Approximate polynomial decomposition

1999 ◽  
Author(s):  
Robert M. Corless ◽  
Mark W. Giesbrecht ◽  
David J. Jeffrey
Keyword(s):  
Polynomial Decomposition ◽  
Approximate Polynomial

Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Fractional Differential Equations ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Variable Order ◽  
Polynomial Solutions ◽  
Fractional Differential ◽  
Approximate Polynomial

AbstractIn this paper a new way to compute analytic approximate polynomial solutions for a class of nonlinear variable order fractional differential equations is proposed, based on the Polynomial Least Squares Method (PLSM). In order to emphasize the accuracy and the efficiency of the method several examples are included.

scholarly journals Hydraulic Conductivity of Compacted Lime-Softening Sludge Used as Landfill Liners

2019 ◽  
Vol 230 (12) ◽  
Author(s):  
Agnieszka Dąbska
Keyword(s):  
Hydraulic Conductivity ◽  
Moisture Content ◽  
Tap Water ◽  
Distilled Water ◽  
Landfill Liners ◽  
Water Permeation ◽  
Lime Softening ◽  
Approximate Polynomial ◽  
Hazardous Waste Landfills

AbstractThe research goal was to investigate the hydraulic conductivity of compacted lime-softening sludge as a material to be applied to landfill liners. In doing so, the effect of compaction and moulding moisture content on the sludge hydraulic conductivity was assessed. An approximate polynomial k10mean at hydraulic gradients ≥30 for degree of compaction (0.95–1.05) and moulding moisture content (28%–36%) was determined. The results of short-term tap water permeation tests revealed that all hydraulic conductivity values were less than 2.5•10–8 m/s. A lowest hydraulic conductivity of 6.5•10–9 m/s, as well as a corresponding moisture content of 31% were then established. The long-term hydraulic conductivity was measured with tap water, distilled water, NaOH and HCl solutions and municipal waste leachate. The factors of permeating liquids and permeation time significantly affected the initial hydraulic conductivity. The long-term hydraulic conductivity increased for NaOH and HCl solutions and decreased for tap and distilled water. A significant reduction of hydraulic conductivity was observed for leachate permeation. The investigated material met the requirements for the liner systems of inert landfill sites regardless of pH and the limit value for hazardous and non-hazardous waste landfills.

scholarly journals Oil Price Forecasting Using a Time-Varying Approach

Energies ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1403
Author(s):  
Lu-Tao Zhao ◽  
Shun-Gang Wang ◽  
Zhi-Gang Zhang
Keyword(s):  
Crude Oil ◽  
Time Window ◽  
Oil Prices ◽  
Oil Price ◽  
Price Forecasting ◽  
Time Varying ◽  
Crude Oil Price ◽  
Trend Prediction ◽  
Oil Market ◽  
Polynomial Decomposition

The international crude oil market plays an important role in the global economy. This paper uses a variable time window and the polynomial decomposition method to define the trend term of time series and proposes a crude oil price forecasting method based on time-varying trend decomposition to describe the changes in trends over time and forecast crude oil prices. First, to characterize the time-varying characteristics of crude oil price trends, the basic concepts of post-position intervals, pre-position intervals and time-varying windows are defined. Second, a crude oil price series is decomposed with a time-varying window to determine the best fitting results. The parameter vector is used as a time-varying trend. Then, to quantitatively describe the continuation of the time-varying trend, the concept of the trend threshold is defined, and a corresponding algorithm for selecting the trend threshold is given. Finally, through the predicted trend thresholds, the historical reference data are selected, and the time-varying trend is combined to complete the crude oil price forecast. Through empirical research, it is found that the time-varying trend prediction model proposed in this paper achieves a better prediction than several common models. These results can provide suggestions and references for investors in the international crude oil market to understand the trends of oil prices and improve their investment decisions.

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