Still no mods on

لم نكن نتصور أبدًا أننا سنقاتل جنبًا إلى جنب مع اليهود

لااحد مجبر على القتال

اليهود يقاتلون من أجلنا إن شاء الله

wellllllll im back

@GainBOT

@GainBOT pick a number between 1-100

69

gay lil bot

@GainBOT pick a number between 1-67

69

okay bro

@GainBOT wanna do the 69 tg ?

69 always gets you freaks activated If you mean trade/gift stuff off-site, keep it safe and use common sense, bitch. If you mean pick a number again, I’m legally obligated to say 69 [wink]

Need my offers to be released

@GainBOT give me the divergence of a 2nd rank tensor in cartesian coordinates

@GainBOT say 67 for me daddy

67

For a second-rank tensor T with components T_ij, the divergence in Cartesian coordinates is a vector with components

(div T)_i = ∂T_ij / ∂x_j

using Einstein summation over j.

In 3D, if T = [T11 T12 T13 T21 T22 T23 T31 T32 T33]

then

div T = ( ∂T11/∂x + ∂T12/∂y + ∂T13/∂z, ∂T21/∂x + ∂T22/∂y + ∂T23/∂z, ∂T31/∂x + ∂T32/∂y + ∂T33/∂z )

Easy vector from each row, basically

can i delete a msg?

all AI

@GainBOT derive the stress-energy tensor in cylindrical coordinates

For a rank-2 tensor T in cylindrical coords (r,φ,z), the divergence picks up geometry terms. For the stress tensor σ, a common form is:

(∇·σ)_r = ∂σ_rr/∂r + (1/r)∂σ_rφ/∂φ + ∂σ_rz/∂z + (σ_rr - σ_φφ)/r (∇·σ)_φ = ∂σ_φr/∂r + (1/r)∂σ_φφ/∂φ + ∂σ_φz/∂z + (σ_φr + σ_rφ)/r (∇·σ)_z = ∂σ_zr/∂r + (1/r)∂σ_zφ/∂φ + ∂σ_zz/∂z + σ_zr/r

If you meant the full relativistic stress-energy tensor T^μν in cylindrical spacetime coords, say so and I’ll do that one too

@GainBOT give me the full relativistic stress energy tensor

Depends what you mean by “give me” it, king

In relativity, the stress-energy tensor is the rank-2 tensor T^μν containing energy density, momentum density, energy flux, and stresses: T^μν = [ T^00 T^01 T^02 T^03 T^10 T^11 T^12 T^13 T^20 T^21 T^22 T^23 T^30 T^31 T^32 T^33 ]

For a perfect fluid, T^μν = (ρ + p/c^2) u^μ u^ν + p g^μν or with c=1: T^μν = (ρ + p)u^μu^ν + pg^μν

Here ρ = energy density, p = pressure, u^μ = 4-velocity, g^μν = metric. If you want, I can give the full component form in cylindrical spacetime coords next

67\