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In mathematics, a Möbius strip, Möbius band, or Möbius loop [a] is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE .
Formally E* can be defined as the set of pairs (x, φ), where x ∈ X and φ ∈ (E x)*. The dual bundle is locally trivial because the dual space of the inverse of a local trivialization of E is a local trivialization of E*: the key point here is that the operation of taking the dual vector space is functorial.
The dark line is the base for a set of transversal lines that are homeomorphic to the fiber and that each touch the edge of the band twice. An annulus is an orientable I-bundle. This example is embedded in 3-space with an even number of twists This image represents the twisted I-bundle over the 2-torus, which is also fibered as a Möbius strip ...
The Möbius strip can be constructed by a non-trivial gluing of two trivial bundles on open subsets U and V of the circle S 1.When glued trivially (with g UV =1) one obtains the trivial bundle, but with the non-trivial gluing of g UV =1 on one overlap and g UV =-1 on the second overlap, one obtains the non-trivial bundle E, the Möbius strip.
The ring opening is disrotatory and suprafacial and both bond length alternation and NICS values indicate that the 6 membered ring is aromatic. The Möbius TS with 8 electrons on the other hand has lower computed activation energy and is characterized by C 2 symmetry, a conrotatory and antarafacial ring opening and 8-membered ring aromaticity.
The NFL playoff schedule is set. As the final components of the playoff picture fell into place in Week 18, the league revealed its slate for the wild-card round.
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