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Our first result gives a double characterization of the VCG prices, first as distances in a certain residue graph and second as the minimal (for buyers) and maximal (for sellers) equilibrium prices.
As a consequence of the above, the next result gives a double inequality refining L < I and involving the four standard means G, L, I, and A. Corollary 5.3 We have 2 e 2 L 2 < G ( A + G ) exp A + G L < 2 e 2 I 2. (5.5).
The T(O…Br) descriptor gives a double structural information: its value increases according to both the number and the distance of bromine substituents, on each phenyl ring, from the oxygen ether.
The sum of topological distances between oxygen and bromine atoms (T(O…Br)) gives a double structural information: its values increases according to both the number and the distance of bromine substituents, thus T(O…Br) also takes into account the information related to the position of the bromine atoms on the phenyl rings (Papa et al., 2009).
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For example, the fact that an aggregate with X = 1 and radius monomer of 0.17 μm gives a double-peaked profile that does not appear with aggregates of the same size parameter but with a radius monomer of 0.1 μm indicates that the radius monomer could be a parameter influencing the appearance of the features on the CO ice stretching mode profile.
And, the fact that the Mentos candies sink to the bottom of the bottle gives a double-whammy.
After match point Novak Djokovic gave a double fist-pump and then shook hands.
The horse was given a double dose which reportedly worked like a charm.
Gaborik was given a double minor, as was Martinek, while Bryan McCabe and Zenon Konpka each received roughing penalties.
Manny Ramirez buttoned his new Red Sox jersey, smiled, gave a double thumbs up and uttered the $160 million word.
Since the New Year, all five of the main polling organisations have given a double digit advantage to the Tories.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com