Recent content by kdbnlin78

I mean this with no patronisation intended, but you've answered your own question because in mathematics, a closed manifold is a special type of topological space, namely a compact manifold without boundary. In contexts where no boundary is possible, any compact manifold is a closed manifold.

The curvature of a surface is (or at least can be) defined as moving a vector through parallel transport around a closed loop.

As LCKurtz writes, the derivative here is lim_{h->0}h^{-2/3} = lim_{h->0}/cuberoot{h^{-2}} = /lim_{h->0}(/frac{1}{\cuberoot{h^2}} -> /infty.

Could approximate-around x=0 x^x looks like; x+x^2 ((log(x))/2-1/4)+1/54 x^3 (9 log^2(x)-6 log(x)+2)+1/768 x^4 (32 log^3(x)-24 log^2(x)+12 log(x)-3)+(x^5 (625 log^4(x)-500 log^3(x)+300 log^2(x)-120 log(x)+24))/75000+(x^6 (324 log^5(x)-270 log^4(x)+180 log^3(x)-90 log^2(x)+30...

Ok so now you have the CDF in terms of the error function erf(/frac{1}{/sqrt{2}}) what is the associating PDF?

Tom Apostol - Calculus. the best textbook I have ever used.

Perhaps try polar coordinates. x=r sin /theta x' = r cos /theta

Stephen Tashi; Should your reply be directed to LeotheLion? I agree with your comment either way.

N=8 supergravity has exactly the same degree of freedom as N=4 Yang-Mills. The maximal number of supersymmetry generators possible is 32. Theories with more than 32 supersymmetry generators automatically have massless fields with spin greater than 2. It is not known how to make massless...

Apologies, can now see the x_{i} are vectors. I'm at work and scanning articles when no-one is looking. I your reasoning has lead to to conclude that /boldsymbol{x_{1}^T}A_{1} = /boldsymbol{0} - How do you know this?

Can any of the x_{i} or A_{i} be inverted? (i.e., do you know anything about their determinants?)

Whoops! Thought it was too easy. didn't read your laTex code correctly. Nor did I fully understand the terminology of "Super"diagonal. I'll have another think. My intial thought here is that you would be dealing with matrices in Jordan Normal form. Are you familiar? If not they are upper...

Only got time to quickly look at your assumption paragraph beginning "If every +ve integer can be expressed as odd * 2^n..." But I can see straight away that you are not considering odd numbers at all in your tree branches as (any number odd or even) * (power of 2) = even. You do...

My PhD c2006 concerned a lot about General Relativity. I don't claim to "know" it but rather I am intruiged by it. It sounds like you are asking yourself the question of whether I am intruiged enough to follow an advanced course. I am not familiar with what you have learned so far but my...

Currently there is no theory to suggest that time can be quantized. However, in order that a theory of "Quantum Gravity" to exist, that is, the cohesion between Quantum Physics and Gravitiation, there is a suggestion that this may be achievable if one were to quantize time as it were. A nice...