scholarly journals Remarks on some monotonicity conditions for the period function

1999 ◽  
Vol 26 (3) ◽  
pp. 243-252 ◽  
Author(s):  
R. Chouikha ◽  
F. Cuvelier
Keyword(s):  
Period Function ◽  
Monotonicity Conditions

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

scholarly journals CK1α Collaborates with DOUBLETIME to Regulate PERIOD Function in the Drosophila Circadian Clock

2018 ◽  
Vol 38 (50) ◽  
pp. 10631-10643 ◽  
Author(s):  
Vu H. Lam ◽  
Ying H. Li ◽  
Xianhui Liu ◽  
Katherine A. Murphy ◽  
Jonathan S. Diehl ◽  
...  
Keyword(s):  
Circadian Clock ◽  
Period Function

scholarly journals A Period-Aware Hybrid Model Applied for Forecasting AQI Time Series

2020 ◽  
Vol 12 (11) ◽  
pp. 4730 ◽  
Author(s):  
Ping Wang ◽  
Hongyinping Feng ◽  
Guisheng Zhang ◽  
Daizong Yu
Keyword(s):  
Time Series ◽  
Air Quality ◽  
Hybrid Model ◽  
Prediction Models ◽  
Time Series Prediction ◽  
Input Vector ◽  
Period Function ◽  
Data Set ◽  
Luenberger Observer ◽  
Extraction Algorithm

An accurate, reliable and stable air quality prediction system is conducive to the public health and management of atmospheric ecological environment; therefore, many models, individual or hybrid, have been implemented widely to deal with the prediction problem. However, many of these models do not take into consideration or extract improperly the period information in air quality index (AQI) time series, which impacts the models’ learning efficiency greatly. In this paper, a period extraction algorithm is proposed by using a Luenberger observer, and then a novel period-aware hybrid model combined the period extraction algorithm and tradition time series models is build to exploit the comprehensive forecasting capacity to the AQI time series with nonlinear and non-stationary noise. The hybrid model requires a multi-phase implementation. In the first step, the Luenberger observer is used to estimate the implied period function in the one-dimensional AQI series, and then the analyzed time series is mapped to the period space through the function to obtain the period information sub-series of the original series. In the second step, the period sub-series is combined with the original input vector as input vector components according to the time points to establish a new data set. Finally, the new data set containing period information is applied to train the traditional time series prediction models. Both theoretical proof and experimental results obtained on the AQI hour values of Beijing, Tianjin, Taiyuan and Shijiazhuang in North China prove that the hybrid model with period information presents stronger robustness and better forecasting accuracy than the traditional benchmark models.

A Higher-Order Period Function and Its Application

2015 ◽  
Vol 25 (10) ◽  
pp. 1550140 ◽  
Author(s):  
Linping Peng ◽  
Lianghaolong Lu ◽  
Zhaosheng Feng
Keyword(s):  
Periodic Orbits ◽  
Upper Bound ◽  
Critical Period ◽  
Higher Order ◽  
Quadratic System ◽  
Critical Periods ◽  
Explicit Formulas ◽  
Period Function ◽  
Isochronous System ◽  
Isochronous Centers

This paper derives explicit formulas of the q th period bifurcation function for any perturbed isochronous system with a center, which improve and generalize the corresponding results in the literature. Based on these formulas to the perturbed quadratic and quintic rigidly isochronous centers, we prove that under any small homogeneous perturbations, for ε in any order, at most one critical period bifurcates from the periodic orbits of the unperturbed quadratic system. For ε in order of 1, 2, 3, 4 and 5, at most three critical periods bifurcate from the periodic orbits of the unperturbed quintic system. Moreover, in each case, the upper bound is sharp. Finally, a family of perturbed quintic rigidly isochronous centers is shown, which has three, for ε in any order, as the exact upper bound of the number of critical periods.

scholarly journals Real-Time Traffic Flow Forecasting via a Novel Method Combining Periodic-Trend Decomposition

2020 ◽  
Vol 12 (15) ◽  
pp. 5891 ◽  
Author(s):  
Wei Zhou ◽  
Wei Wang ◽  
Xuedong Hua ◽  
Yi Zhang
Keyword(s):  
Traffic Flow ◽  
Hybrid Method ◽  
Intelligent Transportation System ◽  
Hybrid Models ◽  
Percentage Error ◽  
Volume Data ◽  
Period Function ◽  
Traffic Flow Forecasting ◽  
Novel Method ◽  
Periodic Trend

Accurate and timely traffic flow forecasting is a critical task of the intelligent transportation system (ITS). The predicted results offer the necessary information to support the decisions of administrators and travelers. To investigate trend and periodic characteristics of traffic flow and develop a more accurate prediction, a novel method combining periodic-trend decomposition (PTD) is proposed in this paper. This hybrid method is based on the principle of “decomposition first and forecasting last”. The well-designed PTD approach can decompose the original traffic flow into three components, including trend, periodicity, and remainder. The periodicity is a strict period function and predicted by cycling, while the trend and remainder are predicted by modelling. To demonstrate the universal applicability of the hybrid method, four prevalent models are separately combined with PTD to establish hybrid models. Traffic volume data are collected from the Minnesota Department of Transportation (Mn/DOT) and used to conduct experiments. Empirical results show that the mean absolute error (MAE), mean absolute percentage error (MAPE), and mean square error (MSE) of hybrid models are averagely reduced by 17%, 17%, and 29% more than individual models, respectively. In addition, the hybrid method is robust for a multi-step prediction. These findings indicate that the proposed method combining PTD is promising for traffic flow forecasting.

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