Differentiability through change of variables

Change of variables

Changing variables is a useful tool that appears in many guises in computer graphics and geometric modeling. Changing the variables allows us to change the way we traverse a curve or surface, change their derivatives or place or interpret textures and other properties associated with them. In calculus, changing variables miraculously converts hard integration problems into simple standard ones ...

Fréchet directional differentiability and Fréchet differentiability

Zaj́ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any realvalued function on a normed linear space, the se...

Differentiability of Peano Derivatives

Peano differentiability is a notion of higher order differentiability in the ordinary sense. H. W. Oliver gave sufficient conditions for the mth Peano derivative to be a derivative in the ordinary sense in the case of functions of a real variable. Here we generalize this theorem to functions of several variables.

Differentiability of Torsion Theories

We prove that every perfect torsion theory for a ring R is differential (in the sense of [2]). In this case, we construct the extension of a derivation of a right R-module M to a derivation of the module of quotients of M . Then, we prove that the Lambek and Goldie torsion theories for any R are differential.

Change Through