Carleman Estimate for a Singulary Perturbed Degenerated Parabolic Equation
Zeine Sid Elemine,
Ibrahima Faye,
Alassane Sy,
Diaraf Seck
Issue:
Volume 9, Issue 5, October 2021
Pages:
113-125
Received:
23 July 2021
Accepted:
18 August 2021
Published:
29 October 2021
Abstract: In this paper, we are concerned with the the internal control of an elliptic singularly perturbed degenerated parabolic equation. This parabolic equation models sand transport problem near the coast in areas subjected to the tide. We study first the null controllability result of the parabolic equation modeling sand transport equation.The limit problem obtained by homogenization problem is also considered. We use distributed and bounded controls supported on a small open set of the initial domain. We prove the null controllability of the system at any time by using observability inequality for both problem. For this purpose, a specific carleman estimate for the solutions of degenerate adjoint limit problem is also proved.
Abstract: In this paper, we are concerned with the the internal control of an elliptic singularly perturbed degenerated parabolic equation. This parabolic equation models sand transport problem near the coast in areas subjected to the tide. We study first the null controllability result of the parabolic equation modeling sand transport equation.The limit pro...
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Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling
Kemei Anderson Kimutai,
Christopher Ouma Onyango,
Mike Wafula
Issue:
Volume 9, Issue 5, October 2021
Pages:
126-132
Received:
16 September 2021
Accepted:
9 November 2021
Published:
17 November 2021
Abstract: Missing data is a real problem in many surveys. To overcome the problems caused by missing data, partial deletion and single imputation methods among others have been proposed. However, problems such as discarding usable data, inaccuracy in reproducing known population parameters and standard errors are associated with them. In ratio, regression and stochastic imputation, it is assumed that there is a variable with complete cases that can be used as a predictor in estimating missing values in the other variable(s) and the relationship between the dependent and independent variable(s) is linear. This might not always be the case. To overcome these problems accompanied to stochastic and regression estimation, two-phase sampling and nonparametric model-based estimation were employed in this research. Estimator of population total in two-phase sampling was modified. The variance of estimator developed by Hidiroglou, Haziza and Rao was used to compare the performance of the proposed non-parametric model-based imputation in reproducing well known population total and standard errors compared to mean, regression and stochastic methods of imputation. The data was simulated and analyzed using R-statistical Software. The empirical study revealed that non-parametric model-base imputation method is better in reproducing both known population total and standard error.
Abstract: Missing data is a real problem in many surveys. To overcome the problems caused by missing data, partial deletion and single imputation methods among others have been proposed. However, problems such as discarding usable data, inaccuracy in reproducing known population parameters and standard errors are associated with them. In ratio, regression an...
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