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Klaus Bering (2011)
Archivum Mathematicum
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We give an elementary proof of Noether's first Theorem while stressing the magical fact that the global quasi-symmetry only needs to hold for one fixed integration region. We provide sufficient conditions for gauging a global quasi-symmetry.
Neda Bokan (2003)
Kragujevac Journal of Mathematics
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Nishimura, Hirokazu (2004)
Beiträge zur Algebra und Geometrie
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Giordano, P. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Nils Dencker (2003)
Journées équations aux dérivées partielles
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We prove the Nirenberg-Treves conjecture : that for principal type pseudo-differential operators local solvability is equivalent to condition (). This condition rules out certain sign changes of the imaginary part of the principal symbol along the bicharacteristics of the real part. We obtain local solvability by proving a localizable estimate for the adjoint operator with a loss of two derivatives (compared with the elliptic case). The proof involves a new metric in the Weyl (or Beals-Fefferman)...
Eastwood, Michael G. (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Fiedler, Bernd (2002)
Séminaire Lotharingien de Combinatoire [electronic only]
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Fesser, Dirk, Seiler, Werner M. (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Kowalski, Oldřich, Vlášek, Zdeněk (2007)
Beiträge zur Algebra und Geometrie
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Zbigniew Szafraniec (1992)
Annales Polonici Mathematici
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Let E → W be an oriented vector bundle, and let X(E) denote the Euler number of E. The paper shows how to calculate X(E) in terms of equations which describe E and W.