Fractional coins and fractional derivatives

This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. Based on the new conceptual perspective, some experiments are performed shading new light into possible future progress.

Mix design process of polyester polymer mortars modified with recycled GFRP waste materials

In this study, the effect of incorporation of recycled glass fibre reinforced plastics (GFRP) waste materials, obtained by means of shredding and milling processes, on mechanical behaviour of polyester polymer mortars (PM) was assessed. For this purpose, different contents of GFRP recyclates, between 4% up to 12% in weight, were incorporated into polyester PM materials as sand aggregates and filler replacements. The effect of the addition of a silane coupling agent to resin binder was also evaluated. Applied waste material was proceeding from the shredding of the leftovers resultant from the cutting and assembly processes of GFRP pultrusion profiles. Currently, these leftovers as well as non-conform products and scrap resulting from pultrusion manufacturing process are landfilled, with additional costs to producers and suppliers. Hence, besides the evident environmental benefits, a viable and feasible solution for these wastes would also conduct to significant economic advantages. Design of experiments and data treatment were accomplish by means of full factorial design approach and analysis of variance ANOVA. Experimental results were promising toward the recyclability of GFRP waste materials as partial replacement of aggregates and reinforcement for PM materials, with significant improvements on mechanical properties of resultant mortars with regards to waste-free formulations.

Electrochemical determination of the herbicide bentazone using a carbon nanotube b-Cyclodextrin modified electrode

An electrochemical sensor has been developed for the determination of the herbicide bentazone, based on a GC electrode modified by a combination of multiwalled carbon nanotubes (MWCNT) with b-cyclodextrin (b-CD) incorporated in a polyaniline film. The results indicate that the b-CD/MWCNT modified GC electrode exhibits efficient electrocatalytic oxidation of bentazone with high sensitivity and stability. A cyclic voltammetric method to determine bentazone in phosphate buffer solution at pH 6.0, was developed, without any previous extraction, clean-up, or derivatization steps, in the range of 10–80 mmolL 1, with a detection limit of 1.6 mmolL 1 in water. The results were compared with those obtained by an established HPLC technique. No statistically significant differences being found between both methods.

Optimal controllers with complex order derivatives

This paper studies the optimization of complex-order algorithms for the discrete-time control of linear and nonlinear systems. The fundamentals of fractional systems and genetic algorithms are introduced. Based on these concepts, complexorder control schemes and their implementation are evaluated in the perspective of evolutionary optimization. The results demonstrate not only that complex-order derivatives constitute a valuable alternative for deriving control algorithms, but also the feasibility of the adopted optimization strategy.

Time-delay and fractional derivatives

This paper proposes the calculation of fractional algorithms based on time-delay systems. The study starts by analyzing the memory properties of fractional operators and their relation with time delay. Based on the Fourier analysis an approximation of fractional derivatives through timedelayed samples is developed. Furthermore, the parameters of the proposed approximation are estimated by means of genetic algorithms. The results demonstrate the feasibility of the new perspective.

Exploiting sensor redundancy for the calculation of fractional derivatives in the presence of noise

In this paper a new method for the calculation of the fractional expressions in the presence of sensor redundancy and noise, is presented. An algorithm, taking advantage of the signal characteristics and the sensor redundancy, is tuned and optimized through genetic algorithms. The results demonstrate the good performance for different types of expressions and distinct levels of noise.

Analysis of the nano-surface of a modified glassy carbon electrode by pseudo phase plane method

This paper presents the Pseudo phase plane (PPP) method for detecting the existence of a nanofilm on the nitroazobenzene-modified glassy carbon electrode (NAB-GC) system. This modified electrode systems and nitroazobenze-nanofilm were prepared by the electrochemical reduction of diazonium salt of NAB at the glassy carbon electrodes (GCE) in nonaqueous media. The IR spectra of the bare glassy carbon electrodes (GCE), the NAB-GC electrode system and the organic NAB film were recorded. The IR data of the bare GC, NAB-GC and NAB film were categorized into five series consisting of FILM1, GC-NAB1, GC1; FILM2, GC-NAB2, GC2; FILM3, GC-NAB3, GC3 and FILM4, GC-NAB4, GC4 respectively. The PPP approach was applied to each group of the data of unmodified and modified electrode systems with nanofilm. The results provided by PPP method show the existence of the NAB film on the modified GC electrode.

Characterization approach to modified glassy carbon electrode-nanofilm system within multidimensional scaling

The aim of this work is to characterize the nanofilm consisting of the benzoic acid-modified glassy carbon (GC) electrode system through multidimensional scaling space analysis. The surface modification is based on the electrochemical reaction between the GC electrode and benzoic acid-diazonium salt (BA-DAS). As a result, the nonofilms regarding the benzoic acid-glassy carbon (BA-GC) electrode surface was obtained. For the analysis of the naonfilm of BC-GC electrode system, the IR spectra of the modified BA-GC electrode surface, GC surface and BA-DAS were recorded in the spectral range of 599.84 – 3996.34 [cm–1]. The IR data vectors of the above three forms were processed by the using the multidimensional scaling space approach to demonstrate the existence of a nanofilm on the modified BA-GC electrode system. Two- and three-dimensional MDS profiles obtained by application of multidimensional scaling approach to the data sets {CG1,...,CG10}, {BA-GC1,...,BA-GC10} and {FILM1,...,FILM10} allow a good recognition of the nanofilm on the modified glassy carbon (GC) electrode system.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Real time fault injection using a modified debugging infrastructure

Dependability is a critical factor in computer systems, requiring high quality validation & verification procedures in the development stage. At the same time, digital devices are getting smaller and access to their internal signals and registers is increasingly complex, requiring innovative debugging methodologies. To address this issue, most recent microprocessors include an on-chip debug (OCD) infrastructure to facilitate common debugging operations. This paper proposes an enhanced OCD infrastructure with the objective of supporting the verification of fault-tolerant mechanisms through fault injection campaigns. This upgraded on-chip debug and fault injection (OCD-FI) infrastructure provides an efficient fault injection mechanism with improved capabilities and dynamic behavior. Preliminary results show that this solution provides flexibility in terms of fault triggering and allows high speed real-time fault injection in memory elements

Approximating fractional derivatives through the generalized mean

This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm.

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Calculation of fractional derivatives of noisy data with genetic algorithms

This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established.

Modified particle swarm optimization for day-ahead distributed energy resources scheduling including vehicle-to-grid

Mestrado em Engenharia Electrotécnica – Sistemas Eléctricos de Energia

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.