Recent content by mad mathematician

You can also publish your work in researchgate, or in your own blog. The only reason to get publish in peer reviewed journals is perhaps to get a "decent" work in academia. When you understand that most papers in the arxiv or in journals aren't being read, you less give an acclaim for this...

Well this book is more semi-popular. Someone who didn't even take a UG course in GR wouldn't understand the terms being used there. I guess he didn't publish his miscalculation, otherwise it was well known I think.

I am reading Hawking's and Penrose's joint book called:" The Nature Of Space and Time". And on page 98 it's written the following:"I have tried to show that the entropy of such a universe would be quarter of the area of the event horizon at the time of maximum expansion (fig. 5.12). However, at...

Hawkinng-Unruh virtual-real explosion... Have you ever wondered when virtual particles meet their real relatives? or anti-real relatives? Just kidding, I tried the other day to read BFSS paper... hard stuff to read. :oldbiggrin:

I really don't understand why I didn't think about it while I learned UG topology back then. The usual definition of Compactness is that every open cover of the compact space can be covered by a finite union from the arbitrary cover. What about looking at a set that is covered by the...

Hi, can anyone tell me how to derive equation eq (3.64) from equation (3.59)? attached are the relevant pages:

Don't trust Gemini, try GPT (the pro version).

An interesting variation may be this one: ##u_{xx}+6u_x+9u_y=0##, which can be solved by the method of characteristics: ##dx/ds=6, dy/ds=9, du/ds=-u_{xx}##, ##x(s)=6s, y(s)=9s## plug and get: ##du/ds=-1/36 d^2u/ds^2## which can be solved by repeated integration to get: ##du/ds+36u=c##. Easy...

it looks like the solution is ##u(x,y)=g(y)e^{rx}##. And as you know you get ##r=-3## with multiplicity 2; so the general solution is: ##u(x,y)=A(y)e^{-3x}+B(y)xe^{-3x}##.

Have fun! (but not too much... :oldbiggrin: ).

Ok, now I can proceed reading the book. Great website! as always.

I am trying to derive equation (3.61) below (the attachments are from pages 51-53). As far as I can tell, one can get (3.61) from (3.59) directly, just plug ##x=x'## and ##t-t'=\Delta \tau##, but then there's this remark that "##(1-v^2)^{1/2}## is absorbed in epsilon". So I think my "direct...

Circulant matrices also appear in the subject of Communication Systems. It's cool seeing all these connections between theoretical physics and Engineering.

Thanks that cleared my perplexion.

There should be a difference between ##r## and ##r^*##, they aren't the same.