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The convolution matrices which were used as benchmark are listed in Table 5.
In the present paper we also investigated the angiogenic properties of collagen matrices which were only cross-linked, i.e. in the absence of heparin.
The output of the simulation program was the expected unaligned medical ultrasonic echo signal matrices which were adopted as the input for the MV adaptive beamforming algorithm implementation.
The climate and land use drivers were used to construct transition matrices which were applied to spatial maps, depicting possible future climate and land use change scenarios, to evaluate directions of change in water quality risks.
Step 9: Apply the inverse SVD operation using the U and V T matrices, which were unchanged, and the S 1 matrix, which has been modified according to Equation (6).
In order to estimate the number of coexisting absorbing species in the reaction systems (i.e., the number of produced complexes), principal component analysis (PCA) was performed on the digitized absorbance mole ratio data matrices, which were obtained from the spectrophotometric titration of Arsenazo III with each lanthanide cation, separately.
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This method requires the operation of pseudo-inverse of non-square matrices, which is not unique.
The reasoning system processes matrices, which are represented by Oz data structures.
The following theorem shows a construction method for GCO matrices, which is proved in [20, 21].
Let us give the definition of some triangle limitation matrices which are needed in the text.
In Basic Methods, we propose three groups of weighting matrices, which are generated by random selection.
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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