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Blanagram: rearranging the letters of a word or phrase and substituting one single letter to produce a new word or phrase; Letter bank: using the letters from a certain word or phrase as many times as wanted to produce a new word or phrase; Jumble: a kind of word game in which the solution of a puzzle is its anagram
Any vector field Y on N defines a pullback section φ ∗ Y of φ ∗ TN with (φ ∗ Y) x = Y φ(x). A vector field X on M and a vector field Y on N are said to be φ-related if φ ∗ X = φ ∗ Y as vector fields along φ. In other words, for all x in M, dφ x (X) = Y φ(x).
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 } .
Pullback, a name given to two different mathematical processes; Pullback (cohomology), a term in topology; Pullback (differential geometry), a term in differential geometry; Pullback (category theory), a term in category theory; Pullback attractor, an aspect of a random dynamical system; Pullback bundle, the fiber bundle induced by a map of its ...
It leads to the existence of pullback maps in other situations, such as pullback homomorphisms in de Rham cohomology. Formally, let f : M → N be smooth, and let ω be a smooth k-form on N. Then there is a differential form f ∗ ω on M, called the pullback of ω, which captures the behavior of ω as seen relative to f.
For example, if X, Y are manifolds, R the field of real numbers, and the cohomology is de Rham cohomology, then the pullback is induced by the pullback of differential forms. The homotopy invariance of cohomology states that if two maps f, g: X → Y are homotopic to each other, then they determine the same pullback: f * = g *.
Throughout the past decade, shares of Wal-Mart (NYS: WMT) hovered in the $50 range, even as the retail giant more than doubled in its net income in that time. The explanation is fairly simple.
This is a list of Latin words with derivatives in English language.. Ancient orthography did not distinguish between i and j or between u and v. [1] Many modern works distinguish u from v but not i from j.