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The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times.
Weak equivalence principle This page was last edited on 27 May 2024, at 02:43 (UTC). Text is available under the Creative Commons Attribution ...
In mathematics, a weak equivalence is a notion from homotopy theory that in some sense identifies objects that have the same "shape". This notion is formalized in the axiomatic definition of a model category. A model category is a category with classes of morphisms called weak equivalences, fibrations, and cofibrations, satisfying several axioms.
Typically, this map is not a weak equivalence. For example, the homotopy pushout encountered above always maps to the ordinary pushout. This map is not typically a weak equivalence, for example the join is not weakly equivalent to the pushout of , which is a point.
In a weak field approximation, clocks tick at a rate of t' = t (1 + Φ / c 2) where Φ is the difference in gravitational potential. In this case, Φ = gh where g is the acceleration of the traveling observer during turnaround and h is the distance to the stay-at-home twin.
Thus, an icosahedral virus is made of 60N protein subunits. The number and arrangement of capsomeres in an icosahedral capsid can be classified using the "quasi-equivalence principle" proposed by Donald Caspar and Aaron Klug. [13] Like the Goldberg polyhedra, an icosahedral structure can be regarded as being constructed from pentamers and hexamers.
The Whitehead theorem states that a weak homotopy equivalence from one CW complex to another is a homotopy equivalence. (That is, the map f: X → Y has a homotopy inverse g: Y → X, which is not at all clear from the assumptions.) This implies the same conclusion for spaces X and Y that are homotopy equivalent to CW complexes.
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