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Accordingly, a probability distribution over sample space is written down in terms of a so-called density function, denoted $P s) ds$, which technically speaking expresses the infinitely small probability assigned to an infinitely small patch $ds$ around the point $s$.
The inverse formula of the generalized Fourier transform in fractal space is written in the form [18, 19] f ( x ) = 1 Γ ( 1 + α ) ∫ − ∞ ∞ f ω F, α E α ( i α h 0 x α ω α ) ( d ω ) α, (3.8).
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"Spaced" was written by and stars Simon Pegg (Shaun of the Dead, Hot Fuzz, Star Trek) and Jessica Hynes (SOTD, Son of Rambow).
The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates.
The owner of Big Bin Studios converted a grain bin into a space where music is written, recorded and appreciated.
If (s=0), then the space (H^{0}(Omega)) is written as (L^{2}(Omega)) with inner product ((cdot, cdot)) and norm (Vert cdot Vert _{0}).
These transfer learning tasks are inherently heterogeneous in nature as the feature space of a source document is written in a different language as the target.
"So Much for That Winter," Nors' second book to be translated into English, consists of two novellas that track women sifting through the fallout of their respective breakups: "Minna Needs a Rehearsal Space" is written as a hypnotic series of sparse headlines, "Days" as a series of numbered lists.
The problem can also be studied from the abstract point of view: every Hilbert space has an orthonormal basis, and every element of the Hilbert space can be written in a unique way as a sum of multiples of these basis elements.
That the span of the basis vectors is dense implies that every vector in the space can be written as the sum of an infinite series, and the orthogonality implies that this decomposition is unique.
For a matrix A to describe a linear map f: V→W, bases for both spaces must have been chosen; recall that by definition this means that every vector in the space can be written uniquely as a (finite) linear combination of basis vectors, so that written as a (column) vector v of coefficients, only finitely many entries vi are nonzero.
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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