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(d_{i},(x,yy)) is the distance between the facility to be located at ((x,yy)) and destination i located at ((a_{i},b_{i}} )); (w_{i}) a constant transforming distances into costs.

Minimum, maximum and median are standard non-parametric statistics (e.g., [ 60]: p. 185; [ 62]: p. 45), but only the minimum can be applied directly in transforming distances (see the methods section).

We also examined the estimated spline terms of distance spline k (distance ij ), RFRS transformation of distance RFRS distance ij ), and estimated spline terms of RFRS transformed distance spline k (RFRS distance ij )) in the PCLR model setting (3). Figure 1 shows the primary and secondary roads in the Detroit city area, along with the locations of asthma cases (as dots).

Such a strategy has allowed a unified and efficient approach to the design of image processing operators, such as edge tracking, region growing, watershed transforms, distance transforms, and connected filters.

The equation for the transformed distance is written as follows.

According to Eq. 3, the collimated beam propagates in free space with a transformed distance Ltrans = 26.7 mm.

Considering that the trench-transform distance likely depends on respective lithosphere thicknesses, it may vary along-strike depending on the plate's age.

According to Siegman [5], a beam with a convergent wavefront with a radius of curvature R propagating for a distance of L generates the same diffraction effects as this beam without the convergent wavefront propagating for a transformed distance.

No association was found using RFRS transformed distance as an argument.

No association was found using RFRS transformed distance as an argument in model (1).

We determined the smallest threshold, for which a correlation of SIZ significant at p = 0.05 with any of the other transformed distance matrices was not observed.

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