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phase periodicity - translation to russian
математика
фазовая периодичность
![A small piece of rapidly melting solid [[argon]] shows two concurrent phase changes. The transition from solid to liquid, and gas to liquid (shown by the white condensed water vapour).](https://commons.wikimedia.org/wiki/Special:FilePath/Argon ice 1.jpg?width=200 "A small piece of rapidly melting solid [[argon]] shows two concurrent phase changes. The transition from solid to liquid, and gas to liquid (shown by the white condensed water vapour).")
![the anomalous behavior of water]].](https://commons.wikimedia.org/wiki/Special:FilePath/Phase-diag2.svg?width=200 "the anomalous behavior of water]].")
нефтегазовая промышленность
фазовое превращение
Definition
1) Период, стадия, этап в развитии чего-л.
2) Само положение, форма чего -л. в данный момент; фазис.
2. ж.
Величина, характеризующая состояние какого-л. процесса в каждый момент времени (в физике).
3. ж.
Однородная часть какой-л. неоднородной системы (в химии).
4. ж.
Отдельная группа обмоток генератора, а также присоединенный к ней провод, передающий электрический ток (в электротехнике).
Wikipedia
In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959), which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. Bott periodicity can be formulated in numerous ways, with the periodicity in question always appearing as a period-2 phenomenon, with respect to dimension, for the theory associated to the unitary group. See for example topological K-theory.
There are corresponding period-8 phenomena for the matching theories, (real) KO-theory and (quaternionic) KSp-theory, associated to the real orthogonal group and the quaternionic symplectic group, respectively. The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, which causes the period 8 Bott periodicity to be visible in the stable homotopy groups of spheres.
