This implies that convexity (the property of being convex) is invariant under affine transformations. An example of generalized convexity is orthogonal convexity. Quadratic terms, when included, can be expressed in terms of (multi-variate) bond convexity. NAS bonds are designed to protect investors from volatility and negative convexity resulting from prepayments. Like all polytopes, 4-polytopes may be classified based on properties like "convexity" and "symmetry". Vomma, volga, vega convexity, or DvegaDvol measures second order sensitivity to volatility. It also requires compactness and convexity of the set. For the ordinary convexity, the first two axioms hold, and the third one is trivial. Archimedes gave the first known precise definition of convexity. The convexity of all the sublevel sets characterizes quasiconvex functions. Gamma is important because it corrects for the convexity of value. Normal formula 24 is directed outside of chamber i.e. in side of convexity of surface. The overwhelmingly vertical decoration of the facade is granted liveliness by horizontal convexity. The adjunct space is continued along normal directed into side of convexity of surface. Given the relation between convexity and duration above, conventional bond convexities must always be positive.