Edit:   Also assuming that the VIH and VIL all worked out with the diode drop and the VOH VOL.   The diodes could also go on the data lines instead, not sure if there would be any benefit/difference (maybe some I2C devices do something special when the clock goes low even if it's not their address? It's probably safer to not clock at all i.e. have the diodes on the clock lines. Quadrilateral problem with midpoints of diagonals For an arbitrary convex quadrialteral $ABCD$:   $$AF=FC, BE=ED, GI=IH$$  Prove that points $F$, $E$ and $I$ are collinear.  I was able to solve the problem by using vectors and I think that it can be also solved analytically but I wanted some more elegant proof, more in the spirit of Euclid. How can we prove that $D(f)\backsimeq\operatorname{Spec} A_f$? Let $$D(f)=\operatorname{Spec}A - V(f)=\{p\in \operatorname{Spec} A:f\notin p\}$$ be the principal open subsets of $\operatorname{Spec}A$ with the Zariski topology. I'm trying to prove that $D(f)\backsimeq \operatorname{Spec} A_f$, where $A_f$ is the localization of $A$ at $f$.  If we consider the canonical homomorphism $\varphi:A\to A_f$ given by $\varphi (a) = \frac {a}{1}$, we can define $\varphi':\operatorname{Spec} A_f\to \operatorname{Spec} A$, given by $\varphi'(p)=\varphi^{-1}(p),\forall p\in \operatorname{Spec}A_f$.  I'm having trouble proving that this map is surjective.  Thanks. What is the status icon that looks like a house? Is there a performance difference between i++ and ++i in C? Is there a performance difference between i++ and ++i if the resulting value is not used? Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$ Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$.   My approach:   Since $p$ is prime, it is of the form $6k+1$ or $6k-1$. Now if $p$ is of the form $6k-1$ then $(p+1)/2 = 3k$ which is not possible as $3|3k$.   So $p$ is of the form $6k+1$. Now $(p-1)/4 = 3k/2$ so $2\mid k$. So $p$ is of the form $12k+1$. But now, how to prove $k=1$?  Please help! Why do heavier objects fall faster in air? Let's say I have Windows installed on drive C, however I install all of my programs on the D drive, and I keep my user profile on the D drive as well (things like My Documents). How can I have Windows use those folders instead of the ones on the C drive? Is there a characterization of the nonconstant entire functions $f$ that satisfy $|f(z)|=1$ for all $|z|=1$?   Clearly, $f(z)=z^n$ works for all $n$. Also, it's not difficult to show that if $f$ is such an entire function, then $f$ must vanish somewhere inside the unit disk. What else can be said about those functions?  Thank you.