A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Alterações da Actividade Autonómica Durante o Teste de Inclinação em Doentes com Fibrilhação Auricular Paroxística: Análise com Wavelets

The autonomic nervous system (ANS) is known to be an important modulator in the pathogenesis of paroxysmal atrial fibrillation (PAF). Changes in ANS control of heart rate variability (HRV) occur during orthostatism to maintain cardiovascular homeostasis. Wavelet transform has emerged as a useful tool that provides time-frequency decomposition of the signal under investigation, enabling intermittent components of transient phenomena to be analyzed. AIM: To study HRV during head-up tilt (HUT) with wavelet transform analysis in PAF patients and healthy individuals (normals). METHODS: Twenty-one patients with PAF (8 men; age 58 +/- 14 yrs) were examined and compared with 21 normals (7 men, age 48 +/- 12 yrs). After a supine resting period, all subjects underwent passive HUT (60 degrees) while in sinus rhythm. Continuous monitoring of ECG and blood pressure was carried out (Task Force Monitor, CNSystems). Acute changes in RR-intervals were assessed by wavelet analysis and low-frequency power (LF: 0.04-0.15 Hz), high-frequency power (HF: 0.15-0.60 Hz) and LF/HF (sympathovagal) were calculated for 1) the last 2 min of the supine period; 2) the 15 sec of tilting movement (TM); and 3) the 1st (TT1) and 2nd (TT2) min of HUT. Data are expressed as means +/- SEM. RESULTS: Baseline and HUT RR-intervals were similar for the two groups. Supine basal blood pressure was also similar for the two groups, with a sustained increase in PAF patients, and a decrease followed by an increase and then recovery in normals. Basal LF, HF and LF/ HF values in PAF patients were 632 +/- 162 ms2, 534 +/- 231 ms2 and 1.95 +/- 0.39 respectively, and 1058 +/- 223 ms2, 789 +/- 244 ms2 and 2.4 +/- 0.36 respectively in normals (p = NS). During TM, LF, HF and LF/HF values for PAF patients were 747 +/- 277 ms2, 387 +/- 94 ms2 and 2.9 +/- 0.6 respectively, and 1316 +/- 315 ms2, 698 +/- 148 ms2 and 2.8 +/- 0.6 respectively in normals (p < 0.05 for LF and HF). During TF1, LF, HF and LF/ HF values for PAF patients were 1243 +/- 432 ms2, 302 +/- 88 ms2 and 7.7 +/- 2.4 respectively, and 1992 +/- 398 ms2, 333 +/- 76 ms2 and 7.8 +/- 0.98 respectively for normals (p < 0.05 for LF). During TF2, LF, HF and LF/HF values for PAF patients were 871 +/- 256 ms2, 242 +/- 51 ms2 and 4.7 +/- 0.9 respectively, and 1263 +/- 335 ms2, 317 +/- 108 ms2 and 8.6 +/- 0.68 respectively for normals (p < 0.05 for LF/HF). The dynamic profile of HRV showed that LF and HF values in PAF patients did not change significantly during TM or TT2, and LF/HF did not change during TM but increased in TT1 and TT2. CONCLUSION: Patients with PAF present alterations in HRV during orthostatism, with decreased LF and HF power during TM, without significant variations during the first minutes of HUT. These findings suggest that wavelet transform analysis may provide new insights when assessing autonomic heart regulation and highlight the presence of ANS disturbances in PAF.

The effect of water inorganic matrix in ibuprofen adsorption onto activated carbon for water and wastewater treatment

Dissertação para obtenção do Grau de Mestre em Engenharia Química e Bioquímica

Spatial neighborhood matrix computation: Inverse distance weighted versus binary contiguity

Paper presented at Geo-Spatial Crossroad GI_Forum, Salzburg, Austria.

Matrix fractional systems

This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole–Cole, Davidson–Cole, and Havriliak–Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.

Leprosy control: perspectives & epidemiological and operational aspects

OBJECTIVES: As a starting point, a vast variety of 200 technical papers and documents published during the ten years 1999-2008, from Brazilian and international organizations dedicated to the control of leprosy, was taken. A study was then undertaken to investigate its future evolutive possibilities by employing resources obtained from scenario analyses. DESIGN: The methodological reconstruction in use was of a qualitative nature, based on a bibliographic review and content analysis techniques. The latter were employed in a documental, categorical, contingent, frequency-based format, in compliance with appropriate and pertinent conditions. RESULTS: Nowadays, important elements on epidemiological and operational aspects have been regained, as well as respective perspectives. CONCLUSIONS: A projection is made towards the fact that the maintenance of the disease's present incidence levels constitute economic and sanitary challenges that confront issues ranging from the neoliberal model of global societal organization to specific competences of actions taken by health teams in the field.

Análise espectral com wavelets do ECoG em crises epilépticas

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Development of mixed matrix membranes with metal - organic framework and ionic liquids for biogas upgrading

Dissertation presented to Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa for obtaining the master degree in Membrane Engineering

The additive effects in matrix dispersed liquid crystals

Dissertation presented at Faculdade de Ciências e Tecnologia from Universidade Nova de Lisboa to obtain the degree of Master in Chemical and Biochemical Engineering

An internal analysis of Amorim Turismo’s operations regarding food and beverage with a focus on operational efficiency and quality of service

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

Microbial contribution to biofuels production

Dissertação para obtenção do Grau de Doutor em Engenharia Química e Bioquímica

The effect of key process operational conditions on enhanced biological phosphorus removal from wastewater

Enhanced biological phosphorus removal (EBPR) is the most economic and sustainable option used in wastewater treatment plants (WWTPs) for phosphorus removal. In this process it is important to control the competition between polyphosphate accumulating organisms (PAOs) and glycogen accumulating organisms (GAOs), since EBPR deterioration or failure can be related with the proliferation of GAOs over PAOs. This thesis is focused on the effect of operational conditions (volatile fatty acid (VFA) composition, dissolved oxygen (DO) concentration and organic carbon loading) on PAO and GAO metabolism. The knowledge about the effect of these operational conditions on EBPR metabolism is very important, since they represent key factors that impact WWTPs performance and sustainability. Substrate competition between the anaerobic uptake of acetate and propionate (the main VFAs present in WWTPs) was shown in this work to be a relevant factor affecting PAO metabolism, and a metabolic model was developed that successfully describes this effect. Interestingly, the aerobic metabolism of PAOs was not affected by different VFA compositions, since the aerobic kinetic parameters for phosphorus uptake, polyhydroxyalkanoates (PHAs) degradation and glycogen production were relatively independent of acetate or propionate concentration. This is very relevant for WWTPs, since it will simplify the calibration procedure for metabolic models, facilitating their use for full-scale systems. The DO concentration and aerobic hydraulic retention time (HRT) affected the PAO-GAO competition, where low DO levels or lower aerobic HRT was more favourable for PAOs than GAOs. Indeed, the oxygen affinity coefficient was significantly higher for GAOs than PAOs, showing that PAOs were far superior at scavenging for the often limited oxygen levels in WWTPs. The operation of WWTPs with low aeration is of high importance for full-scale systems, since it decreases the energetic costs and can potentially improve WWTP sustainability. Extended periods of low organic carbon load, which are the most common conditions that exist in full-scale WWTPs, also had an impact on PAO and GAO activity. GAOs exhibited a substantially higher biomass decay rate as compared to PAOs under these conditions, which revealed a higher survival capacity for PAOs, representing an advantage for PAOs in EBPR processes. This superior survival capacity of PAOs under conditions more closely resembling a full-scale environment was linked with their ability to maintain a residual level of PHA reserves for longer than GAOs, providing them with an effective energy source for aerobic maintenance processes. Overall, this work shows that each of these key operational conditions play an important role in the PAO-GAO competition and should be considered in WWTP models in order to improve EBPR processes.

Epidemiological, clinical, and operational aspects of leprosy patients assisted at a referral service in the state of Maranhão, Brazil

INTRODUCTION: Leprosy is an infectious disease caused by Mycobacterium leprae. The aim of this study was to describe the epidemiological, clinical, and operational aspects of leprosy carriers. METHODS: A cross-sectional study leprosy patients assisted in São Luis, MA, was performed. RESULTS: Of the 85 cases analyzed, 51.7% were male participants, and 60% were brown. Concerning the age, 54.8% of women were between 35 and 49 years, and 57.6% of men were between 20 and 34 years. Lepromatous leprosy was found in 42.3% of cases, and the multibacillary form was found in 72.9%. The skin smear was positive in 42.3%. The occurrence of reaction was found in 43.5% of cases, and 83.5% had no Bacillus Calmette-Guérin scar. Leprosy in the family was reported by 44.7% of the patients. Most of the individuals (96.4%) lived in houses made of brick with more than three rooms (72.6%) and two persons per room (65.1%). Concerning the level of education, 41.4% of women and 34.1% of men had more than one to three years of education. The most evaluated age group in the beginning of the treatment was that of 35 to 49 years with a Grade 0 incapability (64.5%), and that in the end was the age group of 20 to 34 (29.9%) with Grade 0, 30.7% Grade 1, and 11.5% Grade 2. CONCLUSIONS: The frequency of multibacillary forms found in this study and the cases in family members point out delayed diagnoses. Thus, early diagnosis and appropriate treatment are important in decreasing the outcome of disabilities.