Minimal-order polynomial satisfying the equality cTp(A) = 0

1991 ◽  
Vol 138 (1) ◽  
pp. 129
Author(s):  
L.A. Novak ◽  
Z.M. Ranic
Keyword(s):  
Minimal Order ◽  
Order Polynomial

Statistical method of steepest improvement of response

2018 ◽  
Vol 84 (11) ◽  
pp. 74-87
Author(s):  
V. B. Bokov
Keyword(s):  
Statistical Method ◽  
Linear Model ◽  
Response Prediction ◽  
Initial Experiment ◽  
First Order ◽  
Prediction Response ◽  
Conditional Extremum ◽  
Order Polynomial ◽  
Limiting Values

A new statistical method for response steepest improvement is proposed. This method is based on an initial experiment performed on two-level factorial design and first-order statistical linear model with coded numerical factors and response variables. The factors for the runs of response steepest improvement are estimated from the data of initial experiment and determination of the conditional extremum. Confidence intervals are determined for those factors. The first-order polynomial response function fitted to the data of the initial experiment makes it possible to predict the response of the runs for response steepest improvement. The linear model of the response prediction, as well as the results of the estimation of the parameters of the linear model for the initial experiment and factors for the experiments of the steepest improvement of the response, are used when finding prediction response intervals in these experiments. Kknowledge of the prediction response intervals in the runs of steepest improvement of the response makes it possible to detect the results beyond their limits and to find the limiting values of the factors for which further runs of response steepest improvement become ineffective and a new initial experiment must be carried out.

scholarly journals Thematic Maps for the Variation of Bearing Capacity of Soil Using SPTs and MATLAB

Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 329
Author(s):  
Mahdi O. Karkush ◽  
Mahmood D. Ahmed ◽  
Ammar Abdul-Hassan Sheikha ◽  
Ayad Al-Rumaithi
Keyword(s):  
Bearing Capacity ◽  
Mean Squared Error ◽  
Ground Level ◽  
The Other ◽  
Thematic Maps ◽  
First Order ◽  
Squared Error ◽  
Order Polynomial ◽  
Interpolation Polynomials ◽  
Penetration Tests

The current study involves placing 135 boreholes drilled to a depth of 10 m below the existing ground level. Three standard penetration tests (SPT) are performed at depths of 1.5, 6, and 9.5 m for each borehole. To produce thematic maps with coordinates and depths for the bearing capacity variation of the soil, a numerical analysis was conducted using MATLAB software. Despite several-order interpolation polynomials being used to estimate the bearing capacity of soil, the first-order polynomial was the best among the other trials due to its simplicity and fast calculations. Additionally, the root mean squared error (RMSE) was almost the same for the all of the tried models. The results of the study can be summarized by the production of thematic maps showing the variation of the bearing capacity of the soil over the whole area of Al-Basrah city correlated with several depths. The bearing capacity of soil obtained from the suggested first-order polynomial matches well with those calculated from the results of SPTs with a deviation of ±30% at a 95% confidence interval.

scholarly journals High-Order Polynomial Fitting Assistance for Fast Double-Peak Finding in Brillouin-Distributed Sensing

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 187
Author(s):  
Marcelo A. Soto ◽  
Alin Jderu ◽  
Dorel Dorobantu ◽  
Marius Enachescu ◽  
Dominik Ziegler
Keyword(s):  
Optical Fibers ◽  
High Order ◽  
Polynomial Fitting ◽  
Gaussian Fitting ◽  
Peak Finding ◽  
Fitting Method ◽  
Fold Reduction ◽  
Order Polynomial ◽  
Fitting In ◽  
Distributed Brillouin Sensor

A high-order polynomial fitting method is proposed to accelerate the computation of double-Gaussian fitting in the retrieval of the Brillouin frequency shifts (BFS) in optical fibers showing two local Brillouin peaks. The method is experimentally validated in a distributed Brillouin sensor under different signal-to noise ratios and realistic spectral scenarios. Results verify that a sixth-order polynomial fitting can provide a reliable initial estimation of the dual local BFS values, which can be subsequently used as initial parameters of a nonlinear double-Gaussian fitting. The method demonstrates a 4.9-fold reduction in the number of iterations required by double-Gaussian fitting and a 3.4-fold improvement in processing time.

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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