Development of fractional order capacitors based on electrolyte processes

In recent years, significant research in the field of electrochemistry was developed. The performance of electrical devices, depending on the processes of the electrolytes, was described and the physical origin of each parameter was established. However, the influence of the irregularity of the electrodes was not a subject of study and only recently this problem became relevant in the viewpoint of fractional calculus. This paper describes an electrolytic process in the perspective of fractional order capacitors. In this line of thought, are developed several experiments for measuring the electrical impedance of the devices. The results are analyzed through the frequency response, revealing capacitances of fractional order that can constitute an alternative to the classical integer order elements. Fractional order electric circuits are used to model and study the performance of the electrolyte processes.

Modeling Vegetable Fractals by means of Fractional-order Equations

This paper characterizes four ‘fractal vegetables’: (i) cauliflower (brassica oleracea var. Botrytis); (ii) broccoli (brassica oleracea var. italica); (iii) round cabbage (brassica oleracea var. capitata) and (iv) Brussels sprout (brassica oleracea var. gemmifera), by means of electrical impedance spectroscopy and fractional calculus tools. Experimental data is approximated using fractional-order models and the corresponding parameters are determined with a genetic algorithm. The Havriliak-Negami five-parameter model fits well into the data, demonstrating that classical formulae can constitute simple and reliable models to characterize biological structures.

System Modeling and Control Through Fractional-Order Algorithms

The theory of fractional calculus goes back to the beginning of thr throry of differential calculus but its inherent complexity postponed the applications of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of automaticcontrol preliminary work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. The algorithms studied adopt the time domein, which makes them suited for z-transform analusis and discrete-time implementation. The performance of discrete-time fractional-order controllers with linear and non-linear systems is also investigated.

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

Identification of fractional-order transfer functions using a step excitation

This brief proposes a new method for the identification of fractional order transfer functions based on the time response resulting from a single step excitation. The proposed method is applied to the identification of a three-dimensional RC network, which can be tailored in terms of topology and composition to emulate real time systems governed by fractional order dynamics. The results are in excellent agreement with the actual network response, yet the identification procedure only requires a small number of coefficients to be determined, demonstrating that the fractional order modelling approach leads to very parsimonious model formulations.

Tables of Bessel functions of fractional order.

Mode of access: Internet.

Design And Synthesis Of N-acylated Aza-goniothalamin Derivatives And Evaluation Of Their In Vitro And In Vivo Antitumor Activity.

Herein we describe the synthesis of a focused library of compounds based on the structure of goniothalamin (1) and the evaluation of the potential antitumor activity of the compounds. N-Acylation of aza-goniothalamin (2) restored the in vitro antiproliferative activity of this family of compounds. 1-(E)-But-2-enoyl-6-styryl-5,6-dihydropyridin-2(1H)-one (18) displayed enhanced antiproliferative activity. Both goniothalamin (1) and derivative 18 led to reactive oxygen species generation in PC-3 cells, which was probably a signal for caspase-dependent apoptosis. Treatment with derivative 18 promoted Annexin V/7-aminoactinomycin D double staining, which indicated apoptosis, and also led to G2 /M cell-cycle arrest. In vivo studies in Ehrlich ascitic and solid tumor models confirmed the antitumor activity of goniothalamin (1), without signs of toxicity. However, derivative 18 exhibited an unexpectedly lower in vivo antitumor activity, despite the treatments being administered at the same site of inoculation. Contrary to its in vitro profile, aza-goniothalamin (2) inhibited Ehrlich tumor growth, both on the ascitic and solid forms. Our findings highlight the importance of in vivo studies in the search for new candidates for cancer treatment.

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.

A numerical model for shoaling and refraction of second-order cnoidal waves over an irregular bottom /

Mode of access: Internet.

A numerical model for shoaling and refraction of third-order Stokes waves over an irregular bottom /

"May 1987."

Stability and convergence of variable order multistep methods,

Includes bibliographical references.

A Review of Definitions for Fractional Derivatives and Integral

This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.