Documenta Mathematica Band 15, 2010 Jianqiang Zhao Standard Relations of Multiple Polylogarithm Values at Roots of Unity Indranil Biswas and Norbert Hoffmann

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Documenta Mathematica Band 6, 2001 ¨ hrl, Heinz Siedentop Raymond Brummelhuis, Norbert Ro Stability of the Relativistic Electron-Positron Field of Atoms in Hartree-Fock Approximation:

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Documenta Mathematica Band 9, 2004 Mike Develin and Bernd Sturmfels Tropical Convexity 1–27

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Documenta Mathematica, Extra Volume 2015 A Collection of Manuscripts Written in Honour of Alexander S. Merkurjev’s Sixtieth Birthday Edited by: P. Balmer, Univ. of California at Los Angeles, USA, V. Chernousov, Univ. o

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IT.SERVICES Bestellformular für Mathematica Auftraggeber: Titel, Name: Vorname:

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Documenta Mathematica ¨ ndet 1996 durch die Gegru Deutsche Mathematiker-Vereinigung Minimal regular resolution XH (p)0 of XH (p)

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Documenta Mathematica Extra Volume: Alexander S. Merkurjev’s Sixtieth Birthday, 2015 Preface 1

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Optional homework #9 Using Mathematica, show the following for the Hartree–Fock (HF) solution of a homogeneous electron gas (HEG). A normalized HF orbital is written as 1 ϕ k (r) = √ exp(ik · r), (1)

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Documenta Mathematica Journal der Deutschen Mathematiker-Vereinigung BandISSNPrint

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• Abstract algebra
• Algebra
• Mathematics
• Algebraic geometry
• Sheaf theory
• Cohomology theories
• Vector bundles
• Homological algebra
• tale cohomology
• tale morphism
• Sheaf
• Analytic space

Documenta Mathematica Journal der Deutschen Mathematiker-Vereinigung BandISSNPrint

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• Mathematical analysis
• Lie groups
• Mathematics
• Several complex variables
• Complex manifolds
• Group actions
• Plurisubharmonic function
• Stein manifold
• Moment map
• Lie algebra
• Holomorphic function
• Differential geometry of surfaces