Al-Zughair integral transformation in solving improved heat and Poisson PDEs
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Abstract:
In this paper, a modification on Poisson partial differential equation has been performed, the applied modification has increased the domain and range of Poisson equation. The novel integral transformation "Al-Zughair" has been used to solve the improved Poisson and heat partial differential equations, as a new solving method for some partial differential equations.Keywords:
Poisson's equation
Heat equation
p L estimates for the Poisson equation and heat equation are the most basic regularity estimates. In this paper, we mainly study a new class of regularity estimates, weighted p L estimates, for the Poisson equation and heat equation.
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The paper addresses the problem of detecting changes in the parameters of multivariate Poisson sequences. The Neyman Pearson Detector (NPD) and the, Generalized Likelihood Ratio Detector (GLRD) are easily derived for iid Poisson sequences. Unfortunately, the problem is more' complicated for correlated Poisson sequences. This paper studies the performance of the detectors obtained under the iid assumption, when the observed data are distributed according to multivariate correlated Poisson sequences. Theoretical expressions of the receiver operating characteristics are derived when the change location is known. These curves provide a reference to which other detectors can be compared. The more realistic situation of an unknown change location is finally considered.
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