We consider the radiative feedback processes that operate during the formation of the first stars, including the photodissociation of H2, Lyman-α radiation pressure, formation and expansion of an H II region, and disk photoevaporation. These processes may inhibit continued accretion once the stellar mass has reached a critical value, and we evaluate this mass separately for each process. Photod...

We consider a real analytic diffeomorphism ψ0 on a n-dimensional disk D, n ≥ 2, exhibiting a Feigenbaum-Coullet-Trésser (F.C.T.) attractor, being far, in the Cω(D) topology, from the standard F.C.T. map φ0 fixed by the double renormalization. We prove that ψ0 persists along a codimension-one manifold M ⊂ Cω(D), and that it is the bifurcating map along any one-parameter family in Cω(D) transvers...

We provide a generalization of the Schensted insertion algorithm for rc-graphs of Bergeron an Billey [1]. The new algorithm is used to give a new proof of Pieri’s formula.

We investigate the Bondi-Hoyle accretion of gas from a GMC onto young stardisk systems in a cluster. This post-formation accretionary phase can continue for several Myr after young stars are born, until the gas is heated by massive stars and removed from the cluster, or when low-mass stars are ejected from the cluster. We perform N-body simulations of stars orbiting in young model clusters usin...

We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in Bruhat order of the symmetric group. These skew Schubert polynomials expand in the basis of Schub...

We prove that the Lam-Shimozono “down operator” on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of “near rectangles” in the affine nilCoxeter algebra. Consequently, we obtain a combinatorial interpretation of ...

The reduced expressions for a given element w of a Coxeter group (W, S) can be regarded as the vertices of a directed graphR (w); its arcs correspond to the braid moves. Specifically, an arc goes from a reduced expression −→a to a reduced expression −→ b when −→ b is obtained from −→a by replacing a contiguous subword of the form stst · · · (for some distinct s, t ∈ S) by tsts · · · (where both...