Recent content by bchui

A prove that there is another universe which pulls our universe apart by gravity. Dark matters are actually matters in another universe which explains why it has not been detected so far? "Big bang" might actually be a "big pull" - empty space being torn apart fby another universe. The...

For b=x+iy , a^b=a^{x+ i y}=a^x a^{i y} = a^x \exp(i y \ln (a)) = a^x (\cos (y \ln (a))+i \sin (y \ln (a)) by Euler's formula e^{i\theta}=\cos\theta+i\sin\theta. I wonder what happens to A^B where both A and B are matrices

It is a well known fact that vector product of two vectors exists only in 1,3 and 7 dimensions. There is some relation between 7-dimensional vector product and electronmagnetics as studied by Feynmen. One can search for the calssical paper of Alfred Gray or other sources. :smile:

I have the same type of problem and I am looking for a formula for the distance between two quadratic figures in \Re^n but I haven't seen it anywhere.

I wonder if there is any online document available to show us how to compute all the generalized eigenvectors?

I have seen a method of decomposing the matrix A as A=D+N where D is diagonable and N is nilpotent and the method is mentioned in wiki. however I cannot find its original source and other relevant papers. Can anybody tell me something about the details?

I ahve always wondered why only the curvature term R_{\mu,\nu} been considered in GR. From differential Geoetry, how about the torsion tensor?

A very simple "proof" for time travel not possible is that nobody from the future had ever been traveled back to meet us. Further, there is no solid proof ever for any extra terrestial intelligents had ever visited our solar system. I doubt that even space travel is more difficult tahn ever...

The proof for integer n is simple and done by induction. It could be found for example in Chapter 5.9 of W Fleming: "Functions of Several Variables", Springer- Verlag 1977 We generalize n! to \Gamma(n+1) and the formula is obtained. My problem is the physical aspect...

Covariant derivative, Lie derivative and Connection So, if there is a metric structure g(X,Y) on the manifold, would the two derivatives be the same? The definiteion of connection \nabla does not require a metric structure. what is the relationship between a connection, covariant...

The name "force" should be defined as "rate of change of momentum" with respect to some kind of "time". We can write {\vec F}=m_0{\vec A}= m_0 (\gamma {\vec a}+\frac{d\gamma}{dt}{\vec u}) and "define" {\vec A}=\gamma {\vec a}+\frac{d\gamma}{dt}\frac{{d\vec r}}{dt} as some kind of "acceleration"...

Thre are two kind of "forces" in SR: (1) One is "3-force" which is the rate of change of "3-momentum" with respect to "time" {\vec F}=\frac{d {\vec p}}{dt}=\frac{d{\vec u}}{dt}=m{\vec a}+m_0\frac{d\gamma}{dt}{\vec u} where {\vec u} is the 3-velocity {\vec u}=\frac{d {\vec r}}{dt} and {\vec...

Let (M,{\cal T}) be a sub-manifold of a Riemannian manifold (N,{\cal R}) with metric tensor g, If we decompose the tangent space at the point p\in M\subseteq N and accordingly decompose the tangent bundle T_pN=T_pM\circleplus {\tilde T}_pM into tangential to M and normal to M, could we say that...

Where can we find the prove of universe expansion from the equations of General Relativity?

There really is quite a lot of those material in this line of research in biomechanics. The problem is: whether we are doing it for the shake of purely biomechanical research or for martial art trainning. I have been a martial artist for more than 10 years and a certified instructor. However the...