# superposition theorem

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## superposition theorem

[‚sü·pər·pə′zish·ən ′thir·əm]
(electricity)
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The proof of this theorem in [7] is nontrivial and uses the deep and powerful Kolmogorov Superposition Theorem which answered Hilbert's 13th Problem.
Embedding into L(X) and the Kolmogorov Superposition Theorem
First we recall the following definition motivated by the Kolmogorov Superposition Theorem 15.
We shall use the following noncompact version of the Kolmogorov Superposition Theorem.
Applying the Superposition Theorem to the equation (1) yields [[Tilde.A].sub.0] (v) ~ ([sigma] + [m[sigma].sub.j] ([tau]), [rho] + [m[sigma].sub.j]).
Applying the Superposition Theorem and the conclusion of (15) to (18) yields [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Applying the Superposition Theorem and the conclusion of (15) to (19) yields [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Applying the superposition theorem to the network shown in Fig.
Similarly, applying the superposition theorem, the current towards dummy termination [I.sup.L.sub.d] [12] is derived as
From (34), we see that the superposition principle of gravitational field is deduced from the superposition theorem of the velocity field of ideal fluids.

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