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where and denote the scale and translation parameters respectively; denotes complex conjugation.
We suppose that is a real Hilbert space with norm and inner product denoted by and, respectively, denotes the family of all the nonempty subsets of.
where and denote the complex function and shear modulus, respectively, denotes the conjugate of the position vector of the screw dislocation, and denotes the real part.
Where ( {T}_{0,j}^{SL} ) and ( {eta}_{0,j}^{RL} ) respectively denotes the length of shapeable load j and removable load j.
We assume that denote the origins of, respectively, denotes the topological dual space of and denotes the dual cone of, defined by.
where i2 = j2 = -k2 = -1 and i j = j i = k, H x 1 and H x 2 respectively denotes the 1-D Hilbert transform of the lines and columns of the input image.
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Semicolon and comma, respectively, denote covariant differentiation with respect to g ij and partial derivatives with respect to coordinates.
Take sch9Δ for example, the normalized arrays with respect to W1, W2, W3 are respectively denoted by S1\W1, S2\W1, S3\W1, S1\W2, S2\W2, S3\W2, S1\W3, S2\W3, S3\W3.
BiOCl and (BiO 2CO3 nanosheets with predominantly exposed {001} facets (respectively denoted as BiOCl-001 and (BiO 2CO3-001) were easily synthesized at room temperature in aqueous urea solution.
Over the years, I landed plenty of "cocktail" and "tailor" and "chopper" blues -- this is a fish with more nicknames than menacing qualities -- respectively denoting fish of roughly two, five and eight pounds, and admired the ferocity with which they blitzed and decimated hapless baitfish until the sea ran red.
Let H(U) denote the vector space of all complex-valued holomorphic functions on an open subset U of a Banach space E. Let τω and τδ respectively denote the compact-ported topology and the bornological topology on H(U).
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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