First $\text{f}\left( 1 \right)=1$ beacause  $\text{f}\left( a \right)^{\text{f}\left( 1 \right)}=\text{f}\left( a \cdot 1 \right)$, and $\log_{\text{f}\left( a \right)} \text{f}\left( a \right)^{\text{f}\left( 1 \right)} =\text{f}\left( 1 \right) \log_{\text{f}\left( a \right)} \text{f}\left( a \right) =1$  If $\text{f}\left( 2 \right) = c$ then $\text{f}\left( 2 \right)^{\text{f}\left( 2 \right)}=\text{f}\left( 4 \right)$ so $\text{f}\left( 4 \right)=c^c$ so there should be only one  group of functions as a solution.  So if $\overbrace{x^{\text{...}^{x}}}^{\text{n times}}=2$ then $\overbrace{{\text{f}\left( x \right)}^{\text{...}^{{\text{f}\left( x \right)}}}}^{\text{n times}}={\text{f}\left( 2 \right)}$ then the $n$th super root of $c={\text{f}\left( x \right)}$, $n=\text{slog}_x2$ so ${\text{f}\left( x \right)}$=the $\text{slog}_x2$ root of c.  I am rather incompetent of my answer so if someone could look it over that would be great.  Super roots and slogs
Consider the functional equation problem $$ f : \mathbb R \to \mathbb R \text , $$ $$ f \left( a ^ b \right) = f ( a) ^ { f ( b ) } \text , $$ when $ a , b \in \mathbb R $, $ a , b \ge 0 $. So far the only solution I have is the trivial $$ f ( x ) = x \text . $$ Does there exist any other possible solution? Even if the $ f $ doesn't have a closed form in terms of elementary functions, is there some way I could derive a series or an alternative expression for it? I tried to get a little more creative: $$ f ( w ) = f \left( w ^ { \frac 1 w } \right) ^ { f ( w ) } \text , $$ which nests deep into $$ f ( w ) = f \left( w ^ { \frac 1 w } \right) ^ { f \left( w ^ { \frac 1 w } \right) ^ { f \left( w ^ { \frac 1 w } \right) ^ \vdots } } \text , $$ which is equivalent to $$ \ln \big( f ( w ) \big) = \ln \bigg( f \left( w ^ { \frac 1 w } \right) \bigg) f ( w ) \text . $$ I was hoping to generate some sort of series using this.
New line in Sql Query Recovering data from a faulty disk When I plug in a removable 1TB USB disk in my laptop, the operations led keeps blinking for a while and then you can hear the servo mechanism resetting with a short "tack".  I'd like to recover the data.    I believe there might be some way to get the data through low level IOs.    What I believe is that the mounting process assumes the disk is OK and I should prevent this before using ddrescue or something similar.  Does anybody have a solution to this problem? What is the best way to give a C# auto-property an initial value? Strange book where teen protagonist is sent to a warzone, uses illusory magic to grow male genitalia $n$th derivative of $e^x \sin x$ Finding distance between points in two different layers along route in ArcMap? I need to find the distance between points in separate layers along a stream network. I have source sites for macro-invertebrates and sites where they are lacking. I need to find the distance between the source sites and the sites where they are not through the stream network.   I tried the linear referencing toolbox but the locate features along route tool can only use one layer of points and has not way to differentiate between sources and not source sites.  Any ideas?  I am using ArcMap 10.3? Is $\{0\}$ a field? Consider the set $F$ consisting of the single element $I$.  Define addition and multiplication such that $I+I=I$ and $I \times I=I$ .  This ring satisfies the field axioms:   Closure under addition.  If $x, y \in F$, then $x = y = I$, so $x + y = I + I = I \in F$. Closure under multiplication.  $x \times y = I \times I = I \in F$ Existence of additive identity.  $\forall x \in F$ (i.e., for $x=I$), $x + I = x$, so $I$ is the additive identity. Existence of mulitiplicative identity. $\forall x \in F, x \times I = x$, so $I$ is the multiplicative identity. Additive inverse. $\forall x \in F, \exists y = I \in F: x + y = I$ Multiplicative inverse. $\forall x \in F, \exists y = I \in F: x \times y = I$.  However, because the additive identity need not have a multiplicative inverse, this is a vacuous truth. Commutativity of addition.  $\forall x, y \in F, x + y = I = y + x$ Commutativity of multiplication.  $\forall x, y \in F, x \times y = I = y \times x$ Associativity of addition.  $\forall x, y, z \in F$, $(x + y) + z = I + I = I$ and $x + (y + z) = I + I = I$, so $(x + y) + z = x + (y + z)$ Associativity of multiplication.  $\forall x, y, z \in F$, $(x \times y) \times z = I \times I = I$ and $x \times (y \times z) = I \times I = I$, so $(x \times y) \times z = x \times (y \times z)$ Distributivity of multiplication over addition. $I \times (I + I) = I$ and $I \times I + I \times I = I$, so $\forall x,y,z \in F, x(y+z) = xy+xz$   Based on the above, $\{I\}$ seems to qualify as a field.  If $I$ is assumed to be a real number, then the unique solution of $I + I = I$ and $I \times I = I$ is, of course, $I = 0$.  So, is {0} a field, or is there generally considered to be an additional field axiom which would exclude it?  Specifically, is it required for the multiplicative identity to be distinct from the additive identity? Let $f$ be a complex function with the property that $f^{(n)} = 0$.  Does this imply that $f$ is a polynomial?  If so, why?  Upon thinking about this problem myself, I can easily observe that every $n$ degree polynomial satisfies $f^{(n+1)} = 0$.  Still, this doesn't show that some non-polynomial function couldn't also have this property. Rewriting a custom-post-type permalink with taxonomy term? What should one look for when buying a used film camera? I'm planning to buy a used Nikon F5.   I have no experience with a film camera and I want to know what all should one be careful of before buying a used film camera and more specifically a Nikon F5. Transferring a Windows 8 license and proper un- and reinstallation Long story short  I have two computers: a laptop and a desktop computer. Both have Windows 7 on them.  I buy the Windows 8 Pro upgrade. To see if it screws up anything, I install it on my laptop as a guinea pig. I intend to use Windows 8 for my main computer, my desktop, but I want to test it on the laptop, so I know I don’t risk losing access to my desktop and the data on it. I never use my laptop, and only used it, because it already has a Windows 7 installation on it.  The problem  At some point, I must have entered the license key on my laptop, because when I go to the activation screen on my desktop, I get this:    Uh-oh. I can’t use the key on my desktop. Now how the hell do I transfer the key from my laptop to my desktop computer?  Answers and suggestions so far  Let’s just say that I tried everything possible to get some answers on this matter. The best response I got from Microsoft is this:     To install Windows 8 on your desktop, do the following:         Uninstall Windows 8 on your laptop   Afterwards, install Windows 8 on your desktop   If it won’t activate, call product activation at (...)      I am not a fan of that last point. The error message does allude to such a solution, however:     If you’ve reinstalled Windows or made changes to your hardware recently, you may be able to use your current key.   The question  My main question is this: has anyone been in a similar situation, and if so, what did you do to resolve this?  Failing that, what is the proper way to   uninstall the Windows 8 installation on my laptop, and reinstall the Windows 8 installation on my desktop?   Ad 1  I have already tried using the “reset” feature on my laptop, but that only resulted in a new Windows 8 installation that was already activated. But which is the right way to uninstall the installation in a way that allows me to use the license key on the desktop computer?  Ad 2  Which is the proper way to reinstall the Windows 8 installation on my desktop computer? Why do I even have to reinstall it in the first place?  I won’t get around to do this, until my USB key with 3.0 support arrives in the mail, but it is going to be a while, until I find a assuaging response to the best way to go about this anyway. Placement of varistor with respect to fuse My design includes a pretty standard AC/DC converter powered by mains for intended use at home. For overvoltage and overcurrent protection, I am planning to use a combination of varistor and fuse placed before the power converter.  I understand it is good practice to put the fuse before the varistor - in an overvoltage event, the varistor will draw a large current that may blow the fuse, protecting the rest of the circuit and even the upstream circuitry.  However, due to extremely tight layout, it is very hard to put the fuse before the varistor.  What risk am I running if I put the varistor before the fuse?  What if I put a second fuse in series with the varistor? Does it negate the varistor's protection of the downstream circuit? How to convert hex string to float in Java? Conditionals (Past Tense) In terms of conditional sentences, is it correct to say:   if you knew why I WAS here, then I wouldn't need to be here.   or   If you knew why I WERE here, then I wouldn't need to be here.   Which type of conditional is this? Type 2? I was thought at school that there are three types of conditionals. Are there more of them? How can I disable the “News and Interests” Widget on the Windows 10 Taskbar? On Windows 10 version 1909 and newer releases, Microsoft has added a &quot;News and Interests&quot; widget on the Taskbar (see ):  How can I remove this Widget from the Taskbar? "In the Internet" vs. "on the Internet" When should I use "in the Internet" and when "on the Internet"? What happens, if a rocket is filled with a vacuum instead of high pressured air? Suppose you put wheels under a compressed air tank    so that it can move horizontally to the right and to the left. Suppose there is a nozzle on the right hand side of the tank (in the picture on the backside, if you like).  If the tank is filled with high pressured air and you open the nozzle, the tank will move to the left. This is how rockets work and one can easily imagine that.   What happens when the tank is filled with a vacuum and you open the nozzle?  My first impression was, that the tank is moving to the right but someone told me, that it would be stand still. Is this true? What is an intuitive explanation for that? Simple question:     My apples and orange are wrong   or     My apples and orange is wrong   I am not a native English speaker, and I am having some trouble choosing between plural are or singular is for that kind of example. Consequences of a master thesis with errors I finished my master thesis 6 years ago, since then I gained a lot of experience on my field and also in academia. I can say that in that time I was a "child" , very inexperienced. I think that also my advisor did not help a lot, and I tried to do  a lot of things by my own, without someone to really review my things. Despite that, I still received a good mention by the master committee on final results.   Some days ago, I just decided to read part of master thesis, and I just realized a big nightmare coming. I identified a lot of typos, some references errors, and some improvements that I should do, but I did not. The worst thing is that I wrote a paper to a conference with my master thesis results (and some errors are there). The conference is not a high impact conference, but still the paper has my name and is available for everyone...   As I am finishing my PhD studies for now, I am concerning a lot that situation. My dream and goal is to pursue a Professor career. So, my questions are: What are (or could be) the consequences of a master thesis and paper with errors (some minor and some major) in academia? Revoke degree after years by errors in master is possible ( I am concerning a lot this situation that I thought on it)? How can I minimize it (I thought that I can put a fixed version of my thesis and paper in the future, for instance on my personal website)? How those errors can impact me in a Professor recruitment process?  Sorry for the long text, I am blaming myself all the time, and really afraid about the possibilities since I know that Academia career is really competitive. how to add xsl attribute