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The next conditions to be evaluated are those related to coverage and quality issues.
The next conditions hold simultaneously: for all n, uniformly, and. the pair ({u n }, {v n }) verifies the discrete Sawyer's condition, i.e., there exists C > 0 such that.
The next conditions are expressed in terms of the matrix function A and extend condition A3w in the optimal transportation case [20].
To derive necessary conditions under this situation, for ( s ∗, t ∗, y ˜ ) ∈ K ( x ∗ ), we define Z y ˜ ( x ∗ ) = { z ∈ R n : z T ∇ g j ( x ∗ ) ≤ 0, j ∈ J ( x ∗ ), with any one of the next conditions (i - iii) holds }.
The next conditions hold simultaneously: w ∈ A p, n-1,n+2) for all n, n-1,n+2ly, and. the pair ({u n }, {v n }) verifors the discrete two-sided Saller's condition S q, i.e., there exists C > 0 suniformly
The request is redirected if any of the next conditions are true: (a) The number of hops to the redirection node is lower than the number of hops to the destination of the request (e.g., DS).
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The next condition focuses on retrieve queries.
The asymptotic representation of the solutions of (3.7) is given under the next condition.
The samples were next conditioned to different levels of relative humidity (0, 64, 89%) before being sealed in d.s.c.s.c
The next condition is that self-consciousness requires me to represent an objective world distinct from my subjective representations - that is, distinct from my thoughts about and sensations of that objective world.
Since (pin 0,1)) function f is concave, which implies that there is a unique fixed point (x^) of f and that the next condition bigl(f(x -xbigr) bigl(x -xbigr)< 0,quad xin (0,infty)setminusbigl x-x^bigr}, (31) holds.
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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