Roast Chicken vs Roasted Chicken
Roast duck vs. roasted duck
Is there a term for coining a phrase for a word that already exists? My question is the same as . I put my stackexchange flair at the bottom of my sites:     And get a &quot;profile for Ninsuo on Stack Exchange, a network of free, community-driven Q&amp;A sites&quot; link instead of my nice flair. By opening Firebug, I can read the following error:  Or as text:  NetworkError: 500 Internal Server Error -   I did not tried to update a new picture - just in case you want to get further first. Good luck! What to call the attitude of pursuing something Can not make hibernate on UEFI (Secure boot) How can I use colours to separate texture node treatment? How to Split Features in QGIS? prominently sports purple hair.    Is this her natural hair color?  Natural extensions in the answer depending on the correct answer: Is she wholly human and humans in the Galaxy Far Far Away can have this hair color?   Or is she partly human or not human?   Or does she dye her hair?   Or is there another hair color changing technology? A groupoid is defined to be a category where every morphism is an isomorphism. So sometimes a group is said to just be a groupoid with one object.   When I try to make sense of this, I denote the single object as $G$. I view the morphisms as the analogue of "elements." The identity $1_G$ is the analogue of the usual identity $e$, we can compose any two morphisms since they are all arrows on $G$, and for any arrow $f$, we have some $f^{-1}$ such that $f\circ f^{-1}=f^{-1}\circ f=1_G$, so the idea of inverses is still there.  So I informally associate the elements of the group in the usual definition to be the arrows in the groupoid. But what does the sole object $G$ in the groupoid "correspond to" if I were to try to informally make sense of a group in the usual sense? Does it even correspond to anything? Book series about aliens who put "caps" on people to control them I remember reading a series when I was around 7th or 8th grade about aliens who had taken over Earth by putting metal caps on people when they were "entering adulthood" to control them (not direct control, but it would keep them from rebelling). There was a faction of people who able to escape and had fake caps and would save teens who were about to be capped.  The main protagonist was a teen boy who was a boxer (or training to be a boxer or something). The aliens would hold tournaments for the humans and whoever won would be "worthy" to serve as personal slaves to the aliens.     The protagonist won and was able to get inside to try and learn more about the aliens from the inside. Add air resistance to projectile motion I am given an initial x and y position and initial velocity and I was asked to graph the trajectory in 1 second intervals.  This is what I have so far:  If $x_0 = 1, v_{0x} = 70, y_0 = 0, v_{0y} = 80, a_x = 0, a_y = -9.8$, and time will be 0,1,2,3... and so on.  Using these equations on every second you can find the plot will be a bell shaped with the highest point being ~ 325 m at about 600 seconds:   $$ x = x0 + (v_{0x})t + 1/2((a_x)t^2) $$ $$ y = y0 + (v_{0y})t + 1/2((a_y)t^2) $$  Usually in physics, we are taught in perfect condition with no air resistance. But what if there was air resistance? How would it affect this problem? How can i add it to my calculations and see what the difference is? Looking for a short story about an artist and a forger Back in the late 1970s to early 1980s, I read a short story about an artist and a forger.  Between the two of them, they managed to start a revolution that brought down a corrupt dictatorship.  It was science fiction:   The dictatorship was interplanetary, maybe interstellar.   The artist used some kind of advanced technology to make his art works.   Plot:  The artist is one of the best (if not the best) at what he does.  The dictator wants the artist to make what amounts to a family portrait in whatever medium it is he works in.  Think of it like painting - you create the image manually (not a photograph) but it is much more than just a flat image.    The artist doesn't like the dictator - maybe on general principles, maybe because he knows the dictator personally - and refuses to make the "portrait."  The dictator has the artist arrested, and will only let the artist free again if he makes the portrait.  The artists makes the portrait.  He does the work while in the prison or jail.  That's where the forger comes into things. The forger is also in jail for something or other.  The forger makes copies of art works.  He of course recognizes the artist, and knows what the artist works with.  The forger can somehow see what the artist is working on.  The artist finishes the portrait.  At first the dictator is thrilled.  It looks exactly the way he wanted it.  As time goes by, though, the people looking at the picture see that it represents the vileness and corruption of the dictator.  The more you look at it, the more of the evilness of the dictator you see in it.  That is the genius of the artist, and whatever medium he is using.  Once you notice the hidden levels of the portrait, you can't unsee them and you see more and more of it as you look.  I think the effect carries over into reality as well.  Once you've seen the dictator's corruption in the portrait you also begin to see it in the dictator and his works as well.  This of course seriously pisses off the dictator, who has the artist killed and the portrait destroyed.  While in prison, the forger watched as the artist created his masterpiece, and recognized it for the subversive thing it is.  He also recognized it as the ultimate rebellion from the artist - the artist knows what will be seen, and that he will be killed for it.  All of that inspires the forger to do something more meaningful with his life than make forgeries for the money.  The forger is released from prison.  He saw the completed portrait, and knows how it was made.  He begins making forgeries of the portrait - like, hundreds if not thousands of them.  These are distrubuted throughout the nation/empire.  The people realize what evil is controlling them once they see it in the copies of the portrait, and eventually a revolution rises and brings down the dictatorship.  It was probably older than the 1970s.  I expect earlier than 1960.  Any ideas? If $X,Y$ are independent $\chi ^2$ with $m$ and $n$ degrees of freedom, then $\frac{X}{X+Y} \sim\beta(m/2, n/2)$ I was reading  and I find the following problem: Let $X$ and $Y$ be independent $\chi ^2 $ with $m$ and $n$ degrees of freedom then $\dfrac{X}{X+Y} = \beta(m/2, n/2)$. Where $\chi^2(k)$ has density function $$f_{\chi^2(k)}(x)=\begin{cases}\displaystyle \frac{1}{2^{k/2}\Gamma(k/2)}\,x^{(k/2) - 1} e^{-x/2}&amp;\text{if }x&gt;0,\\ 0&amp;\text{if }x\le0 \end{cases} $$  I proved that $X+Y$ is $\chi ^2$ with $n + m$ degrees of freedom using the moment-generating function. If $Z=X+Y$ and $U=\dfrac{X}{X+Y}=\dfrac{X}{Z}$ using the formula for the density of the ratio of two independent random variables: $$f_U(u)= \int_{-\infty}^{\infty}f_X(uv)f_Z(v)|v|dv $$  then  $$\dfrac{u^{m/2-1}}{2^{(m+n/2)} \Gamma(m/2) \Gamma((m+n)/2)} \int_0^{\infty} v^{m+\dfrac{n}{2}-1} e^{-(v/2)(u+1)}dv $$  and using some algebra:  $$f_U(u)=\dfrac{u^{m/2-1} \Gamma(m+n/2)}{\Gamma(m+n/2) \Gamma(m/2) (u+1)^{m+n/2}}$$  and this is not $\beta(m/2, n/2)$, it looks more like $\beta(m/2, m/2+n/2)$ but $(u+1)^{m+n/2}$ is causing troubles.  I need help if something is false or any hint. Probably a basic issue, but still something that irks me and I can't find an answer online. I want to change the default folder for saving new shapes/processing outputs from &quot;last used folder&quot; to &quot;project folder&quot; or &quot;something in relation to project folder&quot; - is this possible? If so, how can I achieve this? How to solve ~(P → Q) : P & ~Q by natural deduction? I'm trying to solve the following by natural deduction:  ~(P → Q) : P &amp; ~Q  It's a trivial problem if identities are used, as can be seen by the following:   {1}      1.   ~(P → Q)                    Prem. {1}      2.   ~(~P ∨ Q)                   1 Mat. Impl. {1}      3.   ~~P & ~Q                    2 De Morgan's {1}      4.   P & ~Q                      3 DNE   Starting from step 2 of the previous proof, it's also fairly straightforward to reach a conclusion using natural deduction; i.e. starting from ~(~P ∨ Q), which is an identity of ~(P → Q):  ~(~P ∨ Q) :  P &amp; ~Q   {1}      1.   ~(~P ∨ Q)                   Prem. {2}      2.   ~P                          Assum. {2}      3.   ~P ∨ Q                      2 ∨I {1,2}    4.   ~(~P ∨ Q) & (~P ∨ Q)        1,3 &I {1}      5.   P                           2,4 RAA {6}      6.   Q                           Assum. {6}      7.   ~P ∨ Q                      6 ∨I {1,6}    8.   ~(~P ∨ Q) & (~P ∨ Q)        1,7 &I {1}      9.   ~Q                          6,8 RAA {1}      10.  P & ~Q                      5,9 &I   I also found that it's fairly easy to conclude ~Q:   {1}      1.   ~(P → Q)                    Prem. {2}      2.   Q                           Assum. {3}      3.   P                           Assum. {2,3}    4.   P & Q                       2,3 &I {2,3}    5.   Q                           4 &E {2}      6.   P → Q                       3,5 CP {1,2}    7.   ~(P → Q) & (P → Q)          1,6 &I {1}      8.   ~Q                          2,7 RAA ... {1,2}    12.  P & ~Q   In spite of how easy it looks, I can't figure out how to do it. I believe it can be done in 12 steps. Thanks! How do I execute a program X times in the terminal?  I read that I have to do a bin/bash txt, but I don't know how to execute this X times. Is a constant condition more costly than switching shaders? In general, branching in shaders is not a good idea. But now I have a shader with a condition that is constant with respect to the entire draw call. So the branch that is executed is always the same for one draw call.  Is such kind of branching still more costly than having multiple shaders without these branches and switch between them? I am able to solve simple differential equations like :  $$\dfrac{dy}{dx} = 3x^2 + 2x$$  We simply bring $dx$ to other site and integrate.  But how do we find solutions of differential equations like :  $$\frac{d^2x}{dt^2} + \dfrac{kx}{m} = 0$$  ?  We have been told the solution is $x(t) = A\cos ( \omega t + \phi_o)$ where $\omega\ =\sqrt{\dfrac{k}{m}}$  but how do we actually find it? Multiplicative inverses for $Z_n$ Improper integral $\sin(x)/x $ converges absolutely, conditionaly or diverges?  We have that $$\int_1^{\infty}\frac{\sin x}{x}dx$$ $$u=\frac{1}{x}$$ $$du=-\frac{1}{x^2}dx$$ $$dv=\sin xdx$$ $$v=-\cos x$$ $$\int_1^{\infty}\frac{\sin x}{x}dx=-\cos(1)-\int_1^{\infty}\frac{\cos x}{x^2}dx$$ $$\int_1^{\infty}\frac{\cos x}{x^2}dx&lt;\int_1^{\infty}\frac{1}{x^2}dx$$ So it converges. Now I need to find out if $\int_1^{\infty}|\frac{\sin x}{x}|dx$ converges or diverges. What does = +_ mean in JavaScript