Terrestrial meteorite ages indicate that some ice at the Allan Hills blue ice area (AH BIA) may be as old as 2.2 Ma. As such, ice from the AH BIA could potentially be used to extend the ice core record of paleoclimate beyond 800 ka. We collected samples from 5 to 10 cm depth along a 5 km transect through the main icefield and drilled a 225 m ice core (S27) at the midpoint of the transect to develop the climate archive of the AH BIA. Stable water isotope measurements (δD) of the surface chips and of ice core S27 yield comparable signals, indicating that the climate record has not been significantly altered in the surface ice. Measurements of 40Aratm and δ18Oatm taken from ice core S27 and eight additional shallow ice cores constrain the age of the ice to approximately 90–250 ka. Our findings provide a framework around which future investigations of potentially older ice in the AH BIA could be based.

Labelle and Rahman [4] showed that if f , g ∈ , the normalized convex functions in the unit disc D, then has a radius of convexity at least as large as the smallest root of 1 – 3r + 2r2 — 2r3 = 0. Their method requires neither the properties of the arithmetic mean nor the strong geometric properties of ; indeed, the procedure works for a linear combination of functions from any linear invariant family of finite order.

Let denote the set of all normalized analytic univalent functions in the open unit disc D. Let f(z), F(z) and φ(z) be analytic in |z| < r. We say that f(z) is majorized by F(z) in we say that f(z) is subordinate to F(z) in where .

Let be the set of all locally univalent (f’(z) ≠ 0) analytic functions in D with order ≦α which are of the form f(z) = z +… . The family is known as the universal linear invariant family of order α [6]. A concise summary of and introduction to properties of linear invariant families which relate to the following material is contained in [1]. The present paper contains the proofs of some of the results announced in [1]