Convex curve itself. A closed regular plane simple curve "C" is convex "if and only if" its curvature is either always non-negative or always non-positive—i.e., if and only if the "turning angle" (the angle of the tangent to the curve) is a weakly monotone function of the parametrization of the curve. Proof: ⇐ If "C" is not convex, then by the parallel tangents lemma there are three points {"p","q1","q2"} such that the tangents at these points are parallel. At least two must have their signed tangents pointing in the same direction. Without loss of generality, assume that these points are "q1" and
Compound refractive lens Compound refractive lens A Compound refractive lens (CRL) is a series of individual lenses arranged in a linear array in order to achieve focusing of X-rays in the energy range of 5-40 keV. They are an alternative to the KB mirror. For all materials the refractive index for X-rays is close to 1, hence a single conventional lens for X-rays has an extremely long focal length (for practical lens sizes). In addition, X-rays attenuate as they pass through a material so that conventional lenses for X-rays have long been considered impractical. The CRL gets its reasonably short focal length, on