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1

Cheng, Peng. "Decomposition of Residual Circulation in Estuaries." Journal of Atmospheric and Oceanic Technology 31, no. 3 (March 1, 2014): 698–713. http://dx.doi.org/10.1175/jtech-d-13-00099.1.

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Abstract The residual currents in estuaries are produced by a variety of physical mechanisms. To understand the contribution of each individual mechanism to the creation of residual circulation, it is necessary to separate the effect of one particular mechanism from the others. In this study, a method based on dynamics is developed to decompose the residual circulation into individual components corresponding to different forcing mechanisms. Specifically, residual flows are partitioned based on the separate contributions by river discharge, horizontal density gradient, internal tidal asymmetry, advection, semi–Stokes transport, and wind. The method includes the effects of the earth’s rotation and can be applied for general conditions. Under the precondition that the ratio between width and length of the estuary is small, the continuity equation can be simplified such that the method only requires the data at a cross-estuary section to decompose residual currents. This makes the method practicable for real estuaries. Results from a generic numerical model are used to illustrate the decomposition method and to demonstrate its validity for weakly stratified estuaries.
2

Alam, Shaista, and Mohammad Sabihuddin Butt. "Assessing Energy Consumption and Energy Intensity Changes in Pakistan: An Application of Complete Decomposition Model." Pakistan Development Review 40, no. 2 (June 1, 2001): 135–47. http://dx.doi.org/10.30541/v40i2pp.135-147.

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Complete decomposition model has been employed in the present study to decompose the changes in energy consumption and energy intensity in Pakistan during 1960 to 1998. A general decomposition model raises a problem due to residual term. In some models the residual term is omitted, which causes a large estimation error, while in some models the residual term is regarded as an interaction that might create a puzzle for the analysis. A complete decomposition model is used here to solve this problem.
3

Kang, Dujuan, and Enrique N. Curchitser. "On the Evaluation of Seasonal Variability of the Ocean Kinetic Energy." Journal of Physical Oceanography 47, no. 7 (July 2017): 1675–83. http://dx.doi.org/10.1175/jpo-d-17-0063.1.

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AbstractThe seasonal cycles of the mean kinetic energy (MKE) and eddy kinetic energy (EKE) are compared in an idealized flow as well as in a realistic simulation of the Gulf Stream (GS) region based on three commonly used definitions: orthogonal, nonorthogonal, and moving-average filtered decompositions of the kinetic energy (KE). It is shown that only the orthogonal KE decomposition can define the physically consistent MKE and EKE that precisely represents the KEs of the mean flow and eddies, respectively. The nonorthogonal KE decomposition gives rise to a residual term that contributes to the seasonal variability of the eddies, and therefore the obtained EKE is not precisely defined. The residual term is shown to exhibit more significant seasonal variability than EKE in both idealized and realistic GS flows. Neglecting its influence leads to an inaccurate evaluation of the seasonal variability of both the eddies and the total flow. The decomposition using a moving-average filter also results in a nonnegligible residual term in both idealized and realistic GS flows. This type of definition does not ensure conservation of the total KE, even if taking into account the residual term. Moreover, it is shown that the annual cycles of the three types of EKEs or MKEs have different phases and amplitudes. The local differences of the EKE cycles are very prominent in the GS off-coast domain; however, because of the spatial inhomogeneity, the area-mean differences may not be significant.
4

Jiang, Rui, Rongrong Li, and Qiuhong Wu. "Investigation for the Decomposition of Carbon Emissions in the USA with C-D Function and LMDI Methods." Sustainability 11, no. 2 (January 10, 2019): 334. http://dx.doi.org/10.3390/su11020334.

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Residual problems are one of the greatest challenges in developing new decomposition techniques, especially when combined with the Cobb–Douglas (C-D) production function and the Logarithmic Mean Divisia Index (LMDI) method. Although this combination technique can quantify more effects than LMDI alone, its decomposition result has residual value. We propose a new approach that can achieve non-residual decomposition by calculating the actual values of three key parameters. To test the proposed approach, we decomposed the carbon emissions in the United States to six driving factors: the labor input effect, the investment effect, the carbon coefficient effect, the energy structure effect, the energy intensity effect, and the technology state effect. The results illustrate that the sum of these factors is equivalent to the CO2 emissions changes from t to t-1, thereby proving non-residual decomposition. Given that the proposed approach can achieve perfect decomposition, the proposed approach can be used more widely to investigate the effects of labor input, investment, and technology state on changes in energy and emission.
5

Tang, Zhenpeng, Tingting Zhang, Junchuan Wu, Xiaoxu Du, and Kaijie Chen. "Multistep-Ahead Stock Price Forecasting Based on Secondary Decomposition Technique and Extreme Learning Machine Optimized by the Differential Evolution Algorithm." Mathematical Problems in Engineering 2020 (July 28, 2020): 1–13. http://dx.doi.org/10.1155/2020/2604915.

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The prediction research of the stock market prices is of great significance. Based on the secondary decomposition techniques of variational mode decomposition (VMD) and ensemble empirical mode decomposition (EEMD), this paper constructs a new hybrid prediction model by combining with extreme learning machine (ELM) optimized by the differential evolution (DE) algorithm. The hybrid model applies VMD technology to the original stock index price sequence to obtain different modal components and the residual item, then applies EEMD technology to the residual item, and then superimposes the prediction results of the DE-ELM model for each modal component and the residual item to obtain the final prediction results. In order to verify the validity of the model, this paper constructs a series of benchmark models and, respectively, tests the samples of the S&P 500 index and the HS300 index by one-step, three-step, and five-step forward forecasting. The empirical results show that the hybrid model proposed in this paper achieves the best prediction performance in all prediction scenarios, which indicates that the modeling idea focusing on the residual term effectively improves the prediction performance of the model. In addition, the prediction effect of the model combined with the decomposition technology is superior to the single DE-ELM model, where the secondary decomposition technique has a significant decomposition advantage compared to the single decomposition technique.
6

Chen, Yuhao, Alexander Wong, Yuan Fang, Yifan Wu, and Linlin Xu. "Deep Residual Transform for Multi-scale Image Decomposition." Journal of Computational Vision and Imaging Systems 6, no. 1 (January 15, 2021): 1–5. http://dx.doi.org/10.15353/jcvis.v6i1.3537.

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Multi-scale image decomposition (MID) is a fundamental task in computer vision and image processing that involves the transformation of an image into a hierarchical representation comprising of different levels of visual granularity from coarse structures to fine details. A well-engineered MID disentangles the image signal into meaningful components which can be used in a variety of applications such as image denoising, image compression, and object classification. Traditional MID approaches such as wavelet transforms tackle the problem through carefully designed basis functions under rigid decomposition structure assumptions. However, as the information distribution varies from one type of image content to another, rigid decomposition assumptions lead to inefficiently representation, i.e., some scales can contain little to no information. To address this issue, we present Deep Residual Transform (DRT), a data-driven MID strategy where the input signal is transformed into a hierarchy of non-linear representations at different scales, with each representation being independently learned as the representational residual of previous scales at a user-controlled detail level. As such, the proposed DRT progressively disentangles scale information from the original signal by sequentially learning residual representations. The decomposition flexibility of this approach allows for highly tailored representations cater to specific types of image content, and results in greater representational efficiency and compactness. In this study, we realize the proposed transform by leveraging a hierarchy of sequentially trained autoencoders. To explore the efficacy of the proposed DRT, we leverage two datasets comprising of very different types of image content: 1) CelebFaces and 2) Cityscapes. Experimental results show that the proposed DRT achieved highly efficient information decomposition on both datasets amid their very different visual granularity characteristics.
7

Jin, Chuantai, and Yong Li. "Cryptocurrency Price Prediction Using Frequency Decomposition and Deep Learning." Fractal and Fractional 7, no. 10 (September 26, 2023): 708. http://dx.doi.org/10.3390/fractalfract7100708.

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Given the substantial volatility and non-stationarity of cryptocurrency prices, forecasting them has become a complex task within the realm of financial time series analysis. This study introduces an innovative hybrid prediction model, VMD-AGRU-RESVMD-LSTM, which amalgamates the disintegration–integration framework with deep learning techniques for accurate cryptocurrency price prediction. The process begins by decomposing the cryptocurrency price series into a finite number of subseries, each characterized by relatively simple volatility patterns, using the variational mode decomposition (VMD) method. Next, the gated recurrent unit (GRU) neural network, in combination with an attention mechanism, predicts each modal component’s sequence separately. Additionally, the residual sequence, obtained after decomposition, undergoes further decomposition. The resultant residual sequence components serve as input to an attentive GRU (AGRU) network, which predicts the residual sequence’s future values. Ultimately, the long short-term memory (LSTM) neural network integrates the predictions of modal components and residuals to yield the final forecasted price. Empirical results obtained for daily Bitcoin and Ethereum data exhibit promising performance metrics. The root mean square error (RMSE) is reported as 50.651 and 2.873, the mean absolute error (MAE) stands at 42.298 and 2.410, and the mean absolute percentage error (MAPE) is recorded at 0.394% and 0.757%, respectively. Notably, the predictive outcomes of the VMD-AGRU-RESVMD-LSTM model surpass those of standalone LSTM and GRU models, as well as other hybrid models, confirming its superior performance in cryptocurrency price forecasting.
8

McMahon, Joseph, Alain Goriely, and Michael Tabor. "Nonlinear morphoelastic plates I: Genesis of residual stress." Mathematics and Mechanics of Solids 16, no. 8 (April 28, 2011): 812–32. http://dx.doi.org/10.1177/1081286510387233.

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Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established.
9

Wang, Junyuan, Xiaofeng Han, Zhijian Wang, Wenhua Du, Jie Zhou, Jiping Zhang, Huihui He, and Xiaoming Guo. "Modified Singular Spectrum Decomposition and Its Application to Composite Fault Diagnosis of Gearboxes." Sensors 19, no. 1 (December 24, 2018): 62. http://dx.doi.org/10.3390/s19010062.

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Under the strong noise environment, the composite fault signal of gearbox is weak, which makes it difficult to extract fault features. For this problem, based on noise-assisted method, we propose a novel method called Modified Singular Spectrum Decomposition (MSSD). Singular Spectrum Decomposition (SSD) has many advantages such as high decomposition precision and strong ability to restrain mode mixing, etc. However, the ability of SSD to extract a weak signal is not ideal, the decomposition results usually contain a lot of redundant noise and mode mixing caused by intermittency, which is also a troubling problem. In order to improve the decomposition efficiency and make up for the defects of SSD, the new method MSSD adds an adaptive and particular noise in every SSD decomposition stage for each trial, and in addition, whenever the input signal is decomposed to obtain an intrinsic module function (IMF), a unique residual is obtained. After multiple decomposition, the average value of the residual is used as input to the next stage, until the residual cannot continue to decompose, which means that the residual component has, at most, one extreme value. Finally, analyzing simulated signals to explain the advantages of MSSD compared to ensemble empirical mode decomposition (EEMD) and complete ensemble local mean decomposition with adaptive noise (CEEMDAN). In order to further prove the effectiveness of MSSD, this new method, MSSD, is applied to the fault diagnosis of an engineering gearbox test stand in an actual engineer project case. The final results show that MSSD can extract more fault feature information, and mode mixing has been improved and suffers less interference compared to SSD.
10

Xing, Guangyuan, Shaolong Sun, and Jue Guo. "A New Decomposition Ensemble Learning Approach with Intelligent Optimization for PM2.5 Concentration Forecasting." Discrete Dynamics in Nature and Society 2020 (March 22, 2020): 1–11. http://dx.doi.org/10.1155/2020/6019826.

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In this study, we focus our attention on the forecasting of daily PM2.5 concentrations. According to the principle of “divide and conquer,” we propose a novel decomposition ensemble learning approach by integrating ensemble empirical mode decomposition (EEMD), artificial neural networks (ANNs), and adaptive particle swarm optimization (APSO) for forecasting PM2.5 concentrations. Our proposed decomposition ensemble learning approach is formulated exclusively to deal with difficulties in quantitating meteorological information with high volatility, irregularity, and complicacy. This decomposition ensemble learning approach mainly consists of three steps. First, we utilize EEMD to decompose original time series of PM2.5 concentrations into a specific amount of independent intrinsic mode functions (IMFs) and residual term. Second, the ANN, whose connection parameters are optimized by APSO algorithm, is employed to model IMFs and residual terms, respectively. Finally, another APSO-ANN is applied to aggregate the forecast IMFs and residual term into a collection as the final forecasting results. The empirical results show that the forecasting of our decomposition ensemble learning approach outperforms other benchmark models in terms of level accuracy and directional accuracy.
11

Imashev, S. A., and S. V. Parov. "Modified Seasonal Decomposition Variations of Earth Magnetic Field Induction Module." Informacionnye Tehnologii 30, no. 2 (February 8, 2024): 59–67. http://dx.doi.org/10.17587/it.30.59-67.

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In this paper, we present a modification of the classic method of seasonal decomposition of the time series, in particular its application for the analysis of geomagnetic data. Seasonal decomposition is a powerful tool for time series analysis, but its classic implementation does not always provide accurate results when the time series contains amplitude outliers and prolonged gaps. We propose a modified approach to solve this task of seasonal decomposition, by applying an average daily profile. This ensures the extraction of various anomalies in the residual component of the decomposition, in particular, global and contextual outliers, as well as disturbances due to magnetic storms in the variations of geomagnetic field induction module. Keywords: geomagnetic field, seasonal decomposition, data gaps, autocorrelation function, residual component, outliers, magnetic storm, DST index
12

Cheng, Yao, and Dong Zou. "Complementary ensemble local means decomposition method and its application to rolling element bearings fault diagnosis." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 233, no. 5 (April 3, 2019): 868–80. http://dx.doi.org/10.1177/1748006x19838129.

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Local means decomposition is an adaptive and nonparametric time–frequency decomposition method for nonstationary and nonlinear signals. However, in practice, local means decomposition is susceptible to mode mixing phenomena and produces different scale oscillations in one mode or similar scale oscillations in different modes, rendering the decomposition results difficult to interpret in terms of physical meansing. The noise-assisted ensemble local means decomposition method not only effectively resolved mode mixing but also generated a new problem, which tolerates residual noise in signal reconstruction. Targeting these shortcomings, this article proposes complementary ensemble local means decomposition, a novel noise-assisted time–frequency analysis method. First, an ensemble of white noise is added to the original signal via complementary positive and negative pairs. Second, local means decomposition is applied to decompose the noisy signals into a series of product functions, and the final results are obtained by averaging. The simulation results confirm that complementary ensemble local means decomposition offers an innovative improvement over ensemble local means decomposition in terms of eliminating residual noise. The superiority of the proposed method was further validated on fault signals obtained from faulty railway bearings (rolling element and outer race fault signals).
13

Feng, Bo, Huazhong Wang, and Ru-Shan Wu. "Automatic traveltime inversion via sparse decomposition of seismic data." GEOPHYSICS 83, no. 6 (November 1, 2018): R659—R668. http://dx.doi.org/10.1190/geo2017-0329.1.

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We have developed an automatic traveltime inversion (ATI) method to estimate the macrovelocity model from reflection seismic data. First, we extract the kinematic information (i.e., source/receiver ray parameters, traveltime, and source/receiver coordinates) of locally coherent events using a sparse-decomposition method. And then we evaluate a new strategy to calculate the reflection traveltime residual based on a ray-intersection criterion, eliminating the influence of seismic amplitude to the estimation of the traveltime residual. The velocity model can be updated iteratively by minimizing the traveltime residual functional with a gradient-based method. To obtain a smooth gradient free of artifacts, we first estimate the high-wavenumber components of the functional gradient with a total variation (TV) regularization method and then subtract it from the full gradient. Because the reflection traveltime residual calculation and velocity update are fully automated procedures, the proposed traveltime inversion method is referred to as ATI. We determine with 2D synthetic and field examples that ATI does not need a good starting model. Furthermore, it requires neither low-frequency seismic data nor long-offset acquisition. Nevertheless, the proposed traveltime residual calculation strategy is only valid for the 2D case, which limits its 3D applicability. We explore a possible solution for 3D extension.
14

MATSUO, ITARU. "Lecture series of residual oil application. 2. Thermal decomposition." Journal of the Fuel Society of Japan 65, no. 10 (1986): 860–68. http://dx.doi.org/10.3775/jie.65.10_860.

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15

Taylor, Jamie M., Manuela Bastidas, Victor M. Calo, and David Pardo. "Adaptive Deep Fourier Residual method via overlapping domain decomposition." Computer Methods in Applied Mechanics and Engineering 427 (July 2024): 116997. http://dx.doi.org/10.1016/j.cma.2024.116997.

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Biegańska, Jolanta, and Krzysztof Barański. "Investigation of Herbicide Decomposition Efficiency by Means of Detonative Combustion." Energies 15, no. 19 (September 23, 2022): 6980. http://dx.doi.org/10.3390/en15196980.

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The decomposition of seven herbicides (atrazine, linuron, lenacil, chloridazon, dinoseb acetate, prometryn, and diuron) was carried out by detonative combustion. The investigated blasting material was produced on the basis of porous ammonium nitrate, which served as an oxidizer, while the pesticides played the role of the fuel. Detonative decomposition of the mixtures was carried out in blast-holes in soil. The efficiency of the decomposition process was assessed using the techniques of gas chromatography, high-efficiency liquid chromatography, and additionally by biological tests according to the grading of the European Weed Research Council. The results demonstrate an efficient decomposition of the tested herbicides. In the tested soil samples taken after the detonation decomposition of the herbicide, no symptoms of phytotoxic effects on the plants were found. This was confirmed by the lack (or at most negligible amounts) of residual herbicides in the soil samples. Only for the samples of chloradizine and diuron were large amounts of residual biologically active substance found.
17

Ali, Muhammad Umair, Amad Zafar, Haris Masood, Karam Dad Kallu, Muhammad Attique Khan, Usman Tariq, Ye Jin Kim, and Byoungchol Chang. "A Hybrid Data-Driven Approach for Multistep Ahead Prediction of State of Health and Remaining Useful Life of Lithium-Ion Batteries." Computational Intelligence and Neuroscience 2022 (June 13, 2022): 1–14. http://dx.doi.org/10.1155/2022/1575303.

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In this paper, a novel multistep ahead predictor based upon a fusion of kernel recursive least square (KRLS) and Gaussian process regression (GPR) is proposed for the accurate prediction of the state of health (SoH) and remaining useful life (RUL) of lithium-ion batteries. The empirical mode decomposition is utilized to divide the battery capacity into local regeneration (intrinsic mode functions) and global degradation (residual). The KRLS and GPR submodels are employed to track the residual and intrinsic mode functions. For RUL, the KRLS predicted residual signal is utilized. The online available experimental battery aging data are used for the evaluation of the proposed model. The comparison analysis with other methodologies (i.e., GPR, KRLS, empirical mode decomposition with GPR, and empirical mode decomposition with KRLS) reveals the distinctiveness and superiority of the proposed approach. For 1-step ahead prediction, the proposed method tracks the trajectory with the root mean square error (RMSE) of 0.2299, and the increase of only 0.2243 RMSE is noted for 30-step ahead prediction. The RUL prediction using residual signal shows an increase of 3 to 5% in accuracy. This proposed methodology is a prospective approach for an efficient battery health prognostic.
18

Duan, Yonghui, Ziru Ming, and Xiang Wang. "A Crude Oil Spot Price Forecasting Method Incorporating Quadratic Decomposition and Residual Forecasting." Journal of Mathematics 2024 (April 15, 2024): 1–20. http://dx.doi.org/10.1155/2024/6652218.

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The world economy is affected by fluctuations in the price of crude oil, making precise and effective forecasting of crude oil prices essential. In this study, we propose a combined forecasting scheme, which combines a quadratic decomposition and optimized support vector regression (SVR). In the decomposition part, the original crude oil price series are first decomposed using empirical modal decomposition (CEEMDAN), and then the residuals of the first decomposition (RES) are decomposed using variational modal decomposition (VMD). Additionally, this work proposes to optimize the support vector regression model (SVR) by the seagull optimization algorithm (SOA). Ultimately, the empirical investigation created the feature-variable system and predicted the filtered features. By computing evaluation indices like MAE, MSE, R2, and MAPE and validating using Brent and WTI crude oil spot, the prediction errors of the CEEMDAN -RES.-VMD -SOA-SVR combination prediction model presented in this paper are assessed and compared with those of the other twelve comparative models. The empirical evidence shows that the combination model being proposed in this paper outperforms the other related comparative models and improves the accuracy of the crude oil price forecasting model.
19

Li, Yong, Hui-Wen Gu, Hai-Long Wu, and Xiang-Yang Yu. "Comparison of the performances of several commonly used algorithms for second-order calibration." Analytical Methods 10, no. 39 (2018): 4801–12. http://dx.doi.org/10.1039/c8ay01443d.

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The present study compared six commonly used algorithms, namely, alternating trilinear decomposition (ATLD), self-weighted alternating trilinear decomposition (SWATLD), alternating coupled two unequal residual functions (ACTUF), parallel factor analysis (PARAFAC), damped Gauss-Newton (dGN) and algorithm combination methodology (ACM).
20

Kuru, Merve, and Gulben Calis. "Application of time series models for heating degree day forecasting." Organization, Technology and Management in Construction: an International Journal 12, no. 1 (April 27, 2020): 2137–46. http://dx.doi.org/10.2478/otmcj-2020-0009.

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AbstractThis study aims at constructing short-term forecast models by analyzing the patterns of the heating degree day (HDD). In this context, two different time series analyses, namely the decomposition and Box–Jenkins methods, were conducted. The monthly HDD data in France between 1974 and 2017 were used for analyses. The multiplicative model and 79 SARIMA models were constructed by the decomposition and Box–Jenkins method, respectively. The performance of the SARIMA models was assessed by the adjusted R2 value, residual sum of squares, the Akaike Information Criteria, the Schwarz Information Criteria, and the analysis of the residuals. Moreover, the mean absolute percentage error, mean absolute deviation, and mean squared deviation values were calculated to evaluate the performance of both methods. The results show that the decomposition method yields more acceptable forecasts than the Box–Jenkins method for supporting short-term forecasting of the HDD.
21

Amato, M., JN Ladd, A. Ellington, G. Ford, JE Mahoney, AC Taylor, and D. Walsgott. "Decomposition of plant material in Australian soils .IV. Decomposition in situ of 14C labeled and 15N labeled legume and wheat materials in a range of southern Australian soils." Soil Research 25, no. 1 (1987): 95. http://dx.doi.org/10.1071/sr9870095.

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14C- and 15N-labelled wheat straw, and tops or roots of a pasture legume (either Medicago littoralis or Trifolium subterraneum) were incorporated into topsoils at 12 field sites in southern Australia. These sites were representative of soil types widely used for wheat growing in each region. The soils varied markedly in their physical and chemical properties (e.g. pH, texture and organic matter content). Based on amounts of residual I4C (averaged for all sites), the legume tops decomposed more extensively than did wheat straw, especially soon after incorporation. To a lesser extent the legume tops decomposed more extensively than legume roots, and T. subterraneum tops more than M. littoralis tops; root decomposition for both legumes was similar. For example, after 1 year, the residual organic 14C from wheat straw, M. littoralis tops, T. subterraneum tops and legume roots accounted for 48%, 41%, 38% and 54% of their respective inputs. After two years, residual 14C of wheat straw accounted for 30% of the input. Differences in decomposition due to climate and soil properties were generally small, but at times were statistically significant; these differences related positively with rainfall and negatively with soil clay content, but showed no relationship with pH or soil organic C and N. Some N was mineralized from all plant materials, the greatest from legume tops, the least from wheat straw. After 1 year, residual organic 15N accounted for 56%, 63% and 78% respectively of input l5N from legume tops and roots and from wheat straw. The influence of climate and soil properties on amounts of residual organic I5N was small and generally was consistent with those found for residual 14C. AS an exception, the residual organic 15N from wheat straw was negatively related to soil organic N levels, whereas residual I5N of legume tops and roots and residual 14C of all plant materials were not influenced by soil organic matter levels. These results are discussed in terms of the turnover of N in soils amended with isotope labelled plant materials of different available C:N ratios.
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Western, Bruce, and Deirdre Bloome. "9. Variance Function Regressions for Studying Inequality." Sociological Methodology 39, no. 1 (August 2009): 293–326. http://dx.doi.org/10.1111/j.1467-9531.2009.01222.x.

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Regression-based studies of inequality model only between-group differences, yet often these differences are far exceeded by residual inequality. Residual inequality is usually attributed to measurement error or the influence of unobserved characteristics. We present a model, called variance function regression, that includes covariates for both the mean and variance of a dependent variable. In this model, the residual variance is treated as a target for analysis. In analyses of inequality, the residual variance might be interpreted as measuring risk or insecurity. Variance function regressions are illustrated in an analysis of panel data on earnings among released prisoners in the National Longitudinal Survey of Youth. We extend the model to a decomposition analysis, relating the change in inequality to compositional changes in the population and changes in coefficients for the mean and variance. The decomposition is applied to the trend in U.S. earnings inequality among male workers, 1970 to 2005.
23

Bai, Yunpeng, Xiangke Zhang, Yajing Wang, Lei Wang, Qinqin Wei, and Wenlei Zhao. "Residual current detection method based on improved VMD-BPNN." PLOS ONE 19, no. 2 (February 8, 2024): e0289129. http://dx.doi.org/10.1371/journal.pone.0289129.

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To further enhance the residual current detection capability of low-voltage distribution networks, an improved adaptive residual current detection method that combines variational modal decomposition (VMD) and BP neural network (BPNN) is proposed. Firstly, the method employs the envelope entropy as the adaptability function, optimizes the [k, ɑ] combination value of the VMD decomposition using the bacterial foraging-particle swarm algorithm (BFO-PSO), and utilizes the interrelation number R as the classification index with the Least Mean Square Algorithm (LMS) to classify, filter, and extract the effective signal from the decomposed signal. Then, the extracted signals are detected by BPNN, and the training data are utilized to predict the residual current signals. Simulation and experimental data demonstrate that the proposed algorithm exhibits strong robustness and high detection accuracy. With an ambient noise of 10dB, the signal-to-noise ratio is 16.3108dB, the RMSE is 0.4359, and the goodness-of-fit is 0.9627 after processing by the algorithm presented in this paper, which are superior to the Variational Modal Decomposition-Long Short-Term Memory (VMD-LSTM) and Normalized-Least Mean Square (N-LMS) detection methods. The results were also statistically analyzed in conjunction with the Kolmogorov-Smirnov test, which demonstrated significance at the experimental data level, indicating the high accuracy of the algorithms presented in this paper and providing a certain reference for new residual current protection devices for biological body electrocution.
24

Watanabe, Takao. "Residual automorphic representations of Sp4." Nagoya Mathematical Journal 127 (September 1992): 15–47. http://dx.doi.org/10.1017/s0027763000004086.

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Let G = Sp4 be the symplectic group of degree two defined over an algebraic number field F and K the standard maximal compact subgroup of the adele group G (A). By the general theory of Eisenstein series ([14]), one knows that the Hilbert space L2(G(F)\G(A)) has an orthogonal decomposition of the formL2(G(F)\G(A)) = L2(G) ⊕ L2(B) ⊕ L2(P1) ⊕ L2(P1),where B is a Borel subgroup and Pi are standard maximal parabolic subgroups in G for i = 1,2. The purpose of this paper is to study the space L2d(B) associated to discrete spectrurns in L2(B).
25

Son, Chang-Hwan. "Layer Decomposition Learning Based on Gaussian Convolution Model and Residual Deblurring for Inverse Halftoning." Applied Sciences 11, no. 15 (July 29, 2021): 7006. http://dx.doi.org/10.3390/app11157006.

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Layer decomposition to separate an input image into base and detail layers has been steadily used for image restoration. Existing residual networks based on an additive model require residual layers with a small output range for fast convergence and visual quality improvement. However, in inverse halftoning, homogenous dot patterns hinder a small output range from the residual layers. Therefore, a new layer decomposition network based on the Gaussian convolution model (GCM) and a structure-aware deblurring strategy is presented to achieve residual learning for both the base and detail layers. For the base layer, a new GCM-based residual subnetwork is presented. The GCM utilizes a statistical distribution, in which the image difference between a blurred continuous-tone image and a blurred halftoned image with a Gaussian filter can result in a narrow output range. Subsequently, the GCM-based residual subnetwork uses a Gaussian-filtered halftoned image as the input, and outputs the image difference as a residual, thereby generating the base layer, i.e., the Gaussian-blurred continuous-tone image. For the detail layer, a new structure-aware residual deblurring subnetwork (SARDS) is presented. To remove the Gaussian blurring of the base layer, the SARDS uses the predicted base layer as the input, and outputs the deblurred version. To more effectively restore image structures such as lines and text, a new image structure map predictor is incorporated into the deblurring network to induce structure-adaptive learning. This paper provides a method to realize the residual learning of both the base and detail layers based on the GCM and SARDS. In addition, it is verified that the proposed method surpasses state-of-the-art methods based on U-Net, direct deblurring networks, and progressively residual networks.
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Liu, Shaodong, Tao Zhao, and Dengfeng Zhang. "Fault Detection of Flow Control Valves Using Online LightGBM and STL Decomposition." Actuators 13, no. 6 (June 13, 2024): 222. http://dx.doi.org/10.3390/act13060222.

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In the process industrial systems, flow control valves are deemed vital components that ensure the system’s safe operation. Hence, detecting faults in control valves is of significant importance. However, the stable operating conditions of flow control valves are prone to change, resulting in a decreased effectiveness of the conventional fault detection method. In this paper, an online fault detection approach considering the variable operating conditions of flow control valves is proposed. This approach is based on residual analysis, combining LightGBM online model with Seasonal and Trend decomposition using Loess (STL). LightGBM is a tree-based machine learning algorithm. In the proposed method, an online LightGBM is employed to establish and continuously update a flow prediction model for control valves, ensuring model accuracy during changes in operational conditions. Subsequently, STL decomposition is applied to the model’s residuals to capture the trend of residual changes, which is then transformed into a Health Index (HI) for evaluating the health level of the flow control valves. Finally, fault occurrences are detected based on the magnitude of the HI. We validate this approach using both simulated and real factory data. The experimental results demonstrate that the proposed method can promptly reflect the occurrence of faults through the HI.
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Noack, Bernd R., Witold Stankiewicz, Marek Morzyński, and Peter J. Schmid. "Recursive dynamic mode decomposition of transient and post-transient wake flows." Journal of Fluid Mechanics 809 (November 21, 2016): 843–72. http://dx.doi.org/10.1017/jfm.2016.678.

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A novel data-driven modal decomposition of fluid flow is proposed, comprising key features of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The first mode is the normalized real or imaginary part of the DMD mode that minimizes the time-averaged residual. The $N$th mode is defined recursively in an analogous manner based on the residual of an expansion using the first $N-1$ modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. Recursive DMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al., J. Nonlinear Sci., vol. 22, 2012, pp. 887–915) for the same snapshot sequence. Unlike POD modes, RDMD structures are shown to have purer frequency content while retaining a residual of comparable order to POD. In contrast to DMD, with exponentially growing or decaying oscillatory amplitudes, RDMD clearly identifies initial, maximum and final fluctuation levels. Intriguingly, RDMD outperforms both POD and DMD in the limit-cycle resolution from the same snapshots. Robustness of these observations is demonstrated for other parameters of the cylinder wake and for a more complex wake behind three rotating cylinders. Recursive DMD is proposed as an attractive alternative to POD and DMD for empirical Galerkin models, in particular for nonlinear transient dynamics.
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Sun, Chengli, Jianxiao Xie, and Yan Leng. "A Signal Subspace Speech Enhancement Approach Based on Joint Low-Rank and Sparse Matrix Decomposition." Archives of Acoustics 41, no. 2 (June 1, 2016): 245–54. http://dx.doi.org/10.1515/aoa-2016-0024.

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Abstract Subspace-based methods have been effectively used to estimate enhanced speech from noisy speech samples. In the traditional subspace approaches, a critical step is splitting of two invariant subspaces associated with signal and noise via subspace decomposition, which is often performed by singular-value decomposition or eigenvalue decomposition. However, these decomposition algorithms are highly sensitive to the presence of large corruptions, resulting in a large amount of residual noise within enhanced speech in low signal-to-noise ratio (SNR) situations. In this paper, a joint low-rank and sparse matrix decomposition (JLSMD) based subspace method is proposed for speech enhancement. In the proposed method, we firstly structure the corrupted data as a Toeplitz matrix and estimate its effective rank value for the underlying clean speech matrix. Then the subspace decomposition is performed by means of JLSMD, where the decomposed low-rank part corresponds to enhanced speech and the sparse part corresponds to noise signal, respectively. An extensive set of experiments have been carried out for both of white Gaussian noise and real-world noise. Experimental results show that the proposed method performs better than conventional methods in many types of strong noise conditions, in terms of yielding less residual noise and lower speech distortion.
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Cirone, Alessandro, Eurípedes Vargas Jr., and Tácio de Campos. "Constitutive modeling of residual soils based on irreversible strains decomposition." Soils and Rocks 43, no. 4 (December 31, 2020): 647–58. http://dx.doi.org/10.28927/sr.434647.

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KITA, Yoshito, Hidetake OKAMOTO, Hiroshi NISHIKAWA, and Tadashi TAKEMOTO. "Decomposition of residual cyanide by bacteria used for Au bioleaching." Journal of Environmental Conservation Engineering 35, no. 12 (2006): 908–15. http://dx.doi.org/10.5956/jriet.35.908.

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Selami, Salim, Mohamed Salah Mecibah, Younes Debbah, and Taqiy Eddine Boukelia. "Gear Crack Detection Using Residual Signal and Empirical Mode Decomposition." Mechanics and Mechanical Engineering 22, no. 4 (September 2, 2020): 1133–44. http://dx.doi.org/10.2478/mme-2018-0089.

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AbstractDiagnosis of gearbox defects at an early stage is very important to avoid catastrophic failures. This article presents experimental results of tests made to evaluate the cracks of the cylindrical gears of a transfer case under advanced test conditions. For the diagnosis of a gearbox, various signal processing techniques are mainly used for the vibration study of the gears, such as: Fast Fourier Transform, synchronous time average, and time-based wavelet transformation, etc. Various methods can be found in the literature which can be used to calculate the residual signal (RS), however, in this paper, we suggest a new method combined empirical mode decomposition (EMD) technique with RS for detection of the crack gear. In order to extract the associated defect characteristics of the transfer box vibration signals, the EMD has been performed. The results show the effectiveness of the EMD method in the evaluation of tooth cracking in spur gears. This effectiveness can be proved by the obtained results of the experimental tests, which were presented and carried out on a test rig equipped with a transfer box.
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Abalo, Koffi E., and Donatien N. Niango. "Residual division, primary decomposition and filtrations. application to dedekind domains." Communications in Algebra 27, no. 2 (January 1999): 811–20. http://dx.doi.org/10.1080/00927879908826463.

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Wynn, A., D. S. Pearson, B. Ganapathisubramani, and P. J. Goulart. "Optimal mode decomposition for unsteady flows." Journal of Fluid Mechanics 733 (September 24, 2013): 473–503. http://dx.doi.org/10.1017/jfm.2013.426.

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AbstractA new method, herein referred to as optimal mode decomposition (OMD), of finding a linear model to describe the evolution of a fluid flow is presented. The method estimates the linear dynamics of a high-dimensional system which is first projected onto a subspace of a user-defined fixed rank. An iterative procedure is used to find the optimal combination of linear model and subspace that minimizes the system residual error. The OMD method is shown to be a generalization of dynamic mode decomposition (DMD), in which the subspace is not optimized but rather fixed to be the proper orthogonal decomposition (POD) modes. Furthermore, OMD is shown to provide an approximation to the Koopman modes and eigenvalues of the underlying system. A comparison between OMD and DMD is made using both a synthetic waveform and an experimental data set. The OMD technique is shown to have lower residual errors than DMD and is shown on a synthetic waveform to provide more accurate estimates of the system eigenvalues. This new method can be used with experimental and numerical data to calculate the ‘optimal’ low-order model with a user-defined rank that best captures the system dynamics of unsteady and turbulent flows.
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Noack, Bernd R. "From snapshots to modal expansions – bridging low residuals and pure frequencies." Journal of Fluid Mechanics 802 (August 1, 2016): 1–4. http://dx.doi.org/10.1017/jfm.2016.416.

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Data-driven low-order modelling has been enjoying rapid advances in fluid mechanics. Arguably, Sirovich (Q. Appl. Maths, vol. XLV, 1987, pp. 561–571) started these developments with snapshot proper orthogonal decomposition, a particularly simple method. The resulting reduced-order models provide valuable insights into flow physics, allow inexpensive explorations of dynamics and operating conditions, and enable model-based control design. A winning argument for proper orthogonal decomposition (POD) is the optimality property, i.e. the guarantee of the least residual for a given number of modes. The price is unpleasant frequency mixing in the modes which complicates their physical interpretation. In contrast, temporal Fourier modes and dynamic mode decomposition (DMD) provide pure frequency dynamics but lose the orthonormality and optimality property of POD. Sieber et al. (J. Fluid Mech., vol. 792, 2016, pp. 798–828) bridge the least residual and pure frequency behaviour with an ingenious interpolation, called spectral proper orthogonal decomposition (SPOD). This article puts the achievement of the TU Berlin authors in perspective, illustrating the potential of SPOD and the challenges ahead.
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Zhan, Linjie, and Zhenpeng Tang. "Natural Gas Price Forecasting by a New Hybrid Model Combining Quadratic Decomposition Technology and LSTM Model." Mathematical Problems in Engineering 2022 (December 5, 2022): 1–13. http://dx.doi.org/10.1155/2022/5488053.

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Research on the price prediction of natural gas is of great significance to market participants of all kinds. In order to predict natural gas prices more reliably, this paper introduces a quadratic decomposition technology based on the combination of variational modal decomposition (VMD) and ensemble empirical modal decomposition (EEMD), which decomposes the residual term (Res) after VMD by EEMD; then, a new hybrid model called VMD-EEMD-Res.-LSTM is constructed in combination with the long short-term memory (LSTM) prediction model. The contribution of this new hybrid model is that, unlike existing application research that combines existing decomposition technology with the LSTM model, it does not ignore the important information contained in the residual after the VMD. In order to verify the predictive performance of the proposed new model, this paper uses the data of the spot price of natural gas in the United States to conduct a multistep-ahead empirical comparative analysis. The results show that the new hybrid model constructed in this paper has significant predictive advantages.
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Sun, Changxia, Menghao Pei, Bo Cao, Saihan Chang, and Haiping Si. "A Study on Agricultural Commodity Price Prediction Model Based on Secondary Decomposition and Long Short-Term Memory Network." Agriculture 14, no. 1 (December 28, 2023): 60. http://dx.doi.org/10.3390/agriculture14010060.

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In order to address the significant prediction errors resulting from the substantial fluctuations in agricultural product prices and the non-linear features, this paper proposes a hybrid forecasting model based on variational mode decomposition (VMD), ensemble empirical mode decomposition (EEMD), and long short-term memory networks (LSTM). This combined model is referred to as the VMD–EEMD–LSTM model. Initially, the original time series of agricultural product prices undergoes decomposition using VMD to obtain a series of variational mode functions (VMFs) and a residual component with higher complexity. Subsequently, the residual component undergoes a secondary decomposition using EEMD. All components are then fed into an LSTM model for training to obtain predictions for each component. Finally, the predictions for each component are linearly combined to generate the ultimate price forecast. To validate the effectiveness of the VMD–EEMD–LSTM model, empirical analyses were conducted for one-step and multi-step forecasts using weekly price data for pork, Chinese chives, shiitake mushrooms, and cauliflower from China’s wholesale agricultural markets. The results indicate that the composite model developed in this study provides enhanced forecasting accuracy.
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Landmesser, Joanna Małgorzata. "Decomposition of Differences between Household Income Distributions in Poland in Years 2002 and 2012." Acta Universitatis Lodziensis. Folia Oeconomica 4, no. 336 (September 4, 2018): 103–15. http://dx.doi.org/10.18778/0208-6018.336.07.

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In this study we present the decomposition of income inequalities between household income distributions in Poland in 2002 and 2012. The difference between two distributions may be decomposed using the counterfactual distribution, which can be constructed in various ways. Techniques such as the residual imputation approach and RIF‑regression method (recentered influence function) were considered. The application of these methods made it possible to show the aggregate detailed decompositions in different quantile points along the income distribution. The influence of several person’s characteristics on the differences in income distributions was examined. By decomposing the inequalities into the explained and unexplained components it was possible to receive additional information about their causes.
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Goodbrake, Christian, Alain Goriely, and Arash Yavari. "The mathematical foundations of anelasticity: existence of smooth global intermediate configurations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2245 (January 2021): 20200462. http://dx.doi.org/10.1098/rspa.2020.0462.

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A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption is on unsatisfactory ground. Here, we derive a sufficient condition for the existence of global intermediate configurations, starting from a multiplicative decomposition of the deformation gradient. We show that these global configurations are unique up to isometry. We examine the result of isometrically embedding these configurations in higher-dimensional Euclidean space, and construct multiplicative decompositions of the deformation gradient reflecting these embeddings. As an example, for a family of radially symmetric deformations, we construct isometric embeddings of the resulting intermediate configurations, and compute the residual stress fields explicitly.
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Liu, Yuhu, Yi Chai, Bowen Liu, and Yiming Wang. "Impulse Signal Detection for Bearing Fault Diagnosis via Residual-Variational Mode Decomposition." Applied Sciences 11, no. 7 (March 29, 2021): 3053. http://dx.doi.org/10.3390/app11073053.

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A novel method named residual-variational mode decomposition (RVMD) is proposed in this study to extract bearing fault features accurately. RVMD can determine the number of modes and the balance parameter adaptively, and it has two stages. In the first stage, the signal is decomposed into a series of modes until the correlation coefficient between the raw signal and the decomposition results reaches the threshold. A redefined kurtosis, which can resist the interferences from aperiodic impulse efficiency, is applied to rebuild the ensemble kurtosis index. The mode that has the largest rebuild-ensemble kurtosis, and its neighbors, are kept. By putting the residual signal into the second stage, an iteration process is applied to determine the optimal parameters for variational mode decomposition (VMD). VMD is re-run with the optimal parameters, and the sub-mode filtered with the larger rebuild-ensemble kurtosis is examined by the envelope analysis technology to observe the fault feature. The effectiveness of RVMD is verified by the simulation signal and three experiment signals. Its superiority is shown by comparing it with some existing methods.
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Liu, Jing Chong, Jing Song, Yu Wang, Qian Qian Wang, Tao Qi, Chang Qiao Zhang, and Jing Kui Qu. "Kinetics Studies on a Novel Decomposition Method of Zircon Sand." Advanced Materials Research 953-954 (June 2014): 1113–16. http://dx.doi.org/10.4028/www.scientific.net/amr.953-954.1113.

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A novel method was proposed for preparing oxychloride octahydrate by the two – step decomposition of zircon sand concentrate in sodium hydroxide system. The effect of decomposition temperature and NaOH – to – zircon mass ratio of each stage on the decomposition of zircon sand was investigated. The macrokinetics of the two – step decomposition process was also examined. The experimental date showed that the shrinking core model with diffusion through the residual layer is most applicable for the first step decomposition process with the apparent activation energy of 42.9 kJ/mol, but the second step process was controlled by chemical reaction with the apparent activation energy of 30.1 kJ/mol.
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Wang, Ruidong, Xia Yang, Yong Gao, Xiaohong Dang, Yumei Liang, Shuai Qi, Chen Zhao, and Xiaoting Duan. "Decomposition characteristics of long-established Salix psammophila sand barriers in an arid area, Northwestern China." BioResources 16, no. 3 (July 13, 2021): 5947–63. http://dx.doi.org/10.15376/biores.16.3.5947-5963.

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Salix psammophila has been extensively used as a sand barrier material for various desertification control applications. Elucidating the long-term decomposition characteristics and nutrient cycling process of this sand barrier in desert environments is of great importance. In this study, which was conducted for 1 to 9 years, changes in the mass loss percentage and the residual percentage in the decomposition process were explored of S. psammophila sand barriers in arid Northwestern China. In addition, the S. psammophila analysis nutrient elements release rule and its influence on soil properties were evaluated. The results showed that the decomposition process of S. psammophila sand barriers exhibited a “slow-fast” trend. After decomposition time for 9 years, mass decreased remarkably, and the residual percentage was 33.6%. Further, the nutrient release characteristics differed. C, P, and K were in the release state, whereas N was in the enrichment state. The decomposition percentage of the sand barriers was significantly correlated with N, P, K, C/N, C/P, and N/P (p < 0.05). The soil nutrient contents of C, P, and K contents increased 3.43, 2.23, and 2.08 g/kg compared to the initial values, respectively. The soil nutrient contents of N contents decreased 0.19 g/kg.
42

Ferraro, Peter. "Improved Fabrication of Micro Channels in LTCC Circuitry and MEMS Using QPAC® Polyalkylene Carbonate as a Sacrificial Structure." International Symposium on Microelectronics 2014, no. 1 (October 1, 2014): 000673–76. http://dx.doi.org/10.4071/isom-wp32.

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QPAC® Polyalkylene carbonates polymers are currently used as a sacrificial material in many applications because they decompose at very low temperatures and leave virtually no contamination or residual behind after the debind step. This includes applications for air gaps in microfluidics, micro electro mechanical systems and microelectronics. QPAC® decomposition properties are very critical in applications with temperature sensitive materials or where residuals can cause electrical and or mechanical problems in the final product. Past work by academia and industry has been done with QPAC® to make enclosed air channels by providing temporary scaffolding in the pattern of the air gap. There are several methods of forming a cavity in an electronic device. This includes removal of the sacrificial material by thermal decomposition and wet etching. Thermal decomposition is the method employed to form the cavity using QPAC®. The results have been promising and show that this is a viable method to fabricate air gaps in Microelectromechanical, MEM systems and LTCC modules. Several new Polyalkylene carbonate polymers have recently been commercially produced to support further growth into this area.
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Jiang, Yu Ting, and Zhong Ke Yin. "Adaptive Image Denoising Based on Sparse Decomposition." Applied Mechanics and Materials 130-134 (October 2011): 2932–35. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2932.

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Different behaviors of image information and noise in sparse decomposition were studied to identify the differences between image information and noise. According to the different coherences between image (or residual image), noise and over-complete dictionary, image information and noise are distinguished. One image adaptive filtering is realized by taking coherent ratio threshold as the constraints of extracting available information.
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Chen, Xing Hong. "Study on the Remaining Oil Distribution with Domain Decomposition Simulation Method." Advanced Materials Research 962-965 (June 2014): 469–72. http://dx.doi.org/10.4028/www.scientific.net/amr.962-965.469.

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Block 127 reservoir was a typical heavy oil reservoir with normal pressure system, high density and viscosity. The block was low production because formation water invaded seriously. Well condition and effects of measure were badly year after year. In order to clarify remaining oil distribution rule, east and west typical well group of block in 127 was chosen. Careful research in typical well group and multiple well group synthesis research method was used to research with numerical simulation method. The sub-zone sand body residual oil saturation chorizo-gram of well groups and entire block were mapped, qualitative and quantity analysis residual oil distribution rule was studied on plane and vertical. The larger and more complex structure reservoir, used to Domain decomposition method with the typical well group fine research, multi-well-group integrated research method is feasible. The knowledge of residual oil is made deeply and these works offer technique support for block heavy oil reservoir.
45

Torzilli, A. P., and G. Andrykovitch. "Degradation of Spartina lignocellulose by individual and mixed cultures of salt-marsh fungi." Canadian Journal of Botany 64, no. 10 (October 1, 1986): 2211–15. http://dx.doi.org/10.1139/b86-295.

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Spartina alterniflora tissue, either in the absence or presence of a nitrogen supplement, was inoculated with a single-species or a mixed-species inoculum of salt-marsh fungi. After 42 days of incubation at 25 °C, lignocellulose decomposition was determined by measuring the amount of residual total lignocellulose, cellulose, hemicellulose, and lignin. A two-way analysis of variance of these results indicated an interaction between fungal treatments and nitrogen treatments. Pairwise comparisons of mean residual weights showed that all individual and mixed fungal inocula resulted in significant degradation of the total lingo-cellulosic, cellulosic, and hemicellulosic fractions of Spartina tissue with levels of decomposition ranging from approximately 16 to 40%, depending on the fungal – nitrogen treatment and the cell wall fraction examined. Lignin degradation was not detected for any of the treatments. Cultures with a mixture of fungi showed less decomposition than was observed for the most efficient decomposer when it occurred alone.
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Nogueira, Maria Cristina Stolf. "Specific residue: application of orthogonal contrasts when heteroscedasticity is present." Scientia Agricola 67, no. 1 (February 2010): 117–25. http://dx.doi.org/10.1590/s0103-90162010000100016.

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When experimental data are submitted to analysis of variance, the assumption of data homoscedasticity (variance homogeneity among treatments), associated to the adopted mathematical model must be satisfied. This verification is necessary to ensure the correct test for the analysis. In some cases, when data homoscedascity is not observed, errors may invalidate the analysis. An alternative to overcome this difficulty is the application of the specific residue analysis, which consists of the decomposition of the residual sum of squares in its components, in order to adequately test the correspondent orthogonal contrasts of interest between treatment means. Although the decomposition of the residual sum of squares is a seldom used procedure, it is useful for a better understanding of the residual mean square nature and to validate the tests to be applied. The objective of this review is to illustrate the specific residue application as a valid and adequate alternative to analyze data from experiments following completely randomized and randomized complete block designs in the presence of heteroscedasticity.
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Zhu, Neng, Feng Qian, Xiaowei Xu, Mingda Wang, and Qi Teng. "Thermogravimetric Experiment of Urea at Constant Temperatures." Materials 14, no. 20 (October 18, 2021): 6190. http://dx.doi.org/10.3390/ma14206190.

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There are still many unsolved mysteries in the thermal decomposition process of urea. This paper studied the thermal decomposition process of urea at constant temperatures by the thermal gravimetric–mass spectrometry analysis method. The results show that there are three obvious stages of mass loss during the thermal decomposition process of urea, which is closely related to the temperature. When the temperature was below 160 °C, urea decomposition almost did not occur, and molten urea evaporated slowly. When the temperature was between 180 and 200 °C, the content of biuret, one of the by-products in the thermal decomposition of urea, reached a maximum. When the temperature was higher than 200 °C, the first stage of mass loss was completed quickly, and urea and biuret rapidly broke down. When the temperature was about 240 °C, there were rarely urea and biuret in residual substance; however, the content of cyanuric acid was still rising. When the temperature was higher than 280°C, there was a second stage of mass loss. In the second stage of mass loss, when the temperature was higher than 330 °C, mass decreased rapidly, which was mainly due to the decomposition of cyanuric acid. When the temperature was higher than 380 °C, the third stage of mass loss occurred. However, when the temperature was higher than 400 °C, and after continuous heating was applied for a sufficiently long time, the residual mass was reduced to almost zero eventually.
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Zerrad, E., A. S. Khan, K. Zerrad, and G. Rawitscher. "Singular-value decomposition method in atomic scattering." Canadian Journal of Physics 81, no. 10 (October 1, 2003): 1215–21. http://dx.doi.org/10.1139/p03-089.

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A new numerical method for solving the integro-differential equations that appear in the theory of atomic scattering is devised. It consists of decomposing the kernel into separable terms via the method of singular-value decomposition. A set of integro-differential equations involving the residual integral kernel are then solved to obtain the wave function and from this the phase shift is evaluated. PACS Nos.: 23.23.+x, 56.65.DY
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Rajan, Rejitha, Siby Varghese, and K. E. George. "Kinetics of Peroxide Vulcanization of Natural Rubber." Progress in Rubber, Plastics and Recycling Technology 28, no. 4 (November 2012): 201–20. http://dx.doi.org/10.1177/147776061202800405.

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This study was undertaken to optimize the vulcanization conditions and explore the effect of residual peroxide in the peroxide vulcanization of natural rubber. The study was followed through the kinetics of the vulcanization reaction at various temperatures viz. 150,155,160 and 165°C. Dicumyl peroxide (DCP) was used as the crosslinking agent. The Monsanto Rheometer was used to investigate the different crosslinking stages and vulcanization kinetics. The thermal decomposition of peroxide followed a first order free radical decomposition reaction. Half-lives at various temperatures were determined. The percentage of residual peroxide was calculated from the cure kinetic data. The effect of residual peroxide on mechanical properties was studied at various peroxide levels and also by extending the cure time (from t90 to t95 and then to t100). Mechanical properties such as tensile strength, elongation at break, modulus and compression set (70 and 100°C) were measured. Excess peroxide was found to cause a high compression set at elevated temperature and the cure time was selected to achieve minimum residual peroxide in the product. Results indicate that peroxide concentration is the dominant factor controlling the crosslink density and hence the properties of the vulcanizates.
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Zixing, Shen, Shen Quntai, Li Sheng, and Liu Xuelin. "Study on the Technology of Leakage Protection." Open Electrical & Electronic Engineering Journal 8, no. 1 (December 31, 2014): 412–18. http://dx.doi.org/10.2174/1874129001408010412.

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Failure leakage of equipment or electric shock may make the residual current amplitude decrease, which causes effective protection of the fault and the existence of dead zone of operation. This paper presents the principle of residual current leakage protection based on vector, using residual current amplitude and residual current variation of fault leakage protection, the realization of mutation leakage, continuous slow change leakage detection and recognition, triangle formulas residual current variation calculation method, orthogonal decomposition calculation method and three-phase equivalent calculation method. Through the analysis of the residual current vector variation, we put forward the corresponding method of delayed electrical leakage protection. According to the residual current amplitude, mutation leakage, slowly varying leakage, electric leakage comprehensive protection, we can reduce the leakage protection action area; improve the reliability of power system.

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