Recent content by LHS1

Does there general formula for k-Statistic? If yes, what is this formula? How to derive it ?

Thank you very much!

I spend some time studying special functions recently. I found two definitions of gamma function, one in form of integral and the other in form of infinite products, and I cannot prove of their equivalence. I found the definition in infinite product form important in proofing many properties of...

I spend much time to study a theorem - Let G be a nonzero free abelian group of finite rank n, and let K be a nonzero subgroup of G. Then K is free abelian of rank s smaller or equal to n. Furthermore, there exists a basis (x1,x2,...,xn) for G and positive integers d1,d2,...,ds where di divides...

Thanks to all who response to my question. After a throughout revision of general relativity, especially equivalent principle, I see what's wrong with me and I make clear the difference between coordiante velocity and observed (proper) velocity. Thanks again to help me.

I spent some time to study general relativity recently and I found something that confuse me. According to my unserstanding about general relativity, the coordinate velocity of light should be (1-2GM/c2r)c, while the wavelength should be (1-2GM/c2r)1/2times its wavelength at infinity, for a...

I realized that there is no strict derivation of Einstein's Field Equations. However I found no 'derivation' that make me feel 'comfortable' and 'logical'. Could anyone post a 'derivation' with smooth logical sense ? Thank you.

Because of my poor editing, I cannot write it down here. In fact, I am not quite sure what you are asking. But I believe you can find your answer by looking at the differential expression of conservation of momentum of EM field which is in the form of divergence equation on the internet or other...

If anyone found my explanation above is not satisfactory, please let me know. Thank you for everyone who made their attempt to help me.

Reply to pmb_phy, I am sorry for not responding because I did not visit the site for a while. The answer for this is, in fact, simple. I simply asked the wrong question! I should ask 'if there exist a potential vector as a 4 vector?'. There is a important point I did not realized that 'there is...

The most important mathematical tool needed for studying relativity is tensor calculus. I believe any mathematical book on tensor should do the job. But I still recommend a book, Schaum's outline series Theory and Problems of Tensor Calculus by David C. Kay. I studied this book and found that it...

Here I have to thanks those who have attempted to help me solve my problems, expecially to pmb phy and pam.

Reply to pmb phy, I am still skeptic about this. It is because when I refer to the derivation of quotient theorem, I found that even though it only requires the transformation properties of the quantity acting on the tensor, but that quantity must be arbitrary. Am I wrong about this? Anyway, I...

The total energy of a particle = relativistic mass times c^2. As many physicsts do not like the term relativistic mass, the equation may be written as E = gamma times rest mass times c^2. Here the total energy means the so called ' rest mass energy ', which includes energy from chemical bonding...

Reply to pam, I do not think you are right. What you said is just like x^2=1, then x must be equal to 1. But it is not true, x can be -1. This is just A-level logic tells us that a proposition is true does not mean its converse is true.