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The aim of this study was to investigate the potential of using structural analysis parameters for estimating the higher heating value (HHV) of biomass by obtaining information on the composition of cellulose, lignin, and hemicellulose. To achieve this goal, several nonlinear mathematical models were developed, including polynomials, support vector machines (SVMs), random forest regression (RFR) and artificial neural networks (ANN) for predicting HHV. The performed statistical analysis "goodness of fit" showed that the ANN model has the best performance in terms of coefficient of determination (R2 = 0.90) and the lowest level of model error for the parameters X2 (0.25), RMSE (0.50), and MPE (2.22). Thus, the ANN model was identified as the most appropriate model for determining the HHV of different biomasses based on the specified input parameters. In conclusion, the results of this study demonstrate the potential of using structural analysis parameters as input for HHV modeling, which is a promising approach for the field of biomass energy production. The development of the model ANN and the comparative analysis of the different models provide important insights for future research in this field. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the potential of using structural analysis parameters for estimating the higher heating value (HHV) of biomass by obtaining information on the composition of cellulose, lignin, and hemicellulose. To achieve this goal, several nonlinear mathematical models were developed, including polynomials, support vector machines (SVMs), random forest regression (RFR) and artificial neural networks (ANN) for predicting HHV. The performed statistical analysis “goodness of fit” showed that the ANN model has the best performance in terms of coefficient of determination (R2 = 0.90) and the lowest level of model error for the parameters X2 (0.25), RMSE (0.50), and MPE (2.22). Thus, the ANN model was identified as the most appropriate model for determining the HHV of different biomasses based on the specified input parameters. In conclusion, the results of this study demonstrate the potential of using structural analysis parameters as input for HHV modeling, which is a promising approach for the field of biomass energy production. The development of the model ANN and the comparative analysis of the different models provide important insights for future research in this field.

Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes approximately 12.5% of the polynomial coefficients, and then symmetry relations are employed to compute the rest of the polynomial coefficients. The proposed method is evaluated against existing methods in terms of computational cost and maximum size can be generated. In addition, a reconstruction error analysis for image is performed using the proposed method for large signal sizes. The evaluation shows that the proposed method outperforms other existing methods. [ABSTRACT FROM AUTHOR]

Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes approximately 12.5% of the polynomial coefficients, and then symmetry relations are employed to compute the rest of the polynomial coefficients. The proposed method is evaluated against existing methods in terms of computational cost and maximum size can be generated. In addition, a reconstruction error analysis for image is performed using the proposed method for large signal sizes. The evaluation shows that the proposed method outperforms other existing methods.

The efficient numerical simulation of population balance equations requires sophisticated techniques in order to combine accuracy with efficiency. We will focus on the numerical treatment of aggregation integrals that often dominate the overall time in population balance simulations. Following a finite element approach, the density distribution is discretized through a piecewise polynomial of order p > 0 on a nested grid that is refined locally toward an arbitrary point. The proposed method conserves mass while reducing the quadratic complexity (in the dimension of the solution space) of the direct computation to an almost linear complexity. The complexity improvement is based on recursion formulas exploiting orthogonality properties of basis functions along with FFT on locally equidistant portions of the grid. We present numerical results for various initial conditions and provide heuristic criteria for the choice of polynomial degree and grid refinement. [ABSTRACT FROM AUTHOR]

In this paper, a detailed theoretical and experimental study on some computational aspects of high order discrete orthogonal Racah polynomials (RPs) and their corresponding moments is carried out. Initially, the numerical overflow problem related to RPs computation is solved by using modified recurrence relations of RPs with respect to the polynomial order n and the variable s. Moreover, the recursive nature of the resulting relations considerably accelerates the computation of RPs. Then, the problem of numerical errors propagation that occurs during the recursive computation of RPs is solved. Indeed, the proposed solution relies on the use of a new numerical method that detects unstable values and sets them to zero. This ensures the numerical stability of high-order RPs. Next, a fast method is presented to significantly reduce the required time for reconstructing large-size 1D signal. This method involves the transformation of a 1D signal into a 2D array, then using matrix reconstruction formulas in the 2D domain. The simulation and comparison results clearly show that the proposed computation methods are very useful for the fast and stable analysis of large-size signals and 2D/3D images by Racah moments (RMs). [ABSTRACT FROM AUTHOR]

This paper presents a fully implicit scheme for approximating two-phase flow in heterogeneous porous media. The primary unknowns are the wetting phase pressure and non-wetting phase saturation. At each time step, a Jacobian matrix is computed. Convergence of the scheme is shown via increase of the polynomial degree. No slope limiters are needed. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]