This paper discusses comparison of two time series decomposition methods: The Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. As noted by Iwueze and Nwogu (2014), there exists a research gap f...This paper discusses comparison of two time series decomposition methods: The Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. As noted by Iwueze and Nwogu (2014), there exists a research gap for the choice of appropriate model for decomposition and detection of presence of seasonal effect in a series model. Estimates of trend parameters and seasonal indices are all that are needed to fill the research gap. However, these estimates are obtainable through the Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. Hence, there is need to compare estimates of the two methods and recommend. The comparison of the two methods is done using the Accuracy Measures (Mean Error (ME)), Mean Square Error (MSE), the Mean Absolute Error (MAE), and the Mean Absolute Percentage Error (MAPE). The results from simulated series show that for the additive model;the summary statistics (ME, MSE and MAE) for the two estimation methods and for all the selected trending curves are equal in all the simulations both in magnitude and direction. For the multiplicative model, results show that when a series is dominated by trend, the estimates of the parameters by both methods become less precise and differ more widely from each other. However, if conditions for successful transformation (using the logarithmic transform in linearizing the multiplicative model to additive model) are met, both of them give similar results.展开更多
We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representat...We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.展开更多
As a result of socio-economic changes and land abandonment,the main ecological driver of the Carpathian landscape is the progression of the natural forest succession process.Thus,aspects of this process have become wo...As a result of socio-economic changes and land abandonment,the main ecological driver of the Carpathian landscape is the progression of the natural forest succession process.Thus,aspects of this process have become worthy of attention,especially in the context of carbon sequestration and the management of protected areas.Soil processes,especially within the topsoil,are some of the most susceptible to change,due to the accumulation of organic matter during such land-use transformations.The purposes of this study were to investigate the differences in topsoil development using the A Horizon Development Index(ADI)and to study the composition of humic substances and advanced organic matter humification in different land-use areas in selected Carpathian national parks,i.e.Bieszczady,Magura and Pieniny National Parks in southern Poland.Additionally,a goal of this study was to compare the ADI and the spectroscopic coefficients of humic substances as indicators of the degree of humus horizon shaping as well as advanced organic matter humification.In total,ten transects were selected,each consisting of three different land-use areas:semi-natural meadow,successional forest and old-growth forest.Soil colour was determined in fresh and air-dried samples using the Munsell colour chart.In air-dried soil samples p H,soil texture,total organic carbon and total nitrogen were measured.Humic substances were extracted and further characterized by UV-VIS spectroscopy.The ADI confirmed the influence of natural forest succession on soil colour darkening and the development of the uppermost soil layer.Spectroscopic analyses of humic substances showed two different patterns depending on soil depth.In the 0–10 cm layer,natural forest succession reduced the rate of the humification process and decreased the degree of maturity of fulvic acids;in the 10–20 cm layer,it led to an increase in the rate of the humification process and a decrease in the content of humic and fulvic acids at the beginning of the transformation.The comparison of 展开更多
文摘This paper discusses comparison of two time series decomposition methods: The Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. As noted by Iwueze and Nwogu (2014), there exists a research gap for the choice of appropriate model for decomposition and detection of presence of seasonal effect in a series model. Estimates of trend parameters and seasonal indices are all that are needed to fill the research gap. However, these estimates are obtainable through the Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. Hence, there is need to compare estimates of the two methods and recommend. The comparison of the two methods is done using the Accuracy Measures (Mean Error (ME)), Mean Square Error (MSE), the Mean Absolute Error (MAE), and the Mean Absolute Percentage Error (MAPE). The results from simulated series show that for the additive model;the summary statistics (ME, MSE and MAE) for the two estimation methods and for all the selected trending curves are equal in all the simulations both in magnitude and direction. For the multiplicative model, results show that when a series is dominated by trend, the estimates of the parameters by both methods become less precise and differ more widely from each other. However, if conditions for successful transformation (using the logarithmic transform in linearizing the multiplicative model to additive model) are met, both of them give similar results.
文摘We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.
基金supported by Statutory financial support of Ministry of Science and Higher Education RP Department of Soil Science and Agrophysics[010013D011 in 2021]University of Agriculture in Krakow。
文摘As a result of socio-economic changes and land abandonment,the main ecological driver of the Carpathian landscape is the progression of the natural forest succession process.Thus,aspects of this process have become worthy of attention,especially in the context of carbon sequestration and the management of protected areas.Soil processes,especially within the topsoil,are some of the most susceptible to change,due to the accumulation of organic matter during such land-use transformations.The purposes of this study were to investigate the differences in topsoil development using the A Horizon Development Index(ADI)and to study the composition of humic substances and advanced organic matter humification in different land-use areas in selected Carpathian national parks,i.e.Bieszczady,Magura and Pieniny National Parks in southern Poland.Additionally,a goal of this study was to compare the ADI and the spectroscopic coefficients of humic substances as indicators of the degree of humus horizon shaping as well as advanced organic matter humification.In total,ten transects were selected,each consisting of three different land-use areas:semi-natural meadow,successional forest and old-growth forest.Soil colour was determined in fresh and air-dried samples using the Munsell colour chart.In air-dried soil samples p H,soil texture,total organic carbon and total nitrogen were measured.Humic substances were extracted and further characterized by UV-VIS spectroscopy.The ADI confirmed the influence of natural forest succession on soil colour darkening and the development of the uppermost soil layer.Spectroscopic analyses of humic substances showed two different patterns depending on soil depth.In the 0–10 cm layer,natural forest succession reduced the rate of the humification process and decreased the degree of maturity of fulvic acids;in the 10–20 cm layer,it led to an increase in the rate of the humification process and a decrease in the content of humic and fulvic acids at the beginning of the transformation.The comparison of
