Re: [math-fun] "stealth" dark matter
To E. Salamin: No, the "stealth dark matter" hypotheses need not imply the existence of "dark atoms." Let "macroscopic" mean "with length scale greater than the length scale of the dark-stealth-analogue of the strong force." There are by assumption no macroscopic charged particles made of dark stealrth matter. Hence, no dark electrons. Hence no dark atoms. There are "dark nuclei" which would be detectable with photons since thery contain charged microsopic components, but only very shortwave photons could detect them, i.e. very high energy gamma rays.
2 (1 - 2 x) 1 -------------------- + ------------------- 3/2 Sqrt[-((-1 + x) x)] 4 (-((-1 + x) x)) Out[N]= ------------------------------------------ 2 (1 - 2 x) 3/2 (1 - ------------) 4 (-1 + x) x In[N+1]:= FullSimplify[%] 1 Out[N+1]= 2 Sqrt[-((-1 + x) x)] Sqrt[------] 2 x - x In[N+2]:= Simplify[%] 1 Out[N+2]= 2 Sqrt[-((-1 + x) x)] Sqrt[------] 2 x - x In[N+3]:= Expand[%] 1 Out[N+3]= 2 Sqrt[-((-1 + x) x)] Sqrt[------] 2 x - x --------------------------------------------- Okay, why does it not say 1 here? —Dan
On 2015-09-28 17:44, Dan Asimov wrote:
2 (1 - 2 x) 1 -------------------- + ------------------- 3/2 Sqrt[-((-1 + x) x)] 4 (-((-1 + x) x)) Out[N]= ------------------------------------------ 2 (1 - 2 x) 3/2 (1 - ------------) 4 (-1 + x) x
In[N+1]:= FullSimplify[%]
1 Out[N+1]= 2 Sqrt[-((-1 + x) x)] Sqrt[------] 2 x - x
In[N+2]:= Simplify[%]
1 Out[N+2]= 2 Sqrt[-((-1 + x) x)] Sqrt[------] 2 x - x
In[N+3]:= Expand[%]
1 Out[N+3]= 2 Sqrt[-((-1 + x) x)] Sqrt[------] 2 x - x
---------------------------------------------
Okay, why does it not say 1 here?
—Dan
Try Plot3D[Abs[ 2*Sqrt[x - x^2]*Sqrt[1/(x - x^2)] - 2 /. x -> u + I*v], {u, -2, 2}, {v, -2, 2}, PlotRange -> All, AxesLabel -> Automatic] If you want to live dangerously, In[408]:= PowerExpand[2*Sqrt[x - x^2]*Sqrt[1/(x - x^2)]] Out[408]= 2 FullSimplify[2*Sqrt[x - x^2]*Sqrt[1/(x - x^2)], Im[x] != 0||0 < Re[x] < 1] not giving 2 looks like a bug. --rwg
participants (3)
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Dan Asimov -
rwg -
Warren D Smith