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The smaller maps (71 × 71 pixels) form the transform matrices of corresponding dimensions (2 × 1) through image processing.
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The levels of association between the scores for corresponding dimensions on both questionnaires are shown in Figure 1.
In C-WMMG, each player is characterized by a nonnegative vector with a fixed dimension, and players in the same coalition cooperate by producing a characteristic vector for this coalition (each dimension of this vector equals the maximum of the corresponding dimensions of its members).
The present study was designed to determine the cross-national invariance of the original Dutch factors and the construct validity of the corresponding dimensions.
We note that their elements are uniquely described by matrices of the corresponding dimensions (mathbb {C}^{(n+1 times(m+1)}) and (mathbb{C}^{(m+1 times(n+1)}), respectively.
(2) Here (x(l)) is an n-dimensional phase vector, (u(i)) an m-dimensional vector of control influences, (psi (i)), (Gamma (i)) ((i = 0,1,ldots,l - 1)) matrices of the corresponding dimensions, being a controllability pair [4, 6], (Phi_{1},Phi_{2},Phi_{3}) are constant matrices, such that the system (2) satisfies the Kronecker-Capelli condition [3, 4], (0< s< l).
It is required to find such a control (u(i)) as minimizes the following quadratic functional: J = sum_{i = 0}^{l - 1} bigl( x'(i)Q(i x(i) + u'(i C i u(i) bigr), (3) under the conditions (1), (2), where (Q(i) = Q'(i) ge 0), (C i) = C'(i) ge 0) are the periodic matrices of the corresponding dimensions.
Determination of the degree of accordance between corresponding dimensions in the 27-version and the longer 52-version have shown coefficients ranging from r = 0.63 to r = 0.96 [ 9].
If a choice is made by oversight, the choice opportunity do not view that dimension of the code as one of particular interest for the institution, and it defaults to the value of the corresponding dimension of reality.
The formulation is first developed by defining cones for the input, state and output spaces of the dynamic system, and then extended, in particular, to cones being the three first orthants each being of the corresponding dimension of the input, state, and output spaces.
The multi-chamber device is designed on the basis of a PBPK model of a 220 g rat with the corresponding dimensions of the individual chambers (W × L in mm): lung, 2 × 2; liver, 3.5 × 4.6; fat, 0.42 × 50.6; and other tissues, 0.4 × 109.
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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