Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals A Note on the Decomposition Methods for Support Vector Regression

2002 ◽  
Vol 14 (6) ◽  
pp. 1267-1281 ◽  
Author(s):  
Shuo-Peng Liao ◽  
Hsuan-Tien Lin ◽  
Chih-Jen Lin
Keyword(s):  
Support Vector Regression ◽  
Decomposition Method ◽  
Decomposition Methods ◽  
Support Vector ◽  
Dual Formulation ◽  
Working Set ◽  
Number Of Iterations

The dual formulation of support vector regression involves two closely related sets of variables. When the decomposition method is used, many existing approaches use pairs of indices from these two sets as the working set. Basically, they select a base set first and then expand it so all indices are pairs. This makes the implementation different from that for support vector classification. In addition, a larger optimization subproblem has to be solved in each iteration. We provide theoretical proofs and conduct experiments to show that using the base set as the working set leads to similar convergence (number of iterations). Therefore, by using a smaller working set while keeping a similar number of iterations, the program can be simpler and more efficient.

scholarly journals Customized depolarization spatial patterns with dynamic retardance functions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
David Marco ◽  
Guadalupe López-Morales ◽  
María del Mar Sánchez-López ◽  
Ángel Lizana ◽  
Ignacio Moreno ◽  
...  
Keyword(s):  
Spatial Patterns ◽  
Detection System ◽  
Temporal Integration ◽  
Matrix Decomposition ◽  
Decomposition Methods ◽  
Time Dependent ◽  
Light Modulator ◽  
Dynamical Time ◽  
Depolarization Effect ◽  
Spatially Variant

AbstractIn this work we demonstrate customized depolarization spatial patterns by imaging a dynamical time-dependent pixelated retarder. A proof-of-concept of the proposed method is presented, where a liquid–crystal spatial light modulator is used as a spatial retarder that emulates a controlled spatially variant depolarizing sample by addressing a time-dependent phase pattern. We apply an imaging Mueller polarimetric system based on a polarization camera to verify the effective depolarization effect. Experimental validation is provided by temporal integration on the detection system. The effective depolarizance results are fully described within a simple graphical approach which agrees with standard Mueller matrix decomposition methods. The potential of the method is discussed by means of three practical cases, which include non-reported depolarization spatial patterns, including exotic structures as a spirally shaped depolarization pattern.

scholarly journals Mercury Speciation in Various Coals Based on Sequential Chemical Extraction and Thermal Analysis Methods

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2361
Author(s):  
Yinjiao Su ◽  
Xuan Liu ◽  
Yang Teng ◽  
Kai Zhang
Keyword(s):  
Thermal Stability ◽  
Coal Combustion ◽  
Decomposition Methods ◽  
Chemical Extraction ◽  
Anthropogenic Source ◽  
Coal Rank ◽  
Coal Pyrolysis ◽  
Mercury Emissions ◽  
Sequential Chemical Extraction ◽  
Removal Technology

Coal combustion is an anthropogenic source of mercury (Hg) emissions to the atmosphere. The strong toxicity and bioaccumulation potential have prompted attention to the control of mercury emissions. Pyrolysis has been regarded as an efficient Hg removal technology before coal combustion and other utilization processes. In this work, the Hg speciation in coal and its thermal stability were investigated by combined sequential chemical extraction and temperature programmed decomposition methods; the effect of coal rank on Hg speciation distribution and Hg release characteristics were clarified based on the weight loss of coal; the amount of Hg released; and the emission of sulfur-containing gases during coal pyrolysis. Five species of mercury were determined in this study: exchangeable Hg (F1), carbonate + sulfate + oxide bound Hg (F2), silicate + aluminosilicate bound Hg (F3), sulfide bound Hg (F4), and residual Hg (F5), which are quite distinct in different rank coals. Generally, Hg enriched in carbonates, sulfates, and oxides might migrate to sulfides with the transformation of minerals during the coalification process. The order of thermal stability of different Hg speciation in coal is F1 < F5 < F2 < F4 < F3. Meanwhile, the release of Hg is accompanied with sulfur gases during coal pyrolysis, which is heavily dependent on the coal rank.

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