Semi-differentiation, or convolution as it is sometimes known, a mathematical technique commonly used to disentangle overlapping peaks in cyclic linear sweep voltammograms. However, this often misapplied due misunderstandings of fractional calculus. Additionally, rigorous treatment and validation the theory semi-differential analysis reversible, soluble-insoluble electrochemical reactions lacki...

Fractional calculus; Conformable operators; Calculus on time scales Abstract A conformable time-scale fractional calculus of order a 2 0; 1 is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger timescale calculus is obtained as a particular case, by choosing a 1⁄4 1. a 2015 The Authors. Production and hosting by Elsevier B.V. on ...

Automatic differentiation, or as it has more recently been termed, algorithmic differentiation, (AD) is the process of determining accurate derivatives of a function defined by computer programs [Griewank 2008] using the rules of differential calculus. The objective of AD is to employ the rules of differential calculus in an algorithmic manner in order to efficiently obtain a derivative that is...

The problems formulated in the fractional calculus framework often require numerical fractional integration/differentiation of large data sets. Several existing fractional control toolboxes are capable of performing fractional calculus operations, however, none of them can efficiently perform numerical integration on multiple large data sequences. We developed a Fractional Integration Toolbox (...

This paper proposes a generic FPGA realization of an IP core for fractional-order integration and differentiation based on the Grünwald–Letnikov approximation. All dependent terms are approximated to simpler relations using curve fitting enable efficient hardware realization. Compared previous works, proposed design introduces enhancements in range covering both differentiation. An error analys...

background and aims. previous researches, conducted mostly on extracted teeth, have shown that efficacy of calculus removal decreases with increasing pocket depth, but there is still a lack of clinical studies concerning the correlation be-tween residual calculus and varying pocket depths. the objective of the present clinical study was to assess the efficiency of mechanical tooth depuration by...

Regge manifolds are piecewise continuous manifolds constructed from a finite nutnber of basic building blocks. On such manifolds piecewise continuous forms can be defined in a way similar to differential forms on a differentiable manifold. Regge manifolds are used extensively in the construction ofspace-times in numerical general relativity. In this paper a definition ofexterior differentiation...

This paper revisits the authors’ notion of a differential category from a different perspective. A differential category is an additive symmetric monoidal category with a comonad (a “coalgebra modality”) and a differential combinator. The morphisms of a differential category should be thought of as the linear maps; the differentiable or smooth maps would then be morphisms of the coKleisli categ...