Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Analysis of financial indices by means of the windowed Fourier transform

The goal of this study is to analyze the dynamical properties of financial data series from nineteen worldwide stock market indices (SMI) during the period 1995–2009. SMI reveal a complex behavior that can be explored since it is available a considerable volume of data. In this paper is applied the window Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional order systems.

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Robotic manipulators with vibrations: short time fourier transform of fractional spectra

This paper analyzes the signals captured during impacts and vibrations of a mechanical manipulator. In order to acquire and study the signals an experimental setup is implemented. The signals are treated through signal processing tools such as the fast Fourier transform and the short time Fourier transform. The results show that the Fourier spectrum of several signals presents a non integer behavior. The experimental study provides valuable results that can assist in the design of a control system to deal with the unwanted effects of vibrations.

Application of Continuous Wavelet Transform to the Analysis of the Modulus of the Fractional Fourier Transform Bands for Resolving Two Component Mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Entropy analysis of DNA code dynamics in human chromosomes

Deoxyribonucleic acid, or DNA, is the most fundamental aspect of life but present day scientific knowledge has merely scratched the surface of the problem posed by its decoding. While experimental methods provide insightful clues, the adoption of analysis tools supported by the formalism of mathematics will lead to a systematic and solid build-up of knowledge. This paper studies human DNA from the perspective of system dynamics. By associating entropy and the Fourier transform, several global properties of the code are revealed. The fractional order characteristics emerge as a natural consequence of the information content. These properties constitute a small piece of scientific knowledge that will support further efforts towards the final aim of establishing a comprehensive theory of the phenomena involved in life.

Fractional dynamics in DNA

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.

On the DNA of eleven mammals

This paper studies the DNA code of eleven mammals from the perspective of fractional dynamics. The application of Fourier transform and power law trendlines leads to a categorical representation of species and chromosomes. The DNA information reveals long range memory characteristics.

Structural, physical, and chemical modifications induced by microwave heating on native agar-like galactans

Native agars from Gracilaria vermiculophylla produced in sustainable aquaculture systems (IMTA) were extracted under conventional (TWE) and microwave (MAE) heating. The optimal extracts from both processes were compared in terms of their properties. The agars’ structure was further investigated through Fourier transform infrared and NMR spectroscopy. Both samples showed a regular structure with an identical backbone, β-D-galactose (G) and 3,6-anhydro-α-L-galactose (LA) units; a considerable degree of methylation was found at C6 of the G units and, to a lesser extent, at C2 of the LA residues. The methylation degree in the G units was lower for MAEopt agar; the sulfate content was also reduced. MAE led to higher agar recoveries with drastic extraction time and solvent volume reductions. Two times lower values of [η] and Mv obtained for the MAEopt sample indicate substantial depolymerization of the polysaccharide backbone; this was reflected in its gelling properties; yet it was clearly appropriate for commercial application in soft-texture food products.

Removal of sulfamethoxazole from solution by raw and chemically treated walnut shells

Purpose: The sorption of sulfamethoxazole, a frequently detected pharmaceutical compound in the environment, onto walnut shells was evaluated. Methods: The sorption proprieties of the raw sorbent were chemically modified and two additional samples were obtained, respectively HCl and NaOH treated. Scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and thermogravimetric (TG/DTG) techniques were applied to investigate the effect of the chemical treatments on the shell surface morphology and chemistry. Sorption experiments to investigate the pH effect on the process were carried out between pH 2 and 8. Results: The chemical treatment did not substantially alter the structure of the sorbent (physical and textural characteristics) but modified the surface chemistry of the sorbent (acid–base properties, point of zero charge—pHpzc). The solution pH influences both the sorbent’s surface charge and sulfamethoxazole speciation. The best removal efficiencies were obtained for lower pH values where the neutral and cationic sulfamethoxazole forms are present in the solution. Langmuir and Freundlich isotherms were applied to the experimental adsorption data for sulfamethoxazole sorption at pH 2, 4, and 7 onto raw walnut shell. No statistical difference was found between the two models except for the pH 2 experimental data to which the Freundlich model fitted better. Conclusion: Sorption of sulfamethoxazole was found to be highly pH dependent in the entire pH range studied and for both raw and treated sorbent.

Desenvolvimento e validação de um sistema de recolha de sinal eletromiográfico baseado em placa de aquisição

A eletromiografia é, hoje em dia, uma das técnicas mais utilizadas no estudo dos músculos, estando presente em áreas como a medicina, a biomecânica e a fisiologia, possibilitando o desenvolvimento científico e contribuindo para proporcionar melhorias na qualidade da vida humana. Sendo assim, este trabalho apresenta um protótipo de um aparelho de aquisição de sinais eletromiográficos, explicando também toda a teoria, técnicas, componentes utilizadas e softwares que estiveram presentes na sua implementação. De uma forma sucinta, para a aquisição do sinal eletromiográfico usou-se uma placa de aquisição NI-USB 6009 e para a visualização do mesmo recorreu-se ao software LabVIEW. Para validar o sinal adquirido com o equipamento desenvolvido, utilizou-se um outro equipamento, o Biopac MP36 Student Lab System, fazendo-se assim recolhas de sinais eletromiográficos com ambos os equipamentos. Os sinais recolhidos pelos dois equipamentos foram analisados no software Acknowledge 3.9.0 (Biopac Systems, Inc.), podendo observar-se os espetros de frequência correspondentes a cada sinal e retirar valores para posterior análise estatística. Feita essa análise, concluiu-se que não foram detetadas diferenças significativas entre os sinais eletromiográficos recolhidos com ambos os equipamentos, validando-se assim, o equipamento desenvolvido.

Diagnóstico de máquinas elétricas pela análise de vibração

O diagnóstico de máquinas elétricas pela análise de vibração é utilizado num plano de manutenção, onde é dado a conhecer a “real condição do equipamento”, e surgiu da necessidade de detetar vibrações indesejáveis nas máquinas elétricas, de uma forma simples e com custos acessíveis. Numa fase inicial é obtido um sinal correspondente á vibração da máquina, recorrendo a um acelerômetro, que dependendo da aceleração da máquina, constrói uma forma de onda correspondente. A forma de onda fica guardada em formato de áudio *.wav. Posteriormente, em software Matlab o ficheiro *.wav irá ser carregado, e comparado com o ficheiro *.wav original da máquina. Ao comparar os ficheiros o software analisa o espectro original da máquina através da transformada de Fourier, com o espectro atual. Se este espectro sair do intervalo de segurança, o software deteta nesse espectro a origem da vibração, pois cada vibração tem uma frequência associada. Percorridos os passos descritos, o software disponibiliza ao utilizador as respetivas formas de onda e todo o restante diagnóstico de forma a uma possível intervenção antecipada da avaria.

Analysis of stock market indices with multidimensional scaling and wavelets

Stock market indices SMIs are important measures of financial and economical performance. Considerable research efforts during the last years demonstrated that these signals have a chaotic nature and require sophisticated mathematical tools for analyzing their characteristics. Classical methods, such as the Fourier transform, reveal considerable limitations in discriminating different periods of time. This paper studies the dynamics of SMI by combining the wavelet transform and the multidimensional scaling MDS . Six continuous wavelets are tested for analyzing the information content of the stock signals. In a first phase, the real Shannon wavelet is adopted for performing the evaluation of the SMI dynamics, while their comparison is visualized by means of the MDS. In a second phase, the other wavelets are also tested, and the corresponding MDS plots are analyzed.

Fractional dynamics in liquid manipulation

This paper presents a fractional calculus perspective in the study of signals captured during the movement of a mechanical manipulator carrying a liquid container. In order to study the signals an experimental setup is implemented. The system acquires data from the sensors, in real time, and, in a second phase, processes them through an analysis package. The analysis package runs off-line and handles the recorded data. The results show that the Fourier spectrum of several signals presents a fractional behavior. The experimental study provides useful information that can assist in the design of a control system and the trajectory planning to be used in reducing or eliminating the effect of vibrations.

Fractional dynamics in financial indexes

The goal of this study is the analysis of the dynamical properties of financial data series from 32 worldwide stock market indices during the period 2000–2009 at a daily time horizon. Stock market indices are examples of complex interacting systems for which a huge amount of data exists. The methods and algorithms that have been explored for the description of physical phenomena become an effective background in the analysis of economical data. In this perspective are applied the classical concepts of signal analysis, Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional dynamical systems.