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Discover LudwigSuggestions(5)
The phrase "Throughout this manuscript" is correct and usable in written English.
It can be used to indicate that something applies or is referenced at various points within the manuscript. Example: "Throughout this manuscript, we will explore the implications of climate change on biodiversity."
Exact(60)
Throughout this manuscript.
Throughout this manuscript Y represents a complex-valued metric space, unless otherwise specified.
Throughout this manuscript, m and k will denote non-negative integers.
Throughout this manuscript, m and k will denote nonnegative integers and i, j, s ∈ { 1, 2, …, n }.
Throughout this manuscript, we assume that (mathbb{R}^=[0,infty )), (mathbb{N}) = the set of all positive integers. (see [10]).
Throughout this manuscript, X will be a non-empty set and ⪯ will denote a partial order on X.
Throughout this manuscript, m and k will denote non-negative integers and i, j, s ∈ { 1, 2, …, n }.
Throughout this manuscript, let ( X, d ) be a metric space, and let ≼ be a preorder (or a partial order) on X.
Throughout this manuscript, let ( X, d ) be a metric space, and let ≼ be a preorder (or a partial order) on X. Definition 2 (Roldán [32]).
Throughout this manuscript, we use the NVIDIA convention of referring to the CPU and GPU s) as the host and device(s), respectively.
Throughout this manuscript, Ω ¯ will denote the closure of Ω in R p, while R + ¯ will represent the closure of the set R + of positive numbers in ℝ.
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