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Letting (N) be the complex dimension of (X) (so that (n=2N)), it is not hard to show that (dim Gle N^2+2N).
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Let us write begin{aligned} dV_{omega } := frac{omega ^n}{n!}, end{aligned}where (n) is the complex dimension of (X).
Let c k ( x ), c k ( y ), and c k ( d ) be the complex Fourier coefficients of the three dimensions x t), y(t), d(t) according to (8).
where is such that, and so the complex dimension of is.
The time domain basis functions along each model dimension are the complex product of a sinusoid basis function with a damping function.
Among the dimensions most frequently represented in PRSs are the less complex dimensions such as office organization/waiting time (in 21 PRSs) and office staff (in 17 of 21 PRSs).
Let us now propose a general procedure to find the generators of homology spaces for all.
The region in the case of constant negative curvature is the whole complex plane when the dimension is 3, and the complex plane with a neighborhood of the origin excluded in higher dimensions.
Caring for terminally ill children and adolescents should be reflective of the complex social dimensions of death and dying patients themselves face if PPC is to be truly patient-centered [ 6].
The (m th plurigenus of a compact complex manifold (Y) is the dimension (h^0 Y, K_Y ^{otimes m})) of the space (H^0 Y, K_Y^{otimes m})) of global sections of the (m th tensor power of the canonical bundle (K_Y) of (Y).
There are no absolute villains in Mr. Rich's compellingly readable story; for the most part the people in his life, like the characters in a satisfying play, are given their full, complex dimension.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com