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1. Fractal Boundary

okay, I am thinking on it. thank you.
2. Fractal Boundary

They can be, yes, but I also need to know their boundary term in terms of volume element. Is there a rule to generalise any kind of fractal object to d-dimension? Because I may try to apply, I remember I found a fractal with boundary term with dimension less than 3. thank you very much.
3. Fractal Boundary

For my work, I need to check my calculations with an example of a fractal object. I searched on the internet, there are some examples of fractals with their hausdorff dimensions, but no boundary terms related. Also found some 1-d examples, but I need d>3 dimensional objects since my calculations...
4. Lorentz Transformation

Correction: I was trying to ask is there a matrix which includes all the "four vector information" in itself and we can act it on salt \vec{v} 's as (c, \vec{v} ) (not a four velocity but still) Maybe it seems meaningless but I was confused with all the γ factors because I couldn't find...
5. Lorentz Transformation

I didn't encounter the matrix anywhere, they always use the addition of the velocities, so I wasn't sure. I think I should construct on my own that matrix. Thank you
6. Lorentz Transformation

Can Lorentz Transformation be applied directly to a four velocity vector? I mean let v_{α} be a four velocity vector. Is there a form of Lorentz tfm matrix such that: v^{'}_{α} = \Lambda^{β}_{α}v_{β} ?
7. Energy levels for a 3D cubical box

n_x , n_y , n_z are your quantum numbers, they describe your state, when you solve the Schr. Eqn. for ψ's, which are sinusoidal functions as mentioned below, n_x,y,z will appear in the energy values.
8. Curvature Scalar in 2-d

Thank you very much. Yes I rewrited everything with g lower index. I am not sure about that symmetry: R^{αβ}_{αβ}= - R^{βα}_{βα} But I feel I am close to it. Thank you again.
9. Curvature Scalar in 2-d

Ok here is my thoughts, I try to stay away from the connection coefficients. So, I don't write the R tensors in form of \Gamma's. So I am trying: R= g^{αβ} R_{αβ} = g^{αβ} R^{c}_{αcβ} = g^{αβ} g^{αb} R_{bαcβ} but now I can't have the R_{αβαβ} form. Since it is 2-d, I put α=1 and...
10. Curvature Scalar in 2-d

I am asked to show it by the symmetries of the Riemann tensor by the way.
11. Curvature Scalar in 2-d

Where should I start from to show that curvature scalar (RiemannScalar) is 2\frac{R_1212}{det (g_μ√)} ?
12. Is there a map from real numbers to non integers?

Yes, thank you very much. I thought that my function such as 2n+1/2 should be valid for any real number but I think the remaining non-integers from half integers are included in f(x)=x otherwise case. thank you
13. Is there a map from real numbers to non integers?

thank you very much. I am trying to figure out Cantor's method. I think I should construct disjoint one countable and one uncountable sets and their union should be real numbers.
14. Is there a map from real numbers to non integers?

thank you very much. I don't fully understant how I can pick real numbers with n indices. I am not familiar with the notation, I need a valid function to show this map is one to one and onto. my real numbers set is non countable, non integers set is also.I thought the function can be...
15. Is there a map from real numbers to non integers?

I came up with some idea but not sure. I can only map all the real numbers to (0,1) interval. And then try to enlarge it to (n,n+1) where n goes to infinity. Is it valid?
16. Is there a map from real numbers to non integers?

Can you help me to construct a 1-1 mapping from real numbers onto non-integers? thanks
17. Classical Angular Momentum

Yes, exactly. Thank you very much. Using square brackets may be confusing in classical mechanics. I figured out to make this with levi civita symbol. But there is another problem I have now. if I replace the Li with some general vector Vi, it should still be hold {Vi,Lj}=εijkVk how should...
18. Classical Angular Momentum

[Li,Lj]=εijkLk how can I prove this expression classically?