Limit Cycle Prediction of Systems with Fractional Controllers and Backlash

This article investigates the limit cycle (LC) prediction of systems with backlash by means of the describing function (DF) when using discrete fractional-order (FO) algorithms. The DF is an approximate method that gives good estimates of LCs. The implementation of FO controllers requires the use of rational approximations, but such realizations produce distinct dynamic types of behavior. This study analyzes the accuracy in the prediction of LCs, namely their amplitude and frequency, when using several different algorithms. To illustrate this problem we use FO-PID algorithms in the control of systems with backlash.

Compreensões de conceitos de cálculo diferencial no primeiro ano de matemática: uma abordagem integrando oralidade, escrita e informática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

La comprensión de la aproximación a un número en el acceso al significado de límite de una función en un punto

Esta investigación estudia la influencia de la comprensión de la aproximación a un número y de los modos de representación en la construcción de la concepción dinámica del límite en estudiantes de Bachillerato. El análisis de realizó usando el análisis implicativo (Gras, Suzuki, Guillet y Spagnolo, 2008). Los resultados indican que la construcción paulatina de la concepción dinámica del límite se realiza mediante procesos diferenciados de aproximación en el dominio y en el rango, y, dentro de estos últimos, aquellos en los que las aproximaciones laterales coinciden de las que no coinciden. Además, nuestros resultados indican que el modo numérico o el modo algebraico-numérico desempeñan un papel relevante en el desarrollo de la comprensión de la concepción dinámica de límite.

Un experimento de enseñanza sobre el límite de una función. Factores determinantes en una trayectoria de aprendizaje

El objetivo del estudio fue identificar características de la construcción del significado de límite de una función en estudiantes de bachillerato (16-17 años). Se diseñó un experimento de enseñanza utilizando una descomposición genética (APOE) del concepto de límite de una función integrando recursos informáticos. Se usó el constructo “Reflexión sobre la Relación Actividad-Efecto” (Simon, Tzur, Heinz y Kinzel, 2004) como una particularización de la abstracción reflexiva para identificar factores que configuran la Trayectoria de Aprendizaje. Los resultados indican que la trayectoria está determinada por la coordinación de las aproximaciones en el dominio y en el rango en diferentes tipos de funciones.

The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12

Studies of evolutionary temperature adaptation: Muscle function and locomotor performance in Antarctic fish

1, Studies of evolutionary temperature adaptation of muscle and locomotor performance in fish are reviewed with a focus on the Antarctic fauna living at subzero temperatures. 2. Only limited data are available to compare the sustained and burst swimming kinematics and performance of Antarctic, temperate and tropical species. Available data indicate that low temperatures limit maximum swimming performance and this is especially evident in fish larvae. 3, In a recent study, muscle performance in the Antarctic rock cod Notothenia coriiceps at 0 degrees C was found to be sufficient to produce maximum velocities during burst swimming that were similar to those seen in the sculpin Myoxocephalus scorpius at 10 degrees C, indicating temperature compensation of muscle and locomotor performance in the Antarctic fish. However, at 15 degrees C, sculpin produce maximum swimming velocities greater than N, coriiceps at 0 degrees C, 4, It is recommended that strict hypothesis-driven investigations using ecologically relevant measures of performance are undertaken to study temperature adaptation in Antarctic fish, Recent detailed phylogenetic analyses of the Antarctic fish fauna and their temperate relatives will allow a stronger experimental approach by helping to separate what is due to adaptation to the cold and what is due to phylogeny alone.

Briefing: Factored material properties and limit state loads-unlikely extreme or impossible pretense

In the limit state design (LSD) method each design criterion is formally stated and assessed using a performance function. The performance function defines the relationship between the design parameters and the design criterion. In practice, LSD involves factoring up loads and factoring down calculated strengths and material parameters. This provides a convenient way to carry out routine probabilistic-based design. The factors are statistically calculated to produce a design with an acceptably low probability of failure. Hence the ultimate load and the design material properties are mathematical concepts that have no physical interpretation. They may be physically impossible. Similarly, the appropriate analysis model is also defined by the performance function and may not describe the real behaviour at the perceived physical equivalent limit condition. These points must be understood to avoid confusion in the discussion and application of partial factor LSD methods.

Determinants of tissue Doppler measures of regional diastolic function during dobutamine stress echocardiography

Background Diastolic dysfunction induced by ischemia may alter transmitral blood flow, but this reflects global ventricular function, and pseudonormalization may occur with increased preload. Tissue Doppler may assess regional diastolic function and is relatively load-independent, but limited data exist regarding its application to stress testing. We sought to examine the stress response of regional diastolic parameters to dobutomine echocardiography (DbE). Methods Sixty-three patients underwent study with DbE: 20 with low probability of coronary artery disease (CAD) and 43 with CAD who underwent angiography. A standard DbE protocol was used, and segments were categorized as ischemic, scar, or normal. Color tissue Doppler was acquired at baseline and peak stress, and waveforms in the basal and mid segments were used to measure early filling (Em), late filling (Am), and E deceleration time. Significant CAD was defined by stenoses >50% vessel diameter. Results Diastolic parameters had limited feasibility because of merging of Em and Am waves at high heart rates and limited reproducibility. Nonetheless, compared with normal segments, segments subtended with significant stenoses showed a lower Em velocity at rest (6.2 +/- 2.6 cm/s vs 4.8 +/- 2.2 cm/s, P < .0001) and peak (7.5 +/- 4.2 cm/s vs 5.1 +/- 3.6 cm/s, P < .0001), Abnormal segments also showed a shorter E deceleration time (51 +/- 27 ms vs 41 +/- 27 ms, P = .0001) at base and peak. No changes were documented in Am. The same pattern was seen with segments identified as ischemic with wall motion score. However, in the absence of ischemia, segments of patients with left ventricular hypertrophy showed a lower Em velocity, with blunted Em responses to stress. Conclusion Regional diastolic function is sensitive to ischemia. However, a number of practical limitations limit the applicability of diastolic parameters for the quantification of stress echocardiography.

Fractional describing function of systems with nonlinear friction

This paper studies the describing function (DF) of systems consisting in a mass subjected to nonlinear friction. The friction force is composed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective revealing a fractional-order behaviour. The reliability of the DF method is evaluated through the signal harmonic content and the limit cycle prediction.

Non-classical error bounds in the central limit theorem

The classical central limit theorem states the uniform convergence of the distribution functions of the standardized sums of independent and identically distributed square integrable real-valued random variables to the standard normal distribution function. While first versions of the central limit theorem are already due to Moivre (1730) and Laplace (1812), a systematic study of this topic started at the beginning of the last century with the fundamental work of Lyapunov (1900, 1901). Meanwhile, extensions of the central limit theorem are available for a multitude of settings. This includes, e.g., Banach space valued random variables as well as substantial relaxations of the assumptions of independence and identical distributions. Furthermore, explicit error bounds are established and asymptotic expansions are employed to obtain better approximations. Classical error estimates like the famous bound of Berry and Esseen are stated in terms of absolute moments of the random summands and therefore do not reflect a potential closeness of the distributions of the single random summands to a normal distribution. Non-classical approaches take this issue into account by providing error estimates based on, e.g., pseudomoments. The latter field of investigation was initiated by work of Zolotarev in the 1960's and is still in its infancy compared to the development of the classical theory. For example, non-classical error bounds for asymptotic expansions seem not to be available up to now ...

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

Protein intake and exercise for optimal muscle function with aging: recommendations from the ESPEN Expert Group.

The aging process is associated with gradual and progressive loss of muscle mass along with lowered strength and physical endurance. This condition, sarcopenia, has been widely observed with aging in sedentary adults. Regular aerobic and resistance exercise programs have been shown to counteract most aspects of sarcopenia. In addition, good nutrition, especially adequate protein and energy intake, can help limit and treat age-related declines in muscle mass, strength, and functional abilities. Protein nutrition in combination with exercise is considered optimal for maintaining muscle function. With the goal of providing recommendations for health care professionals to help older adults sustain muscle strength and function into older age, the European Society for Clinical Nutrition and Metabolism (ESPEN) hosted a Workshop on Protein Requirements in the Elderly, held in Dubrovnik on November 24 and 25, 2013. Based on the evidence presented and discussed, the following recommendations are made (a) for healthy older people, the diet should provide at least 1.0-1.2 g protein/kg body weight/day, (b) for older people who are malnourished or at risk of malnutrition because they have acute or chronic illness, the diet should provide 1.2-1.5 g protein/kg body weight/day, with even higher intake for individuals with severe illness or injury, and (c) daily physical activity or exercise (resistance training, aerobic exercise) should be undertaken by all older people, for as long as possible.

Pulmonary artery pressure and cardiac function in children and adolescents after rapid ascent to 3,450 m.

High-altitude destinations are visited by increasing numbers of children and adolescents. High-altitude hypoxia triggers pulmonary hypertension that in turn may have adverse effects on cardiac function and may induce life-threatening high-altitude pulmonary edema (HAPE), but there are limited data in this young population. We, therefore, assessed in 118 nonacclimatized healthy children and adolescents (mean ± SD; age: 11 ± 2 yr) the effects of rapid ascent to high altitude on pulmonary artery pressure and right and left ventricular function by echocardiography. Pulmonary artery pressure was estimated by measuring the systolic right ventricular to right atrial pressure gradient. The echocardiography was performed at low altitude and 40 h after rapid ascent to 3,450 m. Pulmonary artery pressure was more than twofold higher at high than at low altitude (35 ± 11 vs. 16 ± 3 mmHg; P < 0.0001), and there existed a wide variability of pulmonary artery pressure at high altitude with an estimated upper 95% limit of 52 mmHg. Moreover, pulmonary artery pressure and its altitude-induced increase were inversely related to age, resulting in an almost twofold larger increase in the 6- to 9- than in the 14- to 16-yr-old participants (24 ± 12 vs. 13 ± 8 mmHg; P = 0.004). Even in children with the most severe altitude-induced pulmonary hypertension, right ventricular systolic function did not decrease, but increased, and none of the children developed HAPE. HAPE appears to be a rare event in this young population after rapid ascent to this altitude at which major tourist destinations are located.

Abnormal Lung Function and Risk for Heart Failure in the Elderly: The Health, Aging, and Body Composition Study

Background: Chronic obstructive pulmonary disease (COPD) has been associated with increased risk for heart failure (HF). The impact of subclinical abnormal spirometric findings on HF risk among older adults without history of COPD is not well elucidated. Methods: We evaluated 2125 participants (age 73.6±2.9 years; 50.5% men; 62.3% white; 45.6/9.4% past/current smokers; body mass index [BMI] 27.2±4.6 kg/m2) without prevalent COPD or HF who underwent baseline spirometry in the Health ABC Study. Abnormal lung function was defined either as forced vital capacity (FVC) below lower limit of normal (LLN) or forced expiratory volume in 1st sec (FEV1) to FVC ratio below LLN. Results: On follow-up (median, 9.4 years), 68 of 350 (19.4%) participants with abnormal lung function developed HF, as compared to 172 of 1775 (9.7%) participants with normal lung function (hazard ratio [HR], 2.31; 95% confidence interval [CI], 1.74 -3.06; P<.001). This increased risk persisted after adjusting for all other independent predictors of HF in the Health ABC Study, BMI, incident coronary events, and several inflammatory markers (HR, 1.82; 95% CI, 1.30 -2.54; P<.001), and remained constant over time. Baseline FVC and FEV1 had a linear association with HF risk (Figure). In adjusted models, HF risk increased by 21% (95% CI, 10 -36%) per 10% decrease in FVC and 18% (95% CI, 10 -28%) per 10% decrease in FEV1 (both P<.001); this association persisted among participants with normal lung function at baseline. Findings were consistent across sex, race, and smoking status. Conclusions: Subclinical abnormal spirometric findings are prevalent among older adults and are independently associated with risk for incident HF.

Intensity correlation function of dye lasers: Short-time behavior

We propose an equation to calculate the intensity correlation function of a dye-laser model with a pump parameter subject to finite-bandwidth fluctuations. The equation is valid, in the weak-noise limit, for all times. It incorporates novel non-Markovian features. Results are given for the short-time behavior of the correlation function. It exhibits a characteristic initial plateau. Our findings are supported by a numerical simulation of the model.