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In this paper, we introduce vector-valued non-separable higher-dimensional wavelet packets with an arbitrary integer dilation factor.
Having chosen p and q, the user selects an arbitrary integer e less than n and relatively prime to p − 1 and q − 1, that is, so that 1 is the only factor in common between e and the product (p − 1)(q − 1).
where q′ is an arbitrary integer.
then for an arbitrary integer, the following expansions hold: (2.9).
Here, k is an arbitrary integer between 0 and n.
Since m ≥ 1 is an arbitrary integer, let m → ∞, we have a contradiction.
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A highly efficient video downscaling algorithm for any arbitrary integer scaling factor performed in a hybrid pixel transform domain is proposed.
Throughout this section, we assume that all hops of the network are independent th-order Markov channels, where is a fixed arbitrary integer.
Van der Waerden's theorem states that if the positive integers are divided into any finite number of disjoint sets (i.e., sets without any members in common) and k is an arbitrary positive integer, then at least one of the sets contains an arithmetic progression of length k.
where N is an arbitrary positive integer.
Let be an arbitrary positive integer.
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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.
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CEO of Professional Science Editing for Scientists @ prosciediting.com