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It provides direct visual perception for exploring structures of a given data matrix and its corresponding proximity matrices, for variables and subjects.
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By applying these rules, an initial reachability matrix for variables for effective customer involvement in green concept implementation in the supply chain has been obtained (Table 5).
a) a file in.XLS (2003 format) containing: the raw data for the 134 objects after median computation of the replicates in the engraved points and the data for the different methods of grouping; some sheets with frequency distribution charts for the elements and HLOC charts showing elements' distribution in different manners; as well as the correlation and the covariance matrix for variables.
For each city, we calculated Spearman's rank correlation coefficient matrices for the variables soil moisture, wind speed, PM10, and temperature; interaction variables; and monthly dummy variables (M1 to M11).
The definition of the L N×L N matrix leads directly to the extraction of the covariance matrix for variable y given that the primary channel is free ( ℋ 0 ).
Figure 5 illustrates an example of the matrix for F lkt with the element in the first row and the second column being equal to 3; showing that location 1 in period 2 is assigned to the cell number 2. Similarly, in Fig. 6, the matrix for variable w wkt is formed by six workforces and four periods.
Let G j be the n × g j indicator matrix for variable j (j ∈ (1,... q)), with g j the number of categories of variable j.
That is for each j (j = 1,..., q) with G j the n × g j indicator matrix for variable j with g j the number of categories of variable j.
The correlation matrices for 17 variables were prepared for both summer (Table 3) and winter season (Table 4) using SPSS 16.0.
Moreover, the survey of Black and Devereux (2011) contains a detailed discussion of the estimation issues concerning the IE. Note that the IE, the IC, and the transition matrices for quantitative variables grouped in quantiles treat downward and upward intergenerational mobility symmetrically.
Similarly, Z ∈ ℜ k × q is a matrix for explanatory variables (differentiation variables) and have k gene sites and q differentiation programmes (do not include replicates).
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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