Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Rhapsody in Fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

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.

Effects of Acute Autonomic Modulation on Atrial Conduction Delay and Local Electrograms Duration in Paroxysmal Atrial Fibrillation

Slowed atrial conduction may contribute to reentry circuits and vulnerability for atrial fibrillation (AF). The autonomic nervous system (ANS) has modulating effects on electrophysiological properties. However, complex interactions of the ANS with the arrhythmogenic substrate make it difficult to understand the mechanisms underlying induction and maintenance of AF. AIM: To determine the effect of acute ANS modulation in atrial activation times in patients (P) with paroxysmal AF (PAF). METHODS AND RESULTS: 16P (9 men; 59±14years) with PAF, who underwent electrophysiological study before AF ablation, and 15P (7 men; 58±11years) with atrioventricular nodal reentry tachycardia, without documentation or induction of AF (control group). Each group included 7P with arterial hypertension but without underlying structural heart disease. The study was performed while off drugs. Multipolar catheters were placed at the high right atrium (HRA), right atrial appendage (RAA), coronary sinus (CS) and His bundle area (His). At baseline and with HRA pacing (600ms, shortest propagated S2) we measured: i) intra-atrial conduction time (IACT, between RAA and atrial deflection in the distal His), ii) inter-atrial conduction time (interACT, between RAA and distal CS), iii) left atrial activation time (LAAT, between atrial deflection in the distal His and distal CS), iv) bipolar electrogram duration at four atrial sites (RAA, His, proximal and distal CS). In the PAF group, measurements were also determined during handgrip and carotid sinus massage (CSM), and after pharmacological blockade of the ANS (ANSB). AF was induced by HRA programmed stimulation in 56% (self-limited - 6; sustained - 3), 68.8% (self-limited - 6; sustained - 5), and 50% (self-limited - 5; sustained - 3) of the P, in basal, during ANS maneuvers, and after ANSB, respectively (p=NS). IACT, interACT and LAAT significantly lengthened during HRA pacing in both groups (600ms, S2). P with PAF have longer IACT (p<0.05), a higher increase in both IACT, interACT (p<0.01) and electrograms duration (p<0.05) with S2, and more fragmented activity, compared with the control group. Atrial conduction times and electrograms duration were not significantly changed during ANS stimulation. Nevertheless, ANS maneuvers increased heterogeneity of the local electrograms duration. Also, P with sustained AF showed longer interACT and LAAT during CSM. CONCLUSION: Atrial conduction times, electrograms duration and fractionated activity are increased in PAF, suggesting a role for conduction delays in the arrhythmogenic substrate. Acute vagal stimulation is associated with prolonged interACT and LAAT in P with inducible sustained AF and ANS modulation may influence the heterogeneity of atrial electrograms duration.

Equations for defining the mismatch between students and school furniture: A systematic review

The present study reviews the scientific literature that describes the criteria equations for defining the mismatch between students and school furniture. This mismatch may negatively affect students' performance and comfort. Seventeen studies met the criteria of this review and twenty-one equations to test six furniture dimensions were identified. There was substantial mismatch between the relative heights of chairs and tables. Some systematic errors have been found during the application of the different equations, such as the assumption that students are sitting on chairs with a proper seat height. Only one study considered the cumulative fit. Finally, some equations are based on contradictory criteria and need to develop and evaluate new equations for these cases. Relevance to industry: Ultimately, the present work is a contribution toward improving the evaluation of school furniture and could be used to design ergonomic-oriented classroom furniture.

Measuring end-to-end delay in real-time auralisation systems

One of the major challenges in the development of an immersive system is handling the delay between the tracking of the user’s head position and the updated projection of a 3D image or auralised sound, also called end-to-end delay. Excessive end-to-end delay can result in the general decrement of the “feeling of presence”, the occurrence of motion sickness and poor performance in perception-action tasks. These latencies must be known in order to provide insights on the technological (hardware/software optimization) or psychophysical (recalibration sessions) strategies to deal with them. Our goal was to develop a new measurement method of end-to-end delay that is both precise and easily replicated. We used a Head and Torso simulator (HATS) as an auditory signal sensor, a fast response photo-sensor to detect a visual stimulus response from a Motion Capture System, and a voltage input trigger as real-time event. The HATS was mounted in a turntable which allowed us to precisely change the 3D sound relative to the head position. When the virtual sound source was at 90º azimuth, the correspondent HRTF would set all the intensity values to zero, at the same time a trigger would register the real-time event of turning the HATS 90º azimuth. Furthermore, with the HATS turned 90º to the left, the motion capture marker visualization would fell exactly in the photo-sensor receptor. This method allowed us to precisely measure the delay from tracking to displaying. Moreover, our results show that the method of tracking, its tracking frequency, and the rendering of the sound reflections are the main predictors of end-to-end delay.

Biomass equations for forest regrowth in the eastern Amazon using randomized branch sampling

Forest regrowth occupies an extensive and increasing area in the Amazon basin, but accurate assessment of the impact of regrowth on carbon and nutrient cycles has been hampered by a paucity of available allometric equations. We develop pooled and species-specific equations for total aboveground biomass for a study site in the eastern Amazon that had been abandoned for 15 years. Field work was conducted using randomized branch sampling, a rapid technique that has seen little use in tropical forests. High consistency of sample paths in randomized branch sampling, as measured by the standard error of individual paths (14%), suggests the method may provide substantial efficiencies when compared to traditional procedures. The best fitting equations in this study used the traditional form Y=a×DBHb, where Y is biomass, DBH is diameter at breast height, and a and b are both species-specific parameters. Species-specific equations of the form Y=a(BA×H), where Y is biomass, BA is tree basal area, H is tree height, and a is a species-specific parameter, fit almost as well. Comparison with previously published equations indicated errors from -33% to +29% would have occurred using off-site relationships. We also present equations for stemwood, twigs, and foliage as biomass components.

Clinical Epidemiology of Buruli ulcer from Benin (2005-2013): effect of time-delay to diagnosis on clinical forms and severe phenotypes

Buruli Ulcer (BU) is a neglected infectious disease caused by Mycobacterium ulcerans that is responsible for severe necrotizing cutaneous lesions that may be associated with bone involvement. Clinical presentations of BU lesions are classically classified as papules, nodules, plaques and edematous infiltration, ulcer or osteomyelitis. Within these different clinical forms, lesions can be further classified as severe forms based on focality (multiple lesions), lesions' size (>15 cm diameter) or WHO Category (WHO Category 3 lesions). There are studies reporting an association between delay in seeking medical care and the development of ulcerative forms of BU or osteomyelitis, but the effect of time-delay on the emergence of lesions classified as severe has not been addressed. To address both issues, and in a cohort of laboratory-confirmed BU cases, 476 patients from a medical center in Allada, Benin, were studied. In this laboratory-confirmed cohort, we validated previous observations, demonstrating that time-delay is statistically related to the clinical form of BU. Indeed, for non-ulcerated forms (nodule, edema, and plaque) the median time-delay was 32.5 days (IQR 30.0-67.5), while for ulcerated forms it was 60 days (IQR 20.0-120.0) (p = 0.009), and for bone lesions, 365 days (IQR 228.0-548.0). On the other hand, we show here that time-delay is not associated with the more severe phenotypes of BU, such as multi-focal lesions (median 90 days; IQR 56-217.5; p = 0.09), larger lesions (diameter >15 cm) (median 60 days; IQR 30-120; p = 0.92) or category 3 WHO classification (median 60 days; IQR 30-150; p = 0.20), when compared with unifocal (median 60 days; IQR 30-90), small lesions (diameter =15 cm) (median 60 days; IQR 30-90), or WHO category 1+2 lesions (median 60 days; IQR 30-90), respectively. Our results demonstrate that after an initial period of progression towards ulceration or bone involvement, BU lesions become stable regarding size and focal/multi-focal progression. Therefore, in future studies on BU epidemiology, severe clinical forms should be systematically considered as distinct phenotypes of the same disease and thus subjected to specific risk factor investigation.

Kinematic constraint equations

This chapter presents a general methodology for the formulation of the kinematic constraint equations at position, velocity and acceleration levels. Also a brief characterization of the different type of constraints is offered, namely the holonomic and nonholonomic constraints. The kinematic constraints described here are formulated using generalized coordinates. The chapter ends with a general approach to deal with the kinematic analysis of multibody systems.

Equations of motion for constrained systems

"Series title: Springerbriefs in applied sciences and technology, ISSN 2191-530X"

Methods to solve the equations of motion

"Series title: Springerbriefs in applied sciences and technology, ISSN 2191-530X"

Stabilized finite element methods applied to transient convection-diffusion-reaction and population balance equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Numerical approximations of population balance equations in particulate systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2006

Sex-Specific Equations to Estimate Maximum Oxygen Uptake in Cycle Ergometry

AbstractBackground:Aerobic fitness, assessed by measuring VO2max in maximum cardiopulmonary exercise testing (CPX) or by estimating VO2max through the use of equations in exercise testing, is a predictor of mortality. However, the error resulting from this estimate in a given individual can be high, affecting clinical decisions.Objective:To determine the error of estimate of VO2max in cycle ergometry in a population attending clinical exercise testing laboratories, and to propose sex-specific equations to minimize that error.Methods:This study assessed 1715 adults (18 to 91 years, 68% men) undertaking maximum CPX in a lower limbs cycle ergometer (LLCE) with ramp protocol. The percentage error (E%) between measured VO2max and that estimated from the modified ACSM equation (Lang et al. MSSE, 1992) was calculated. Then, estimation equations were developed: 1) for all the population tested (C-GENERAL); and 2) separately by sex (C-MEN and C-WOMEN).Results:Measured VO2max was higher in men than in WOMEN: -29.4 ± 10.5 and 24.2 ± 9.2 mL.(kg.min)-1 (p < 0.01). The equations for estimating VO2max [in mL.(kg.min)-1] were: C-GENERAL = [final workload (W)/body weight (kg)] x 10.483 + 7; C-MEN = [final workload (W)/body weight (kg)] x 10.791 + 7; and C-WOMEN = [final workload (W)/body weight (kg)] x 9.820 + 7. The E% for MEN was: -3.4 ± 13.4% (modified ACSM); 1.2 ± 13.2% (C-GENERAL); and -0.9 ± 13.4% (C-MEN) (p < 0.01). For WOMEN: -14.7 ± 17.4% (modified ACSM); -6.3 ± 16.5% (C-GENERAL); and -1.7 ± 16.2% (C-WOMEN) (p < 0.01).Conclusion:The error of estimate of VO2max by use of sex-specific equations was reduced, but not eliminated, in exercise tests on LLCE.

Simulations for modelling of population balance equations of particulate processes using the discrete particle model (DPM)

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009