Automatic differentiation is a powerful technique for evaluating derivatives of functions given in the form of a high-level programming language such as Fortran, C, or C++. The program is treated as a sequence of elementary statements to which the chain rule of differential calculus is applied mechanically. A key feature of this technique is its ability to generate accurate derivatives rather t...

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student problems that once required the ingenuity of an Archime...

The parametric identification of Hammerstein structured nonlinear systems with discontinuous asymmetric (two segment piecewise-linear a dead-zone) nonlinearity and input time delay is presented using fractional-order modeling technique. effect the unknown dead-zone separated from linear dynamics special excitation signals to simplify process. use fractional calculus permits reduced order dynami...

The differential λ-calculus is a paradigmatic functional programming language endowed with a syntactical differentiation operator that allows to apply a program to an argument in a linear way. One of the main features of this language is that it is resource conscious and gives the programmer suitable primitives to handle explicitly the resources used by a program during its execution. The diffe...

The differential λ-calculus is a paradigmatic functional programming language endowed with a syntactical differentiation operator that allows to apply a program to an argument in a linear way. One of the main features of this language is that it is resource conscious and gives the programmer suitable primitives to handle explicitly the resources used by a program during its execution. The diffe...

This paper is devoted to the study, for first time in literature, of optimal control problems sweeping processes governed by integro-differential inclusions Volterra type with different classes functions acting nonconvex moving sets, external dynamic perturbations, and integral parts dynamics. We establish existence solutions then obtain necessary optimality conditions a broad class local minim...