Study on the mud swimming motion of Paramisgurnus dabryanus

In the context of the rapid development of bionic technology, inspired by the swimming behavior of fish, a variety of robotic fish have been designed and applied to different underwater works and even military applications. However, in some operations, such as detection and salvage, vehicles need to travel under mud, a medium that is different from fluids. This complicating factor put higher requirements on robotic fish design. In this study, Paramisgurnus dabryanus, a fish species adept at swimming into the mud, was taken as a research object to investigate its profile and mud swimming behavior. First, a three-dimensional (3D) image scanner is used for profile scanning to acquire the point cloud data of the profile features of the loach. After modification, data coordinate points are extracted and used to fit the profile curve of loach and build geometric and mathematical models by means of Fourier function fitting. The next step includes the analysis of the motion of loach, determination of main parameters of the wave equation, and establishment of the fish body wave curve of a loach in the swimming using MATLAB software. Saturated mud having a water content of 37% is adopted as an environmental medium to numerically simulate the swimming behavior in mud, identifying the distribution of vortex path, and velocity field of loach’s motion. The rationality of simulation results is verified by the loach mud swimming test, and the simulating results agree well with the experimental data. This study lays a preliminary foundation for the outer contour design of the robotic fish operating under mud and aims to carry out the drag reduction and accelerating design of the robotic fish. The robotic loach may be applied in fishery breeding, shipwreck salvage operations, and so on.

High Persistence and Nonlinear Behavior in Financial Variables: A More Powerful Unit Root Testing in the ESTAR Framework

In this study, we consider the hybrid nonlinear features of the Exponential Smooth Transition Autoregressive-Fractional Fourier Function (ESTAR-FFF) form unit root test. As is well known, when developing a unit root test for the ESTAR model, linearization is performed by the Taylor approximation, and thereby the nuisance parameter problem is eliminated. Although this linearization process leads to a certain amount of information loss in the unit root testing equation, it also causes the resulting test to be more accessible and consistent. The method that we propose here contributes to the literature in three important ways. First, it reduces the information loss that arises due to the Taylor expansion. Second, the research to date has tended to misinterpret the Fourier function used with the Kapetanios, Shin and Snell (2003) (KSS) unit root test and considers it to capture multiple smooth transition structural breaks. The simulation studies that we carry out in this study clearly show that the Fourier function only restores the Taylor residuals of the ESTAR type function rather than accounting forthe smooth structural break. Third, the new nonlinear unit root test developed in this paper has very strong power in the highly persistent near unit root environment that the financial data exhibit. The application of the Kapetanios Shin Snell- Fractional Fourier (KSS-FF) test to ex-post real interest rates data of 11 OECD countries for country-specific sample periods shows that the new test catches nonlinear stationarity in many more countries than the KSS test itself.

Mean reversion in a price-earnings ratio and under / overvaluation in the Brazilian stock market

ABSTRACT The market price-earnings ratios differ from those of each share. Despite allowing for several pertinent analyses, authors have rarely addressed these valuation ratios in the Brazilian context. We can use it to evaluate whether the stock market is overvalued (undervalued). In this article, we analyze the mean reversion in a price-earnings ratio based on Ibovespa and identify periods of overvaluation (undervaluation) in the Brazilian stock market. We considered the period from December 2004 to June 2018. Until then, there are no studies that sought to identify periods of overvaluation (undervaluation) in this market. In the analyses, we used non-linear econometric methods. We analyzed the mean reversion in the price-earnings ratio using a unit root test that incorporates a Fourier function in the deterministic term. We identified the periods of market overvaluation (undervaluation) through the regime probabilities obtained from a Markov Switching model, estimated with the price-earnings ratio. The results evidenced that the price-earnings ratio based on the Ibovespa has a non-linear trend and exhibits mean reversion. Thus, this valuation ratio should provide information on the future stock market returns, mostly when it is very dispersed in relation to historical standards. We identified four periods of market overvaluation interposed with five periods of market undervaluation. Mean reversion in the price-earnings ratio contraposes the Efficient Markets Hypothesis. There are no other applications of unit root tests with a Fourier function in the Brazilian context. Furthermore, adopting a Markov Switching model to identify periods of market overvaluation (undervaluation) consists of a methodological contribution. Investors can take advantage of the identification of these periods to establish investment strategies.

Energy Diversification and Economic Development in Emergent Countries: Evidence From Fourier Function-Driven Bootstrap Panel Causality Test

Energy is a crucial development indicator of production, consumption, and nation-building. However, energy diversification highlighting renewables remains salient in economic development across developing economies. This study explores the economic impact of renewables (RE) and fossil fuel (NRE) utilization in 17 emerging nations. We use annual data with timeframe between 1980 and 2016 and propose a bootstrap panel causality approach with a Fourier function. This allows the examination of multiple structural breaks, cross-section dependence, and heterogeneity across countries. We validate four main hypotheses on the causal links attached to the energy consumption (EC)-growth nexus namely neutrality, conservation, growth, and feedback hypotheses. The findings reveal a causal relationship running from RE to GDP for Brazil, Egypt, Indonesia, Korea, Pakistan, and the Philippines, confirming the growth hypothesis. Besides, the results validate the conservation hypothesis with causality from GDP to RE for China, Colombia, Egypt, Greece, India, Korea, South Africa, and Turkey. We identify causality from NRE to GDP for Pakistan, Mexico, Malaysia, Korea, India, Greece, Egypt, and Brazil; and from GDP to NRE for Thailand, Peru, Malaysia, India, Greece, Egypt, and Colombia. We demonstrate that wealth creation can be achieved through energy diversification rather than relying solely on conventional energy sources.

Fractional unit-root tests allowing for a fractional frequency flexible Fourier form trend: predictability of Covid-19

In this study we propose a fractional frequency flexible Fourier form fractionally integrated ADF unit-root test, which combines the fractional integration and nonlinear trend as a form of the Fourier function. We provide the asymptotics of the newly proposed test and investigate its small-sample properties. Moreover, we show the best estimators for both fractional frequency and fractional difference operator for our newly proposed test. Finally, an empirical study demonstrates that not considering the structural break and fractional integration simultaneously in the testing process may lead to misleading results about the stochastic behavior of the Covid-19 pandemic.

Smooth Break Detection and De-Trending in Unit Root Testing

This study explores the methods to de-trend the smooth structural break processes while conducting the unit root tests. The two most commonly applied approaches for modelling smooth structural breaks namely the smooth transition and the Fourier functions are considered. We perform a sequence of power comparisons among alternative unit root tests that accommodate smooth or sharp structural breaks. The power experiments demonstrate that the unit root tests utilizing the Fourier function lead to unexpected results. Furthermore, through simulation studies, we investigate the source of such unexpected outcomes. Moreover, we provide the asymptotic distribution of two recently proposed unit root tests, namely Fourier-Augmented Dickey–Fuller (FADF) and Fourier-Kapetanios, Shin and Shell (FKSS), which are not given in the original studies. Lastly, we find that the selection of de-trending function is pivotal for unit root testing with structural breaks.

A Conceptual Investigation of a Large Radio Telescope Support Point Number Effect on Its Pointing Accuracy

The purpose of this paper is to investigate a large radio telescope support point number effect on its pointing accuracy and provide a useful guideline for the large radio telescope design engineer. In a large radio telescope system, the azimuth track is used to support the whole telescope structure and the mounting error as well as the telescope wheel-track contact in a long term can cause unevenness on the azimuth track, which can further deteriorate the telescope pointing accuracy. Even though various compensation methods have been proposed to compensate for this pointing error, it remains as one of the challenges for the telescope pointing error reduction. In this paper, a general telescope pointing error estimation formula has been proposed to investigate different telescope support-point number designs on its pointing accuracy. In this approach, the azimuth track unevenness has been modelled as the Fourier function using the least square method after the raw track profile has been measured. Next, the elevation position matrix, azimuth position matrix, and the azimuth profile matrix can be constructed for different telescope support point numbers, and the telescope pointing error can then be obtained based on the proposed general formula. The telescope pointing error root mean square (RMS) value is used to quantify the effect of the telescope support point number on the pointing accuracy. Two interesting results can be observed in the numerical example. The first one is that the telescope pointing error curves have different dominant peaks during one azimuth track rotation, which is corresponding to the support point number. Another interesting finding is that the RMS value experienced a complex trend with the support point number change, and they are not a simple monotonous increasing or decreasing relationship with the support number. All the results in this paper can provide a useful guideline for reducing the telescope pointing error in the initial design stage.

A 4-DOF dynamic model for ball bearing with multiple defects on raceways

Localized defects in ball bearing components would cause additional vibration and it is imperative to reveal the vibration mechanism. The relationship between fault characteristic frequency (fBPFI and fBPFO) and multiple defect parameters of ball bearing were given in this paper. Considering elastohydrodynamic lubrication (EHL), radial clearance, time-varying displacement and excitation force generated from multiple defects, a 4 degree-of-freedom (DOF) dynamic model for ball bearing with multiple defects on inner or outer raceway was established, and the model has been verified by experiments. Vibration signals of ball bearing with different defects parameters were simulated, the effects of the angle between two defects ( θIAD and θOAD), the number of defects ( NDI and NDO) and the location of defects on outer raceway on dynamic response were studied. Comparing simulated signals with experimental results, it is shown that more impulses of acceleration signals are generated by multiple defects than that by single defect, meanwhile time delay due to two defects on raceways could also be found, fault characteristic frequency and their harmonics frequencies appeared in the envelope spectrums. Harmonics frequencies of fBPFI are modulated mainly by 2 fs instead of fs in frequency domain for multiple defects on inner raceway. The amplitudes of fBPFO and fBPFI change as Fourier curve when θOAD and θIAD varied within a certain range, and a series of Fourier function are given to describe the mathematic relationship.