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This linear map is known as the pullback (by ), and is frequently denoted by . More generally, any covariant tensor field – in particular any differential form – on N {\displaystyle N} may be pulled back to M {\displaystyle M} using ϕ {\displaystyle \phi } .
The pullback bundle is an example that bridges the notion of a pullback as precomposition, and the notion of a pullback as a Cartesian square. In that example, the base space of a fiber bundle is pulled back, in the sense of precomposition, above. The fibers then travel along with the points in the base space at which they are anchored: the ...
The notion of pushforward in mathematics is "dual" to the notion of pullback, and can mean a number of different but closely related things. Pushforward (differential), the differential of a smooth map between manifolds, and the "pushforward" operations it defines
An example of this strategy is the furniture industry, where production strategy has to follow a pull-based strategy, since it is impossible to make production decisions based on long-term forecasts. However, the distribution strategy needs to take advantage of economies of scale in order to reduce transportation cost, using a push-based strategy.
For most gym-goers, Nelson says, the best bet is to focus on bringing control to the eccentric portion of a movement, then a forceful, fast concentric to finish a rep. Lowering the weight under ...
In general, any measurable function can be pushed forward. The push-forward then becomes a linear operator, known as the transfer operator or Frobenius–Perron operator.In finite spaces this operator typically satisfies the requirements of the Frobenius–Perron theorem, and the maximal eigenvalue of the operator corresponds to the invariant measure.
We continue to deploy a balanced strategy of allocating capital for long-term value creation. Cash flow from operations was 2.6 billion in the quarter and 10.5 billion for the year.
Image source: The Motley Fool. Synchrony Financial (NYSE: SYF) Q4 2024 Earnings Call Jan 28, 2025, 8:00 a.m. ET. Contents: Prepared Remarks. Questions and Answers. Call Participants