Erratum to various proofs of Christol’s theorem

Function fields in positive characteristic: Expansions and Cobham’s theorem

In the vein of Christol, Kamae, Mendès France and Rauzy, we consider the analogue of a problem of Mahler for rational functions in positive characteristic. To solve this question, we prove an extension of Cobham’s theorem for quasi-automatic functions and use the recent generalization of Christol’s theorem obtained by Kedlaya.  2008 Elsevier Inc. All rights reserved.

Erratum: Nonequilibrium Shear Viscosity Computations with Langevin Dynamics

This short note is an erratum to the article [R. Joubaud and G. Stoltz, Nonequilibrium shear viscosity computations with Langevin dynamics, Multiscale Model. Sim., 10 (2012), pp. 191–216]. We present required modifications in the proofs of Theorem 2 and 3.

Algebraic Generalized Power Series and Automata

A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol’s result, we prove that the same assertion holds for generalized power series (whose index sets may be arbitrary well-ordered sets of nonnegative rationals).

(Erratum): Evaluation of Various Biological Activities of the Aerial Parts of Scrophularia frigida Growing in Iran.

Erratum To: Extension of Symmetries on Einstein Manifolds with Boundary

In this note, we point out and correct an error in the proof of Theorem 1.1 in [1]. All of the main results of [1] are correct as stated but the proofs require modification. We use below the same notation as in [1]. ∂M (δ * Y)(N, X) = 0, cannot always be simultaneously enforced with the slice property [1, (5.7)], i.e.