The course will be built around three topics: (1) Prove the almost everywhere equivalence of the L n-th symmetric quantum derivative and the L Peano derivative. (2) Develop a theory of non-linear generalized derivatives, for example of the form ∑ anf(x+ bnh)f(x+ cnh). (3) Classify which generalized derivatives of the form ∑ anf(x + bnh) satisfy the mean value theorem.

In this paper, three state of the art non-stationary sinusoidal analysis methods based on Fourier transform (FT) are compared the derivative method, reassignment and generalized reassignment. 1 The derivative method and reassignment were designed to analyze linear log-AM/linear FM sinusoids. Generalized reassignment can analyze sinusoids containing arbitrary order modulations, however the discu...

The main result of this paper is a generalization of the property that, for smooth u, uxy = 0 implies (*) u(x, y) = a(x) + b(y). Any function having generalized unsymmetric mixed partial derivative identically zero is of the form (*). There is a function with generalized symmetric mixed partial derivative identically zero not of the form (*), but (*) does follow here with the additional assumpt...

A Lagrange multiplierrules that uses small generalized gradients is introduced. It includes both inequality and set constraints. The generalized gradient is the linear generalized gradient. It is smaller than the generalized gradients of Clarke and Mordukhovich but retains much of their nice calculus. Its convex hull is the generalized gradient of Michel and Penot if a function is Lipschitz. Th...