Eulerian calculus, II: An extension of Han's fundamental transformation

SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...

The Transformation Calculus the Transformation Calculus

The lambda-calculus, by its ability to express any computable function, is theoretically able to represent any algorithm. However, notwithstanding their equivalence in expressiveness, it is not so easy to nd a natural translation for algorithms described in an imperative way. The transformation calculus, a conservative extension of lambda-calculus, corrects this aw by re-introducing an implicit...

Fundamental Theorem of Calculus

A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green’s and Stokes’ theorem are discussed, as well as the new theory of monogenic functions, which generalizes the concept of an analytic function of a complex variable ...

Efficient Algorithms for Eulerian Extension

Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in scheduling and routing and are closely related to the Chinese Postman and Rural Postman problems. Our main result is to show that the NP-hard Weighted Multigraph Eulerian Extension is fixed-parameter tractable with respect ...

Eulerian Calculus and Transformations of Rearrangements