A new proof of the analyticity of the electronic density of molecules

We give a new, short proof of the regularity away from the nuclei of the electronic density of a molecule obtained in [1,2]. The new argument is based on the regularity properties of the Coulomb interactions underlined in [3,4] and on well-known elliptic technics. [1] S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oe stergaard Soerensen: The electron density is smooth away from the nuclei. Comm. Math. Phys. 228, no. 3 (2002), 401-415. [2] S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oestergaard Soerensen: Analyticity of the density of electronic wave functions. Ark. Mat. 42, no. 1 (2004), 87-106. [3] W. Hunziker: Distortion analyticity and molecular resonances curves. Ann. Inst. H. Poincar\'e, s. A, t. 45, no 4, 339-358 (1986). [4] M. Klein, A. Martinez, R. Seiler, X.P. Wang: On the Born-Oppenheimer expansion for polyatomic molecules. Comm. Math. Phys. 143, no. 3, 607-639 (1992). The paper is published in Letters in Mathematical Physics 93, number 1, pp. 73-83, 2010. The original publication is available at " www.springerlink.com "

Existence, Regularity, and Properties of Generalized Apparent Horizons

We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.Comment: 16 pages, thoroughly revised, no major changes, to appear in Comm. Math. Phy

Salt Lake County v. Utah Labor Commission, and Steven A. Alexander : Reply Brief

Case No. 20060233-CA Labor Comm. Case No. 03-0089 Appeal from the final agency decision of the Utah Labor Commission Appeals Board, Labor Comm. Case No. 03-0089 REPLY BRIEF OF APPELLANT/PETITIONER SALT LAKE COUNTY

Abstract commensurators of solvable Baumslag - Solitar groups

We prove that for any natural n>1, the abstract commensurator group of the Baumslag - Solitar group BS(1,n) is isomorphic to the group of 2 by 2 upper triangular matrices A over rational numbers with A_{11}=1. We also prove that for any finitely generated group G with the unique root property the natural homomorphisms Aut(G)--> Comm(G)--> QI(G) are embeddings.Comment: 8 pages, no figur

Nonadiabatic Approach to Spin-Peierls Transitions via Flow Equations

The validity of the adiabatic approach to spin-Peierls transitions is assessed. An alternative approach is developed which maps the initial magneto-elastic problem to an effective magnetic problem only. Thus the equivalence of magneto-elastic solitons and magnetic spinons is shown. No soft phonon is required for the transition. Temperature dependent couplings are predicted in accordance with the analysis of experimental data.Comment: Latex, 4 pages, Phys. Rev. B, Rap. Comm. in press final version containing some clarification