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HISTÓRIA DA MATEMÁTICA

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GEOMETRIA DIFERENCIAL

Superfícies

  • Faixa de Möbius
    > Mathworld: Link! Equação implícita, parametrização, primeira e segunda formas fundamentais, curvatura média, curvatura de Gauss, elemento de comprimento de arco, elemento de área, também referências e links.
    > Wikipedia: Link! Fatos matemáticos e uma lista (com referências e links) de aplicações físicas, químicas e biológicas da Faixa de Möbius.
    >
    E. L. Starostin & G. H. M. van der Heijden: The shape of a Möbius strip. Nature Materials 6 (2007): 563-567. DOI: 10.1038/nmat1929. (2007) [Link! 28/06/2012]
    Abstract: "The Möbius strip, obtained by taking a rectangular strip of plastic or paper, twisting one end through 180°, and then joining the ends, is the canonical example of a one-sided surface. Finding its characteristic developable shape has been an open problem ever since its first formulation in refs [1, 2]. Here we use the invariant variational bicomplex formalism to derive the first equilibrium equations for a wide developable strip undergoing large deformations, thereby giving the first non-trivial demonstration of the potential of this approach. We then formulate the boundary-value problem for the Möbius strip and solve it numerically. Solutions for increasing width show the formation of creases bounding nearly flat triangular regions, a feature also familiar from fabric draping [3] and paper crumpling [4, 5]. This could give new insight into energy localization phenomena in unstretchable sheets, which might help to predict points of onset of tearing. It could also aid our understanding of the relationship between geometry and physical properties of nano- and microscopic Möbius strip [7, 8, 9]."

ANÁLISE FUNCIONAL

  • V. Paulsen: Completely Bounded Maps and Operator Algebras. Cambridge University Press, 2002. Link!

    TEORIA DE OPERADORES

    Teoria Espectral
    • Teoria espectral de operadores normais: RS1: "p.246": problems 3,4,5.

    Semigrupos de operadores

    • V. Gorini, A. Frigerio, M. Verri, A. Kossakowski and E. C. G. Sudarshan, Rep.Math. Phys. 13, 149 (1978)
    • H. Spohn and J. Lebowitz, Adv. in Chem. Phys. 38, 109 (1978)
    • H. Spohn, Rev. Mod. Phys. 53 569 (1980)
    • G. Lindblad, Commun. Math. Phys. 48, 119 (1976)

    CCR e CAR

    • S.J. Summers: On the Stone-von Neumann uniqueness theorem and its ramifications. In: M. Rédei, M. Stölzner: John von Neumann and the Foundations of Quantum Physics (Vienna Circle Yearbook series). Kluwer Academic Press, 2001: pp. 135-152. Abstract: "A brief history of the Stone-von Neumann uniqueness theorem and its ramifications is provided. The influence of this theorem on the development of quantum theory, which was its initial source of motivation, is emphasized. In addition, its impact upon mathematics itself is suggested by considering certain subsequent developments in originally unanticipated directions."
    • Giovanni Valente: Studies in History and Philosophy of Modern Physics 39 (2008): 860–871. Nenhuma álgebra que possui traço finito pode suportar uma representação regular das relações canônicas de comutação!
    • S. Cavallaro, G. Morchio, F. Strocchi: A generalization of the Stone–von Neumann theorem to non-regular representations of the CCR-algebra. Letters in Mathematical Physics, 47 (2999): 307.

    MODELAGEM MATEMÁTICA

    • D.L. Shepelyanskya, O.V. Zhirovc: Towards Google matrix of brain. Physics Letters A, Volume 374, Issues 31–32 (12 July 2010): 3206–3209 Doi: http://dx.doi.org/10.1016/j.physleta.2010.06.007 [Link! 19/06/2012]
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