Proof involving convex function and concave function Homework Statement [/B] Let X be a vector space over ##\mathbb{R}## and ## f: X \rightarrow \mathbb{R} ## be a convex function and ##g: X \rightarrow \mathbb{R}## be a concave function. Show: The set {##x \in X: f(...
Convex risk measuresConcave valuationsDualityWeak time consistencyRisk aversion91B3091G9946A2046N10D81We derive dual characterizations of two notions of weak time consistency for concave valuations, which are convex risk measures under a positive sign convention. Combined with a suitable risk aversion ...
The main difference between a concave and convex mirror is their shape. A concave mirror curves inward, while a convex mirror curves outward. This results in different properties, such as converging or diverging light rays, and different types of images being formed. ...
Plano-convex lenses are plane on one side and convex on the other one. Also, it is possible to make biconvex lenses with different curvature radii on both sides. Similarly, defocusing lenses can be biconcave or plano-concave. Figure 4: Different types of optical lenses. According to lens...
diagram. Consider the D A 1 CB 1 and D ACB [when two angles of D A 1 CB 1 and D ACB are equal then the third angle But ED = AB Related Questions What is concave mirror mirror formula: derive the mirror formula for a convex mirror How do a concave mirror and convex mirror ...