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Displaying similar documents to “A basis for Numerical Functionals”

Collective Operations on Number-Membered Sets

Artur Korniłowicz (2009)

Formalized Mathematics

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The article starts with definitions of sets of opposite and inverse numbers of a given number membered set. Next, collective addition, subtraction, multiplication and division of two sets are defined. Complex numbers cases and extended real numbers ones are introduced separately and unified for reals. Shortcuts for singletons cases are also defined.

Inner Products, Group, Ring of Quaternion Numbers

Fuguo Ge (2008)

Formalized Mathematics

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In this article, we define the division of the quaternion numbers, we also give the definition of inner products, group, ring of the quaternion numbers, and we prove some of their properties.MML identifier: QUATERN2, version: 7.8.10 4.100.1011

On the Weierstrass division.

Łojasiewicz, Stanisław, Maszczyk, Tomasz, Rusek, Kamil (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Twisted action of the symmetric group on the cohomology of a flag manifold

Alain Lascoux, Bernard Leclerc, Jean-Yves Thibon (1996)

Banach Center Publications

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Classes dual to Schubert cycles constitute a basis on the cohomology ring of the flag manifold F, self-adjoint up to indexation with respect to the intersection form. Here, we study the bilinear form (X,Y) :=〈X·Y, c(F)〉 where X,Y are cocycles, c(F) is the total Chern class of F and〈,〉 is the intersection form. This form is related to a twisted action of the symmetric group of the cohomology ring, and to the degenerate affine Hecke algebra. We give a distinguished basis for this form,...