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A path isometry or arcwise isometry is a map which preserves the lengths of curves; such a map is not necessarily an isometry in the distance preserving sense, and it need not necessarily be bijective, or even injective. [5] [6] This term is often abridged to simply isometry, so one should take care to determine from context which type is intended.
Bodies that are opaque to thermal radiation that falls on them are valuable in the study of heat radiation. Planck analyzed such bodies with the approximation that they be considered topologically to have an interior and to share an interface. They share the interface with their contiguous medium, which may be rarefied material such as air, or ...
Radiation waves may travel in unusual patterns compared to conduction heat flow. Radiation allows waves to travel from a heated body through a cold non-absorbing or partially absorbing medium and reach a warmer body again. [14] An example is the case of the radiation waves that travel from the Sun to the Earth.
Following Bartoli, Boltzmann considered an ideal heat engine using electromagnetic radiation instead of an ideal gas as working matter. The law was almost immediately experimentally verified. Heinrich Weber in 1888 pointed out deviations at higher temperatures, but perfect accuracy within measurement uncertainties was confirmed up to ...
Once that happens, radiation can travel far enough that the local emission, B λ (T), can differ from the absorption of incoming I λ. The altitude where the transition to semi-transparency occurs is referred to as the "effective emission altitude" or "effective radiating level." Thermal radiation from this altitude is able to escape to space.
Any element of E(n) is a translation followed by an orthogonal transformation (the linear part of the isometry), in a unique way: (+) where A is an orthogonal matrix or the same orthogonal transformation followed by a translation: x ↦ A x + c , {\displaystyle x\mapsto Ax+c,} with c = Ab
In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. [1] [self-published source] [2] [3] The rigid transformations include rotations, translations, reflections, or any sequence of ...
The Unruh effect (also known as the Fulling–Davies–Unruh effect) is a theoretical prediction in quantum field theory that an observer who is uniformly accelerating through empty space will perceive a thermal bath. This means that even in the absence of any external heat sources, an accelerating observer will detect particles and experience ...