# Recent content by kdbnlin78

1. ### Compact manifold question

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.
2. ### What is the physical meaning of curvature?

The curvature of a surface is (or at least can be) defined as moving a vector through parallel transport around a closed loop.
3. ### How cubed root of x is not differentiable at 0

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.
4. ### Integral of y=x^x

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...
5. ### Need help solving CDF (Cumulative distribution function)

Ok so now you have the CDF in terms of the error function erf(/frac{1}{/sqrt{2}}) what is the associating PDF?
6. ### Help me to chose the right calculus textbooks.

Tom Apostol - Calculus. the best textbook I have ever used.
7. ### How to evaluate this double integeration of a gaussian function?

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

9. ### Supersymmetry n=8

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...
10. ### Matrix Equation

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?
11. ### Matrix Equation

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

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...
13. ### Collatz Conjecture - Bouncing Ideas

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...