scholarly journals Improving Numerical Accuracy of Gr�bner Basis Polynomial Equation Solvers

2007 ◽  
Author(s):  
Martin Byrod ◽  
Klas Josephson ◽  
Kalle Astrom
Keyword(s):  
Polynomial Equation ◽  
Numerical Accuracy ◽  
Bner Basis

scholarly journals Accurate Computation of Periodic Regions' Centers in the General M-Set with Integer Index Number

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Wang Xingyuan ◽  
He Yijie ◽  
Sun Yuanyuan
Keyword(s):  
Polynomial Equation ◽  
Negative Integer ◽  
The Other ◽  
Index Number ◽  
Polynomial Equations ◽  
Decimal Point ◽  
Numerical Accuracy ◽  
Index Numbers ◽  
Accurate Computation ◽  
The Relationship

This paper presents two methods for accurately computing the periodic regions' centers. One method fits for the general M-sets with integer index number, the other fits for the general M-sets with negative integer index number. Both methods improve the precision of computation by transforming the polynomial equations which determine the periodic regions' centers. We primarily discuss the general M-sets with negative integer index, and analyze the relationship between the number of periodic regions' centers on the principal symmetric axis and in the principal symmetric interior. We can get the centers' coordinates with at least 48 significant digits after the decimal point in both real and imaginary parts by applying the Newton's method to the transformed polynomial equation which determine the periodic regions' centers. In this paper, we list some centers' coordinates of general M-sets'k-periodic regions(k=3,4,5,6)for the index numbersα=−25,−24,…,−1, all of which have highly numerical accuracy.

Linear Visco-Resistive Computations of Magnetohydrodynamic Waves: I. The Code and Test Cases

1994 ◽  
Vol 144 ◽  
pp. 503-505
Author(s):  
R. Erdélyi ◽  
M. Goossens ◽  
S. Poedts
Keyword(s):  
Resonant Absorption ◽  
Numerical Code ◽  
Mhd Waves ◽  
Test Cases ◽  
Numerical Accuracy ◽  
Element Discretization ◽  
Flux Tubes ◽  
Magnetohydrodynamic Waves ◽  
Viscosity Coefficients ◽  
Magnetic Flux Tubes

AbstractThe stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. Our computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code.

Reconstruction of complex shaped crack from ECT signals based on a fast forward solver using an advanced multi-media element

2020 ◽  
Vol 64 (1-4) ◽  
pp. 621-629
Author(s):  
Yingsong Zhao ◽  
Cherdpong Jomdecha ◽  
Shejuan Xie ◽  
Zhenmao Chen ◽  
Pan Qi ◽  
...  
Keyword(s):  
Coefficient Matrix ◽  
Crack Edge ◽  
Numerical Accuracy ◽  
Gauss Point ◽  
Current Testing ◽  
Efficient Simulation ◽  
Shaped Crack ◽  
Multi Media ◽  
Profile Reconstruction ◽  
Crack Profile

In this paper, the conventional database type fast forward solver for efficient simulation of eddy current testing (ECT) signals is upgraded by using an advanced multi-media finite element (MME) at the crack edge for treating inversion of complex shaped crack. Because the analysis domain is limited at the crack region, the fast forward solver can significantly improve the numerical accuracy and efficiency once the coefficient matrices of the MME can be properly calculated. Instead of the Gauss point classification, a new scheme to calculate the coefficient matrix of the MME is proposed and implemented to upgrade the ECT fast forward solver. To verify its efficiency and the feasibility for reconstruction of complex shaped crack, several cracks were reconstructed through inverse analysis using the new MME scheme. The numerical results proved that the upgraded fast forward solver can give better accuracy for simulating ECT signals, and consequently gives better crack profile reconstruction.

Optimisation of the Oil Extraction from Nigella sativa Seeds Using Response Surface Methodology

2017 ◽  
Vol 68 (2) ◽  
pp. 331-336
Author(s):  
Gabriela Isopencu ◽  
Mirela Marfa ◽  
Iuliana Jipa ◽  
Marta Stroescu ◽  
Anicuta Stoica Guzun ◽  
...  
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Nigella Sativa ◽  
Polynomial Equation ◽  
Herbaceous Plant ◽  
Box Behnken Design ◽  
Pareto Analysis ◽  
Black Cumin ◽  
Mediterranean Countries ◽  
Experimental Values

Nigella sativa, also known as black cumin, an annual herbaceous plant growing especially in Mediterranean countries, has recently gained considerable interest not only for its use as spice and condiment but also for its healthy properties of the fixed and essential oil and its potential as a biofuel. Nigella sativa seeds fixed oil, due to its high content in linoleic acid followed by oleic and palmitic acid, could be beneficial to human health. The objective of this study is to determine the optimum conditions for the solvent extraction of Nigella sativa seeds fixed oil using a three-level, three-factor Box-Behnken design (BBD) under response surface methodology (RSM). The obtained experimental data, fitted by a second-order polynomial equation were analysed by Pareto analysis of variance (ANOVA). From a total of 10 coefficients of the statistical model only 5 are important. The obtained experimental values agreed with the predicted ones.

Viscosity of Dimethyl Sulfoxide + 1,4 Dimethylbenzene System

2008 ◽  
Vol 59 (1) ◽  
pp. 45-48
Author(s):  
Oana Ciocirlan ◽  
Olga Iulian
Keyword(s):  
Free Energy ◽  
Dimethyl Sulfoxide ◽  
Atmospheric Pressure ◽  
Entire Range ◽  
Polynomial Equation ◽  
Energy Of Activation ◽  
Excess Gibbs Free Energy ◽  
Experimental Measurements ◽  
Gibbs Energy Of Activation ◽  
Free Energy Of Activation

This paper reports the viscosities measurements for the binary system dimethyl sulfoxide + 1,4-dimethylbenzene over the entire range of mole fraction at 298.15, 303.15, 313.15 and 323.15 K and atmospheric pressure. The experimental viscosities were correlated with the equations of Grunberg-Nissan, Katti-Chaudhri, Hind, Soliman and McAllister; the adjustable binary parameters have been obtained. The excess Gibbs energy of activation of viscous flow (G*E) has been calculated from the experimental measurements and the results were fitted to Redlich-Kister polynomial equation. The obtained negative excess Gibbs free energy of activation and negative Grunberg-Nissan interaction parameter are discussed in structural and interactional terms.

scholarly journals High Voltage Electric Discharge for Recovery of Chlorogenic Acid from Tobacco Waste

2021 ◽  
Vol 13 (8) ◽  
pp. 4481
Author(s):  
Marija Banožić ◽  
Antun Jozinović ◽  
Jovana Grgić ◽  
Borislav Miličević ◽  
Stela Jokić
Keyword(s):  
Chlorogenic Acid ◽  
Process Parameters ◽  
Electric Discharge ◽  
High Voltage ◽  
Treatment Time ◽  
Strong Dependence ◽  
Extraction Procedure ◽  
Polynomial Equation ◽  
Experimental Conditions ◽  
Tobacco Waste

Three fractions of tobacco waste (scrap, dust and midrib) were subjected to a high voltage electric discharge (HVED) assisted extraction procedure under different experimental conditions: solvent:solid ratio (300, 500, 700 mL/g), frequency (40, 70, 100 Hz) and treatment time (15, 30, 45 min), in order to study the influence of these conditions on the content of chlorogenic acid. The content of chlorogenic acid ranged from 1.54 to 3.66 mg/100 g for scrap, from 1.90 to 2.97 mg/100 g for dust, and from 2.30 to 3.38 mg/100 g for midrib extract, showing a strong dependence on the applied process parameters. The temperature change and the change in pH and electrical conductivity of the extracts after high voltage discharge treatment were also observed. The studied process parameters showed a statistically significant effect on the chemical and physical properties of the extracts from tobacco waste as well as on the content of chlorogenic acid, indicating the potential of HVED assisted processes in the separation of chlorogenic acid from tobacco industry waste. Multiple regression analysis was used to fit the results for the chlorogenic acid to a second order polynomial equation and the optimum conditions were determined.

scholarly journals Formulation and Mathematical Optimization of Controlled Release Calcium Alginate Micro Pellets of Frusemide

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Amitava Ghosh ◽  
Prithviraj Chakraborty
Keyword(s):  
Sodium Alginate ◽  
Calcium Alginate ◽  
Mathematical Optimization ◽  
Extended Period ◽  
Cost Effective ◽  
Polynomial Equation ◽  
Chronic Hypertension ◽  
Order Polynomial ◽  
High Degree

Objective. Frusemide loaded calcium alginate micropellets, an oral microparticulate delivery system, was statistically optimized exhibiting prolonged therapeutic action minimizing its adverse effects.Methods. Ionotropic Gelation technique was adopted employing 32Factorial designs and keeping the entire process free from organic solvents. Physicochemical and the release characteristics of the prepared formulations were studied, keeping variations only in sodium alginate (primary polymer) and Acrycoat E30D (copolymer) dispersion.Result. Sodium alginate was predominant over Acrycoat E30D in all batches. Nonadditives or interaction was observed to be insignificant. Multiple regressions produced second-order polynomial equation, and the predictive results obtained were validated with high degree of correlation. Thein vivostudy applauded that optimized calcium alginate micropellets of frusemide can produce a much greater diuretic effect over an extended period of 24 hours.Conclusion. This study reveals that the potential of a single dose of the mathematically optimized micro pellets of frusemide formulation is sufficient in the management of peripheral edema and ascites in congestive heart failure and as well in the treatment of chronic hypertension, leading to better patient compliance, and can be produced with minimum experimentation and time, proving far more cost-effective formulation than the conventional methods of formulating dosage forms.

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