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Fig. 1 Number of fly-over normal points with respect to the latitude (in degrees) of a ground station, for six geodetic satellites during a 1-year period from July 2014 to June 2015.

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Fig. 3 Simulated improvement rate of three translation parameters and a scale parameter of a terrestrial reference frame when one laser-tracking station (one of the colored circles) is added to the existing laser-tracking network (white triangles; large ones are high productive stations with >2000 normal points during the March April 2015 period).

Fig. 4 Simulated improvement rate of degree-2 Earth gravity parameters when one laser-tracking station (one of the colored circles) is added to the existing laser-tracking network (white triangles; large ones are high productive stations with >2000 normal points during the March April 2015 period).

We therefore conclude that the plane spanned by the bent part of the hairpin, which we labelled III in Fig. 3c, indeed is located in the flow-vorticity plane, with its normal pointing in the gradient direction.

The calibration was done by observing a dense field of stars with the spacecraft in normal pointing mode.

with N i being the plane normal pointing outward from Ω e.

The algorithm uses the idea that a plane is characterized by a set of co-located points with surface normals pointing towards the same direction.

Stool character was characterized as normal (0 points), soft with well-formed pellets (2 points), or diarrhea (4 points).

Each analysis was run twice using the following settings: separate partitions used; ingroup monophyly enforced; uncorrelated lognormal relaxed-clock model; ngen = 40,000,000; samplefreq = 2,000; burnin = 10,001; Yule model; calibration points with normal distribution; the RAxML tolopolgy was used as starting tree for all analyses.

The method is flexible because surfaces can be built for various types of data (e.g. points, points with normals, profile curves).

In contrast to other GC methods evaluated, the Marrero Gani GC method yielded estimated critical properties with realistic, non-negative values, followed more consistent trends with molar mass and yielded normal boiling points consistent with high temperature simulated distillation data.

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