Bifurcation study on fractional non-smooth oscillator containing clearance constraints

Bifurcation characteristics of a fractional non-smooth oscillator containing clearance constraints under sinusoidal excitation are investigated. First, the bifurcation response equation of the fractional non-smooth system is obtained via the K–B method. Second, the stability of the bifurcation response equation is analyzed, and parametric conditions for stability are acquired. The bifurcation characteristics of the fractional non-smooth system are then studied using singularity theory, and the transition set and bifurcation diagram under six different constrained parameters are acquired. Finally, the analysis of the influence of fractional terms on the dynamic characteristics of the system is emphasized through numerical simulation. Local bifurcation diagrams of the system under different fractional coefficients and orders verify that the system will present various motions, such as periodic motion, multiple periodic motion, and chaos, with the change in fractional coefficient and order. This manifestation indicates that fractional parameters have a direct effect on the motion form of this non-smooth system. Thus, these results provide a theoretical reference for investigating and repressing oscillation problems of similar systems.

Audio Signal Processing Using Fractional Linear Prediction

Fractional linear prediction (FLP), as a generalization of conventional linear prediction (LP), was recently successfully applied in different fields of research and engineering, such as biomedical signal processing, speech modeling and image processing. The FLP model has a similar design as the conventional LP model, i.e., it uses a linear combination of “fractional terms” with different orders of fractional derivative. Assuming only one “fractional term” and using limited number of previous samples for prediction, FLP model with “restricted memory” is presented in this paper and the closed-form expressions for calculation of FLP coefficients are derived. This FLP model is fully comparable with the widely used low-order LP, as it uses the same number of previous samples, but less predictor coefficients, making it more efficient. Two different datasets, MIDI Aligned Piano Sounds (MAPS) and Orchset, were used for the experiments. Triads representing the chords composed of three randomly chosen notes and usual Western musical chords (both of them from MAPS dataset) served as the test signals, while the piano recordings from MAPS dataset and orchestra recordings from the Orchset dataset served as the musical signal. The results show enhancement of FLP over LP in terms of model complexity, whereas the performance is comparable.

Placental restriction in multi-fetal pregnancies and between-twin differences in size at birth alter neonatal feeding behaviour in the sheep

Most individuals whose growth was restricted before birth undergo accelerated or catch-up neonatal growth. This is an independent risk factor for later metabolic disease, but the underlying mechanisms are poorly understood. This study aimed to test the hypothesis that natural and experimentally induced in utero growth restriction increase neonatal appetite and milk intake. Control (CON) and placentally restricted (PR) ewes carrying multiple fetuses delivered naturally at term. Outcomes were compared between CON (n=14) and PR (n=12) progeny and within twin lamb pairs. Lamb milk intake and feeding behaviour and ewe milk composition were determined using a modified weigh-suckle-weigh procedure on days 15 and 23. PR lambs tended to have lower birth weights than CON (−15%, P=0.052). Neonatal growth rates were similar in CON and PR, whilst heavier twins grew faster in absolute but not fractional terms than their co-twins. At day 23, milk protein content was higher in PR than CON ewes (P=0.038). At day 15, PR lambs had fewer suckling bouts than CON lambs and in females light twins had more suckling attempts than their heavier co-twins. Birth weight differences between twins positively predicted differences in milk intakes. Lactational constraint and natural prenatal growth restriction in twins may explain the similar milk intakes in CON and PR. Within twin comparisons support the hypothesis that prenatal constraint increases lamb appetite, although this did not increase milk intake. We suggest that future mechanistic studies of catch-up growth be performed in singletons and be powered to assess effects in each sex.

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

The paper discusses asymptotic stability conditions for the linear fractional difference equation∇with real coefficients a, b and real orders α > β > 0 such that α/β is a rational number. For given α, β, we describe various types of discrete stability regions in the (a, b)-plane and compare them with the stability regions recently derived for the underlying continuous patternDinvolving two Caputo fractional derivatives. Our analysis shows that discrete stability sets are larger and their structure much more rich than in the case of the continuous counterparts.

Students' Use of Part-Whole and Direct Comparison Strategies for Comparing Partitioned Rectangles

Thirty-six students, twelve each at the fourth-, sixth-, and eighth-grade levels, were asked to solve 21 comparison-of-area tasks during a clinical interview. The areas were partitioned and shaded so that the tasks could be solved by using rational number knowledge. The types of strategies students used to compare the areas were identified and classified into categories. Initially, fractional terms and symbols were not introduced into the tasks in order to compare the types of strategies students used without and with symbols introduced. Most students tended to ignore the part-whole relationships inherent in the tasks and used a Direct Comparison strategy when they compared the areas. The use of a Part-Whole strategy increased with the introduction of fractional terms and symbols, especially at the eighth-grade level.