We can prove (24) simply by applying the arithmetic-geometric mean inequality to (Zleft (W_{2}^{(1)}right)).
By applying the unweighted pair-group arithmetic average (UPGMA) method (Sneath and Sokal 1973) using the SHAN subroutine through the NTSYS-pc version 2.2 (Rohlf 2002), dendrograms representing the genetic relationship among the 10 CPTs of Pongamia were generated.
For clustering analysis, we detect group relationships among the microbial samples by applying the UPGMA (unweighted pair-group method with arithmetic means) algorithm [ 43] based on the between-samples dissimilarity matrices.
We decided to apply the arithmetic weighting on the ROC enrichment as given in Equation 23.
Phylogenic dendrograms that were based on the presence/absence of a band and band weighting (band density) analyses were constructed by applying the Dice coefficient and the unweighted pair-group method using the arithmetic averages (UPGMA).
In the following, we show a refinement of reverse arithmetic-geometric mean inequality by applying the main lemmas in Section 2.
We apply the arithmetic mean method as group decision rules to integrate expert preference.
This is usually accomplished by applying basic arithmetic to the A-list formula.
Our algorithm decreases the computation time significantly by applying integer arithmetic on floating-point data in the IEEE-754 standard or similar formats.
Using FILTERs, triples can be restricted in a sophisticated way, e.g., by applying arithmetic expressions.
For instance, students had to solve a number of math items by applying arithmetic and combinatorial operations (OECD [2005]).
