Is there another term to specify who is being celebrated - e.g., @ a BD party?  ('Celebrant/celebrator' could be anybody celebrating, I believe. But isn't there a term which will specify the one/ones being celebrated?)  Is there, e.g., such a word as 'celebrantee,' or 'celebratoree'  (&amp;, if not, oughtn't there be (the situation comes up repeatedly))?  Thank you.
Something along the lines of 'hero of the occasion', but specifically for birthday? If there isn't, how would you otherwise say that?  ('the subject of birthday party', 'the hero of this birthday party', 'birthday's hero' all sound stupid somehow).
Error in if/while (condition) {: missing Value where TRUE/FALSE needed I have seen this mentioned a few times and I am not clear on what it means. When and why would you do this?   I know what interfaces do, but the fact I am not clear on this makes me think I am missing out on using them correctly.   Is it just so if you were to do:  IInterface classRef = new ObjectWhatever()   You could use any class that implements IInterface? When would you need to do that? The only thing I can think of is if you have a method and you are unsure of what object will be passed except for it implementing IInterface. I cannot think how often you would need to do that.   Also, how could you write a method that takes in an object that implements an interface? Is that possible? I was reading about the equipartition theorem and I got the following quotations from my books:  A diatomic molecule like oxygen can rotate about two different axes. But rotation about the axis down the length of the molecule doesn't count. - Daniel V. Schröder's Thermal Physics. A diatomic molecule can rotate like a top only about axes perpendicular to the line connecting the atoms but not about that line itself. - Resnick, Halliday, Walker s' Fundamentals of Physics.  Why is it so? Doesn't the rotation take place that way? Can you create images like this:    when you have something like  0 = green (#54ff00) 1 = white (#ffffff) 2 = red   (#ff0000) 3 = blue  (#0048ff)  Image (Python list of integers defined above): [[2,0,0,0,0,0,0],  [0,3,0,0,0,0,0],  [0,3,2,1,1,0,0],  [0,3,2,2,2,1,1],  [0,3,2,0,0,1,0],  [0,0,0,0,0,1,0],  [0,0,0,0,0,1,0]]   with TikZ?  How far I got  The following MWE defines all colors, produces a grid of the correct size (though the size is determined by hand):  \documentclass[varwidth=true, border=2pt]{standalone} \usepackage{tikz} \usepackage{xcolor}  \begin{document}     \newcommand\n{7}     \definecolor{green}{HTML}{54FF00}     \definecolor{wite}{HTML}{FFFFFF}     \definecolor{red}{HTML}{FF0000}     \definecolor{blue}{HTML}{0048FF}     \begin{tikzpicture}         \foreach \x in {1,...,\n}{             \foreach \y in {1,...,\n}{                 \begin{scope}[shift={(\x,\y)}]                   \draw [fill=green] (0,0) rectangle (1,1);                 \end{scope}             }         }     \end{tikzpicture} \end{document}   Of course, I could simpy make a lot of adjusted                   \begin{scope}[shift={(\x,\y)}]                   \draw [fill=green] (0,0) rectangle (1,1);                 \end{scope}   but I've wondered if this can (with reasonable effort) be done in TikZ / LaTeX.  My problem is giving TikZ the color array. I don't have any idea how to do this. I only know two types of looks in TikZ:  \foreach \x in {0,1,2,3,4,5}{...} \foreach \number in {1,...,\n}{...}   I have never seen a nested over a 2D-array. All I have seen so far were 1D-Arrays of tuples (with fixed tuple size). List all columns for a specified table Doesn't Radagast care about trees? In the book The Two Towers, Treebeard refers to Gandalf as "the only wizard that really cares about trees".  But in Fellowship of the Ring, we met the wizard Radagast the Brown, whose special focus is on animals, especially birds.  Of course, animals aren't trees, but it is difficult to imagine a person loving animals without also caring deeply about trees - especially when that person loves birds most of all, and so many birds are so  dependent upon trees for their survival.  More generally, Radagast seems like an all-around nature lover, and this too suggests that he "really cares about trees".  This leads me to imagine several possibilities:   Treebeard doesn't know Radagast (this seems unlikely - they have both been around for thousands of years, so surely they have bumped into each other at some point)   Treebeard forgot about Radagast, possibly because he was annoyed at Saruman and a bit angry at the time    Radagast actually doesn't care about trees    Is there some other alternative I have overlooked, or is one of the options I mentioned correct?  Or does Tolkien never address this apparent problem? Simple way to see a list of installed iOS apps with their storage space size? How do I install transition molding between my new hardwood and existing tile floors? I have ripped out some old carpet and am preparing to install a new solid hardwood floor myself.  In several places, the floor transitions to an existing tile floor.  The hardwood floor guys told me the best transition between the two is a T molding.  You simply leave a gap between the two floors, and then place down the T molding between the two floors, so it sits on both surfaces.  Sounds simple enough.  However, the height difference of the two floors is considerable, and the T molding does not sit flush.  What are my options?  Here is a diagram showing the dimensions.      NOTE:  Using the T molding is not a requirement, I could go some other route if there is a better option. Session lost when switching from HTTP to HTTPS in PHP When sending the user to a checkout page, they are switched from http://sitename.com to https://sitename.com.  As a result, $_SESSION variables are lost.  The site has a valid SSL certificate which may or may not be of some use. How to zero out a drive? How to add new element to Varargs? I've recently been learning about differential equations, and my teacher has been giving some particularly difficult examples out for those of us who finish early. He gave us the following differential equation: $$x=y\frac{dy}{dx}-\left(\frac{dy}{dx}\right)^{2}$$ With the hint "Differentiate with respect to $y$, then let $\frac{dy}{dx}=p$". I've solved it after the lesson and would like someone to check whether or not I've done so correctly.    Following the hint, $$\frac{dx}{dy}=\frac{1}{p}=p+y\frac{dp}{dy}-2p\frac{dp}{dy}$$ Which rearranges to $$p-\frac{1}{p}+y\frac{dp}{dy}=2p\frac{dp}{dy}$$ Multiplying through by $\frac{dy}{dp}$, $$\left(p-\frac{1}{p}\right)\frac{dy}{dp}+y=2p$$ Rearranging into the form $\frac{dy}{dp}+f(p)y=g(p)$, and writing $p-\frac{1}{p}=\frac{p^{2}-1}{p}$ $$\frac{dy}{dp}+\frac{p}{p^{2}-1}y=\frac{2p^{2}}{p^{2}-1}$$ Our integrating factor is $$e^{\int\frac{p}{p^{2}-1}dp}=e^{\frac{1}{2}\ln(p^{2}-1)}=\sqrt{p^{2}-1}$$ So we have $$\sqrt{p^{2}-1}\frac{dy}{dp}+\frac{p}{\sqrt{p^{2}-1}}y=\frac{2p^{2}}{\sqrt{p^{2}-1}}$$ The left hand side is, by design, $\frac{d}{dp}(y\sqrt{p^{2}-1})$, and the right hand side can be integrated as follows: $$\int \frac{2p^{2}}{\sqrt{p^{2}-1}}dp=\int\frac{2(p^{2}-1)+2}{\sqrt{p^{2}-1}}dp=\int 2\sqrt{p^{2}-1}dp+\int \frac{2}{\sqrt{p^{2}-1}} dp$$ These can both be solved using the substitution $p=\cosh(u)$, and gives $$y\sqrt{p^{2}-1}=p\sqrt{p^{2}+1}-\cosh^{-1}(p)+\alpha$$ Where $\alpha$ is an arbitrary constant. Dividing, we finally have $$y=p+\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}$$  Here I was stuck for a long time, until I realised that we also have the equation we began with: $x=py-p^{2}$, which we can solve as a quadratic in $p$ to also get $$p=\frac{y\pm \sqrt{y^{2}-4x}}{2} \implies p^{2}=\frac{y^{2}+y^{2}-4x \pm 2y\sqrt{y^{2}-4x}}{4}$$  Thus, $$y=\frac{y\pm \sqrt{y^{2}-4x}}{2}+\frac{\cosh^{-1}\left(\frac{y\pm \sqrt{y^{2}-4x}}{2}\right)+\alpha}{\sqrt{\frac{y^{2}-2x \pm y\sqrt{y^{2}-4x}}{2}-1}}$$  This is as good as I can do - we have a relation between $y$ and $x$ - am I done? Is this the correct answer? Is there an easier way?     Thank you for your time.    Following the suggestion by @Valentin $$\frac{dy}{dp}=1+\frac{\frac{1}{\sqrt{p^{2}-1}}\sqrt{p^{2}-1}-p\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}}{p^{2}-1}=1+p\frac{1-\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}}{p^{2}-1}$$ Hence, $$dx=\frac{dy}{p}=dp\left(\frac{1}{p}+\frac{1-\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}}{p^{2}-1}\right)$$ How can I debug my JavaScript code? Can we build capacitors on a PCB board? For the magnitude of nF or µF capacitors, I hope I can build them on a PCB board. The capacitor is like a two metal layer and something between them.   Is this possible?   Not buying the capacitor, just design the capacitor on the PCB board. Double metal layers on the PCB board. This is the problem I am currently having trouble with:  If $\lambda_1$ and $\lambda_2$ are eigenvalues of matrix  $$         \begin{bmatrix}         a &amp; b\\         c &amp; d\\         \end{bmatrix}$$prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$.     $$A=\begin{bmatrix}     a^2 &amp; ab &amp; b^2\\     2ac &amp; ad+bc &amp;2bd\\     c^2 &amp; cd &amp;d^2\\     \end{bmatrix}$$  What have I considered so far:   I tried to find characteristic polynomial of first matrix and then find the roots which would be $\lambda_1$ and $\lambda_2$. I was hoping I can make a connection with characteristic polynomial of matrix $A$, but it got too complicated and did not seem like the right idea. Since there are two eigenvalues for first matrix, there are two eigenvectors. I thought about somehow using $A\vec v_i=\lambda_i\vec v_i$, where $i=1,2$  Also, I thought about finding a connection between these two matrices. What I see is that the sum of elements of first and second column, of first matrix, are $(a+c)$ and $(b+d)$, respectively.  Sum of first, second and third column of matrix $A$ are $(a+c)^2, (a+c)(b+d)$ and $(b+d)^2$. Now, if I could assign $\lambda_1$ and $\lambda_2$ to $(a+c)$ and $(b+d)$, then I would get that sum of first, second and third column of matrix $A$ are $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$, but what would be next?   I thought it would be good to combine 2. and 3rd idea, but I am not making any progress.  I appreciate any help. Notation question: $\ll$ Checkbox in listview control Can you have a multicolumn listview control where one of the columns is a checkbox?  Example code or links would be greatly appreciated.  I am using visual studio 2005 How to do integer & float calculations, in bash or other languages/frameworks? Using echo "20+5" literally produces the text "20+5".  What command can I use to get the numeric sum, 25 in this case?  Also, what's the easiest way to do it just using bash for floating point? For example, echo $((3224/3807.0)) prints 0 :(.  I am looking for answers using either the basic command shell ('command line') itself or through using languages that are available from the command line. How to disable automount in nautilus's preferences List creation/manipulation