Carnot's function

Definitions

• Webster's Revised Unabridged Dictionary
• Carnot's function (Thermo-dynamics) a relation between the amount of heat given off by a source of heat, and the work which can be done by it. It is approximately equal to the mechanical equivalent of the thermal unit divided by the number expressing the temperature in degrees of the air thermometer, reckoned from its zero of expansion.
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Usage

In science:

Given a smooth surface S in the Heisenberg group, we compute the Hessian of the function measuring the Carnot-Charath´eodory distance from S in terms of the Mean Curvature of S and of an “imaginary curvature” which was introduced in in order to ﬁnd the geodesics which are metrically normal to S .
The Hessian of the distance from a surface in the Heisenberg group
The function LD : Ω(p, q , D) → R is called the length of horizontal curves and the function dD on S × S is called the Carnot-Carath´eodory metric of S .
A diameter bound for Sasaki manifolds with application to uniqueness for Sasaki-Einstein structure
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