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PHP PDOException: "SQLSTATE[HY093]: Invalid parameter number"
$p=4n+3$ never has a Decomposition into $2$ Squares, right? Primes of the form $p=4k+1\;$  have a unique decomposition as sum of squares $p=a^2+b^2$ with $0&lt;a&lt;b\;$, due to .  Is it correct to say that, primes of the form $p=4n+3$, never have a decomposition into $2$ squares, because sum of the quadratic residues $a^2+b^2$ with $a,b\in \Bbb{N}$ $$ a^2 \bmod 4 +b^2 \bmod 4 \le 2? $$  If so, are there alternate ways to prove it? Find Nearby Accounts migration to Google Maps API v3 we have been using the Find Nearby Accounts app from appexchange for a while now. The app uses the Google Maps API vs 2 which is now deprecated and hence has rendered the app ineffective. I have tried migrating the Google maps API version for the app from v2 to v3 by generating a v3 API key. The URL for my salesforce instance was included in the creation of the Client ID under API Access. After all these steps, I still get the error "Problem with Address. I know the address is right.   Has anyone been able to get this working? Thanks. What is the best regular expression to check if a string is a valid URL? How can I check if a given string is a valid URL address?  My knowledge of regular expressions is basic and doesn't allow me to choose from the hundreds of regular expressions I've already seen on the web. Normal subgroup of a normal subgroup Let $F,G,H$ be groups such that $F\trianglelefteq G \trianglelefteq H$.  I am asked whether we necessarily have $F\trianglelefteq H$. I think the answer is no but I cannot find any counterexample with usual groups. Is there a simple case where this property is not true? This is a homework question. But I am completely stuck.  My only intuition was to go about it inductively from a "greedy algorithm" maybe know as the deletion-contraction algorithm. And to somehow use the information about the jth cycle to solve the j+1th. But I'm not sure how I'd do it. Thank you very much for looking this over. If a tag wiki becomes inaccessible due to a tag being eliminated, is the data destroyed? Or would it be able to be recovered by just recreating the tag?  On Gaming we had one tag for a particularly difficult case that a wiki entry was written for. There has been some debate as to what we should keep the tag as, which has led to the only instance of the tag being renamed a few times and eventually left on a new tag. The nightly script eventually cleaned out the original tag, and the wiki is inaccessible. So would I be able to retrieve this by reverting to the original tag, or is a rewrite of the wiki necessary? Fields finitely generated as $\mathbb Z$-algebras are finite? Suppose $k$ is a field that is finitely generated as a ${\mathbb Z}$-algebra.  (That is, $k$ is a quotient of ${\mathbb Z}[X_1,\dots,X_n]$ for some $n$). Does it follow that $k$ is finite? ascending/descending in LINQ - can one change the order via parameter? What's the best way to version CSS and JS URLs? The following problem was on a math competition that I participated in at my school about a month ago:      Prove that the equation $\cos(\sin x)=\sin(\cos x)$ has no real solutions.   I will outline my proof below.  I think it has some holes.  My approach to the problem was to say that the following equations must have real solution(s) if the above equation has solution(s):  $$ \cos^2(\sin x)=\sin^2(\cos x)\\ 1-\cos^2(\sin x)=1-\sin^2(\cos x)\\ \sin^2(\sin x)=\cos^2(\cos x)\\ \sin(\sin x)=\pm\cos(\cos x)\\ $$  I then proceeded to split into cases and use the identity $\cos t = \sin(\frac{\pi}{2} \pm t\pm y2\pi)$ to get   $$ \sin x=\frac{\pi}{2} \pm \cos x\pm y2\pi\\ $$  and the identity $-\cos t = \sin(-\frac{\pi}{2}\pm t\pm y2\pi) $ to get   $$ \sin x=- \frac{\pi}{2}\pm \cos x \pm y2\pi.\\ $$  where $y$ is any integer.  I argued that $y=0$ was the only value of $y$ that made any sense (since the values of sine and cosine remain between $-1$ and $1$).  Therefore, the above equations become   $$ \sin x=\frac{\pi}{2} \pm \cos x\implies \sin x \pm \cos x=\frac{\pi}{2}\\ $$  and   $$ \sin x=- \frac{\pi}{2}\pm \cos x\implies \cos x\pm\sin x= \frac{\pi}{2}.\\ $$  Then, by a short optimization argument, I showed that these last two equations have no real solutions.  First, does this proof make sense?  Second, if my proof makes sense, then I feel that it was not very elegant nor simple.  Is my approach the best, or is there a better (i.e., more elegant, shorter, simpler) proof? C++ cast syntax styles I want to compile my program with the latest version of gcc.  Ubuntu 14.04 comes with gcc 4.8.2, however there's 4.9.0 available, moreover, I see that it is available as a package: . I tried to install it  sudo apt-get install gcc-4.9   but it says  Reading package lists... Done Building dependency tree        Reading state information... Done Note, selecting 'gcc-4.9-base' for regex 'gcc-4.9' gcc-4.9-base is already the newest version. 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   Looks like it is already installed, just not as the default one? How do I utilize it to build my program? I have a Unicode string in Python, and I would like to remove all the accents (diacritics). I found on the web an elegant way to do this (in Java):  convert the Unicode string to its long normalized form (with a separate character for letters and diacritics) remove all the characters whose Unicode type is &quot;diacritic&quot;.  Do I need to install a library such as pyICU or is this possible with just the Python standard library?  And what about python 3? Important note: I would like to avoid code with an explicit mapping from accented characters to their non-accented counterpart. I have a point layer in QGIS. Each point represents a tree and each tree has information about its height as an attribute. I would like to build a query/expression to select all those trees that have an other tree higher than 7 meters within their 20-meter-buffer (20 meter radius).  I managed to do this "manually" by creating a 20-meter-buffer around all trees higher than 7 meters (after the selection of the trees higher than 7 meters) and then selected the ones within the buffer but I was wondering if its possible with a query/expression.  (maybe with a bit more complex one)  Unfortunately I do not have PostGIS so this should be done with Select by expression or Query Builder if possible.  (It would be also helpful to know if it's simply impossible) I'm reading the Algebra book by Knapp and he mentions in passing that an orthonormal set in an infinite dimension vector space is "never large enough" to be a vector-space basis (i.e. that every vector can be written as a finite sum of vectors from the basis; such bases do exist for infinite dimension vector spaces by virtue of the axiom of choice, but usually one works with orthonormal sets for which infinite sums yield all the elements of the vector space).  So my question is - how can we prove this claim? (That an orthonormal set in an infinite dimension vector space is not a vector space basis).    Edit (by Jonas Meyer): Knapp says in a footnote on  of Basic algebra:     In the infinite-dimensional theory the term "orthonormal basis" is used for an orthonormal set that spans $V$ when limits of finite sums are allowed, in addition to finite sums themselves; when $V$ is infinite-dimensional, an orthonormal basis is never large enough to be a vector-space basis.   Thus, without explicitly using the word, Knapp is referring only to complete infinite-dimensional inner product spaces. How do I create an Ubuntu live USB using a Mac? I'd like to create an Ubuntu live USB stick on a Mac to use to install Ubuntu on another machine. How do I accomplish this? I have a computer with a video card that has no Linux support.  I discovered this issue while trying to use a persistent usb to boot from.   I found that I can boot like that if I change options and edit so as to add nomodeset there (see ).  Also, editing the syslinux.cfg file from my live persistent USB and adding nomodeset in a line there made this setting automatic for booting from the persistent USB.  Can I make a similar edit for proper install from the same live USB?  Is it possible to edit something on the live USB in order to install the SO from it,  -- that is: having automatically the nomodeset setting already there when the installation starts?  My problem is that in order to install I think I already have to have added nomodeset or I'll see nothing on my display. I need a way to be sure that nomodeset it's permanent from the start. Consider a string under tension, for example, a string on a guitar. When a guitar string is plucked, it vibrates at a certain frequency. When the tension on the string is increased by twisting the tuning peg at the end of the neck, the frequency of the string increases. According to , increasing the tension on a string also increases the speed of the wave moving through it. According to  the speed of a wave is higher in a more dense medium.  Does this mean that increasing the tension also increases the density?  This does not seem very logical to me, since density is the "compactness" of a substance, or how close together the individual molecules are. By twisting the tuning peg on a guitar, you rotate the cylinder that the string is fixed to, wrapping it around more tightly. This pulls more of the string around that cylinder, similarly to when you reel in a fishing rod. Since more of the string's molecules are now wrapped around the peg, there should be fewer molecules over the same distance between the bridge and the nut (the two ends of the vibrating portion of the string), therefore bringing the density down. Would it be considered cheating to ask for homework help on the internet, if I openly acknowledge the help received? Roll back from OS X Mavericks ( or any newer OS) to Mountain Lion I installed the developer preview of OS X Mavericks, &amp; too many things broke. I can't stay on it &amp; need to roll back to Mountain Lion. Any ways of doing that? Please help!  I originally installed Mountain Lion &amp; Mavericks through the Mac App Store.