Atmosphere of Earth trend begin above 11 km, where the temperature stabilizes through a large vertical distance through the rest of the troposphere. In the stratosphere, starting above about 20 km, the temperature increases with height, due to heating within the ozone layer caused by capture of significant ultraviolet radiation from the Sun by the dioxygen and ozone gas in this region. Still another region of increasing temperature with altitude occurs at very high altitudes, in the aptly-named thermosphere above 90 km. Because in an ideal gas of constant composition the speed of sound depends only on temperature and not on the gas
S-matrix to black hole to Hawking radiation could not be described with an S-matrix, Stephen Hawking proposed a "not-S-matrix", for which he used the dollar sign, and which therefore was also called "dollar matrix". S-matrix In physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the "in-states" and the "out-states") in the Hilbert