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By Hamilton N. T., Aaboe A.

The authors describe the reconstruction of the Babylonian ACT No. 1050 (Astronomical Cuneiform Texts; O. Neugebauer (1955)) as a textual content giving longitudes, yet now not dates, of synodic phenomena of Venus calculated in accordance with the foundations of approach A.

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Extra info for A Babylonian Venus Text Computed According to System A: ACT No. 1050

Example text

For the autocorrelation to be independent of t, we must have E{cos 2ϕ} = E{sin 2ϕ} = 0. Hence R(τ ) = 12 cosaτ and the process is wide stationary. v. of the process X (t ) at t = ti . 4 Output Density Function f y ( y1 ,L, yk ; t1 ,L, t k ) = f x ( x1 ,L, x k ; t1 ,L, t k ) /[ g ′( x1 ) L g ′( x k ) ] y1 = g( x1 ),L, yk = g( yk ), prime indicates derivative. 1 Linear Operator Y (t ) = L[ X (t )], L[a1 X1 (t ) + a2 X2 (t )] = a1 L[ X1 (t )] + a2 L[ X2 (t )], L[ AX (t )] = AL[ X (t )], A ≡ random variable, Y (t + τ ) = L[ X (t + τ )] implies L (system) is time invariant, L = transformation (system).

3 Density Function fz ( z )dz = P{z < Z ≤ z + dz} = ∫∫ f xy ( x , y )dxdy ∆Dz Example 1 Z = X + Y , x + y ≤ z, Fz ( z ) = pendent then ∞ ∫ ∫ z− y −∞ −∞ ∞ f xy ( x, y)dxdy, dFz ( z ) = fz ( z ) = f xy ( z − y, y)dy. v. are indedz −∞ f xy ( x, y) = f x ( x ) f y ( y) and hence fz ( z ) = ∫ ∫ ∞ −∞ f x ( z − y) f y ( y)dy = ∫ ∞ −∞ f x ( x ) f y ( z − x )dx = f x ( z ) ∗ f y ( z ) = convolution of densities. Example 2 Z = X 2 + Y 2 , if z > 0 so then x2 + y2 ≤ z = circle with radius z , Fz ( z ) = ∫∫ f ( x, y)dxdy, if z < 0, x 2 + y2 ≤ z z Fz ( z ) = 0.

Hence R(τ ) = 12 cosaτ and the process is wide stationary. v. of the process X (t ) at t = ti . 4 Output Density Function f y ( y1 ,L, yk ; t1 ,L, t k ) = f x ( x1 ,L, x k ; t1 ,L, t k ) /[ g ′( x1 ) L g ′( x k ) ] y1 = g( x1 ),L, yk = g( yk ), prime indicates derivative. 1 Linear Operator Y (t ) = L[ X (t )], L[a1 X1 (t ) + a2 X2 (t )] = a1 L[ X1 (t )] + a2 L[ X2 (t )], L[ AX (t )] = AL[ X (t )], A ≡ random variable, Y (t + τ ) = L[ X (t + τ )] implies L (system) is time invariant, L = transformation (system).

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A Babylonian Venus Text Computed According to System A: ACT No. 1050 by Hamilton N. T., Aaboe A.


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