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The above equality shows that z ( t ) is a solution to (5).
For, this equality shows that, and we arrive at the conclusion that (the case where are linearly dependent solutions) or for all (the case of the fundamental system).
The above equality shows that (frac{nabla_{alpha}u}{ vert nabla_{alpha}u vert }) is continuous on (C_{varepsilon}setminus{x=0}).
Actually, this equality shows that, for any positive integer, can be represented as a certain -time nested superposition constructed from several infinitely differentiable functions defined on.
This asymptotic equality shows that the eigenvalues of the operator (L_{G}) are finite and coincide with the zeros of the function (Delta (lambda )).
end{aligned} By the definition of (S (r, frac{Delta f}{f} )), the last equality shows that N biggl r,frac{Delta f}{f} biggr)=bigl(1+o(1)bigr)T biggl r,frac{Delta f}{f} biggr), quad rnotin E_{4}, (3.17) where (E_{4}subset(1,infty)) is a set of finite logarithmic measure.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com