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References 1. , Schr¨ odinger operators with magnetic fields. I. General interactions. Duke Math. J. 235 (1978), 847-883. 2. , Schr¨ odinger operators with magnetic fields. III. Atoms in homogeneous magnetic field. Comm. Math. Phys. 79 (1981), 529-883. 3. , Atoms in strong magnetic fields: the high field limit at fixed nuclear charge. Comm. Math. Phys. 212 (2000), 703-724. 4. Briet, P. , Integrated density of states in strong magnetic fields. J. Funct. Anal. 237 (2006), 540-564. 5. Brummelhuis, R.

Hence, the linear functional η → (Q∗ η, S −1 F ) extends uniquely to a bounded linear functional on H+1 . 1. 1 by showing that H is symmetric and a bijection from its domain D onto H0 . To prove the July 4, 2008 10:4 WSPC - Proceedings Trim Size: 9in x 6in QMATH10-book Self-adjointness via Hardy-like inequalities 45 symmetry we have to show that for both pairs (u, v), (˜ u, v˜) in the domain D, H u , v u ˜ v˜ = (P u + Qv, u ˜) + (T u − Sv, v˜) equals (u, P u ˜ + Q˜ v ) + (v, T u ˜ − S˜ v) = u u ˜ ,H v v˜ .

Physics in a strong magntic field. Gaz. Math. 106 suppl. (2005), 135-161. 11. , Random hamiltonians ergodic in all but one direction. Comm. Math. Phys. 128 (1990), 613-625. 12. , Spectra of Random and Almost-Periodic Operators. Grundlehren der Mathematischen Wissenschaften 297. Springer-Verlag, Berlin, 1992. 13. Fischer, W. , and P. , Spectral localization by gaussian July 4, 2008 10:4 WSPC - Proceedings Trim Size: 9in x 6in QMATH10-book Integrated density of states 14. 15. 16. 17. 18. 19. 20.

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[Article] Detailed mapping of ascorbate distribution in rat brain by K. Milby, A. Oke, R.N. Adams


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