Express in the form $A\sin(x+c)$ a) $\sin x+\sqrt3\cos x$; b) $\sin x-\cos x$ sol: a) $A=\sqrt{1+3}=2$, $\tan c=\frac{\sqrt 3}1$, $c=\frac\pi3$. So $\sin x+\sqrt3\cos x=2\sin(x+\frac\pi3)$ b) $\sqrt 2\sin(x-\frac\pi4)$ Can someone please explain the method used in the provided sol...

I am aware of Gibbs measures, given the energy (Hamiltonian) of an arrangement, one can determine the frequency of the arrangement. Plug the energy level in the Boltzman equation and there you go. I also just found out that the variational theorem is used in the Fock Hartree method in order to ...

I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow, I already have difficulties in penetrating the literature... I'd highly appreciate any help with the following question: My aim is to relate a certain (equivariant) linear sigma mode...

I recently read about the Ring Game on MathOverflow, and have been trying to determine winning strategies for each player on various rings. The game has two players and begins with a commutative Noetherian ring $R$. Player one mods out a nonzero non-unit, and gives the resulting ring to player 2,...

Did the 12-27-2004 gamma ray burst cause any illness affects upon life on earth? Do we know what hemisphere of the earth or portions of the earths surface received the highest radiation? What was the time duration of the radiation as observed on the earth? If one hemisphere was exposed to the maj...