Astract We study here the ring QSn of Quasi-Symmetric Functions in the variables x1, x2, . . . , xn. F. Bergeron and C. Reutenauer [4] formulated a number of conjectures about this ring, in particular they conjectured that it is free over the ring Λn of symmetric functions in x1, x2, . . . , xn. We present here an algorithm that recursively constructs a Λn-module basis for QSn thereby proving o...

Let G be a semisimple Lie group with associated symmetric space D, and let Γ ⊂ G be a cocompact arithmetic group. Let L be a lattice inside a ZΓ-module arising from a rational finite-dimensional complex representation of G. Bergeron and Venkatesh recently gave a precise conjecture about the growth of the order of the torsion subgroup Hi(Γk;L )tors as Γk ranges over a tower of congruence subgrou...

The in-flight ice formation and accretion are highly dependent on weather conditions that essentially affect the heat transfer capability. When the temperature is sufficiently cold, the heat transfer is adequate to remove all of the latent heat from the collected water. The rate of rime ice accretion is controlled by the droplet collection efficiency. Otherwise, when the heat transfer is inadeq...

We study a solid protoplanetary core undergoing radial migration in a protoplanetary disk. We consider cores in the mass range ∼ 1 − 10 M⊕ embedded in a gaseous protoplanetary disk at different radial locations. We suppose the core luminosity is generated as a result of planetesimal accretion and calculate the structure of the gaseous envelope assuming hydrostatic and thermal equilibrium. This ...

We study the formation of a giant gas planet by the core–accretion gas– capture process, with numerical simulations, under the assumption that the planetary core forms in the center of an anti-cyclonic vortex. The presence of the vortex concentrates particles of centimeter to meter size from the surrounding disk, and speeds up the core formation process. Assuming that a planet of Jupiter mass i...

Abstract Mass accretion from the circumstellar disk onto protostar is a fundamental process during star formation. Measuring mass rate particularly challenging for stars belonging to binary systems, because it often difficult discriminate which component accreting. DQ Tau an almost equal-mass spectroscopic system where components orbit each other every 15.8 days. The known display pulsed accret...