means that if and are any two framed closed surfaces in P that intersect transversely, such that \ is (homologous in to) the longitude of and \ is (homologous in to) the meridian of , then the Pontryagin classes of , and form a basis of H 1 (P ;Z). Recalling the construction of M by surgery in T 3 , we observe that there exist two framed double tori L and G in M that intersect S transveresly, a...

We derive the transit timing variations (TTVs) of two planets near a second-order mean motion resonance (MMR) on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of jn j n 2 2 1 ( ) , where  j 3 is an integer characterizing the resonance and n2 and n1 are the mean motions of the outer and inner planets, respectively. The amplitude of the TTV ...

We examine leakage and aliasing problems in a seasonal multiple linear regression model of data taken during the NORPAX Hawaii-to-Tahiti Shuttle Experiment. The model includes a mean, trend, annual harmonic, and semiannual harmonic. Inclusion of the trend can exacerbate leakage, particularly for record lengths of 13 months or less. This is not a major problem for the 15-month shuttle record. Th...