Algebraic Theory of Automata by Abraham Ginzburg PDF

By Abraham Ginzburg

ISBN-10: 0122850505

ISBN-13: 9780122850509

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70: 707-719. [CKR] Cooper NR, Komineas S, Read N,Vortex lattices in the lowest Landau level for confined Bose-Einstein condensates, Phys. Rev. A 10, 033604 (2004). [CW] Cornell EA, Wieman CE, Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, in: Les Prix Nobel 2001 (The Nobel Foundation, Stockholm, 2002) , pp. 87-108, Reprinted in: Rev. Mod. Phys. 14, 875-893; Cern. Phys. Cern. 3, 476-493 (2002). [Ho] Ho TL, Bose-Einstein Condensates with Large Number of Vortices, Phys.

12] T. D'Aprile, Semiclassical states for the nonlinear Schrodinge equation with the electromag­ netic field, preprint. [13] T. Wei, On bound states concentrating on spheres for the Maxwell-Schrodinger equation, SIAM J. Math. Anal. 37 (2005), no. 1, 321-3-12. �-, 30 ANTONIO AMBROSETTI AND ANDREA MALCHIODI [14] M. Del Pino, P. Felmer, Local mountain passes for semilinear elliptic problems in unbounded domains, Cal. Var. PDE 4 (1996) , 121-137. [15] M. Del Pino, M . Kowalczyk, J. Wei, Concentration on curves for Nonlinear Schrodinger Equations, Comm.

In the sequel we denote by 0a generic open set in Rd. If J-L is a nonnegative Borel measure in 0we say that J-L is concentrated on a Borel set F if J-L(O \ F) = O. For a Borel set F c 0, the restriction J-L L F is defined by J-L L F(E) := J-L(F n E) for any Borel set E c O. THE CHAIN RULE FOR THE DIVERGENCE OF VECTOR FIELDS 35 11 The same operation can be defined for vector valued measures with finite total variation in O . Unless otherwise stated, weak* convergence of measures is under­ stood in the duality with continuous and compactly supported functions.

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Algebraic Theory of Automata by Abraham Ginzburg

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