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In this contribution we present a four-dimensional (4-D) model of the electron density consisting of a given reference part, i.e., the International Reference Ionosphere (IRI), and an unknown correction term expanded in terms of multi-dimensional base functions.
To create a control-macrostate configuration consisting of a given number of (N) macrostates, one randomly places N two-dimensional Gaussians within the environment and applies a winner-take-all function to arrive at a discrete partitioning of the environment into N regions.
(1) Existence of the Protein Consisting of a Given Domain Subset.
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In this case, the exposures consisted of a given pollutant's annual average for the period June 2002 through May 2003 based on the monitor at the participants' residence at the start of the follow-up period (June 2003).
These are defined by the experimental design and consist of a given biological material such as the organism, cell type, tissue, etc. and, when applicable, an experimental condition such as treatment, dose or time-point for time-series samples.
For given, let be a set consisting of all given as in Lemma 2.8, then is an increasing map.
The fluid model approach consists of replacing a given fixed finite number of interfering BS by an equivalent continuum of transmitters which are uniformly distributed with density ρ BS.
The technique proposed consists of encrypting a given file and embedding a set of randomly-valued check blocks or sentinels.
For assessment of depressive mood, we applied the 'Eigenschaftswörterliste', a validated multi-dimensional tool consisting of a list of given adjectives describing the emotional state of a person (Janke, 1978).
The first processing step consists of tracing a given input segment through the image sequence.
PHLRP consists of partitioning a given network into sub-networks, locating at least one hub in each sub-network and routing the traffic within the network at minimum cost.
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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