Multiplicative calculus and its applications

Fractional calculus and its applications.

Fractional calculus was formulated in 1695, shortly after the development of classical calculus. The earliest systematic studies were attributed to Liouville, Riemann, Leibniz, etc. [1,2]. For a long time, fractional calculus has been regarded as a pure mathematical realm without real applications. But, in recent decades, such a state of affairs has been changed. It has been found that fraction...

Malliavin calculus and its applications

A Multiplicative Mean Value and Its Applications

We develop a parallel theory to that concerning the concept of integral mean value of a function, by replacing the additive framework with a multiplicative one. Particularly, we prove results which are multiplicative analogues of the Jensen and Hermite-Hadamard inequalities. 1. Introduction Many results in Real Analysis exploits the property of convexity of the subintervals I of R; (A) x; y 2 I...

A calculus of program adaptation and its applications

Traditional programming calculi focus on transforming a specification into a program. With the advent of such recent paradigms as white box reuse, component-based software development, and reengineering, and with the continued predominance of software maintenance, less and less software engineering activity nowadays deals with straightforward development. More and more, software products are de...

A Calculus of Program Transformations and Its Applications

Traditional programming calculi focus on transforming a speci cation into a program With the advent of such recent paradigms as white box reuse component based software development and reengineering and with the continued predominance of software main tenance less and less software engineering activity nowadays deals with straightforward development More and more software products are derived b...