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Youjun Deng,Xiaoping Fang,Jing Li 대한수학회 2015 대한수학회보 Vol.52 No.5
This paper deals with the numerical methods for the reconstruction of the source term in a linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the uniqueness of the inverse problem of determining the source term f(x) from final overdetermination. We present the regularization methods for reconstruction of the source term in the whole real line and with Neumann boundary conditions. Moreover, we show the connection of the solutions between the problem with Neumann boundary conditions and the problem with no boundary conditions (on the whole real line) by using the extension method. Numerical experiments are done for the inverse problem with the boundary conditions.
DENG, YOUJUN,FANG, XIAOPING,LI, JING Korean Mathematical Society 2015 대한수학회보 Vol.52 No.5
This paper deals with the numerical methods for the reconstruction of the source term in a linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the uniqueness of the inverse problem of determining the source term f(x) from final overdetermination. We present the regularization methods for reconstruction of the source term in the whole real line and with Neumann boundary conditions. Moreover, we show the connection of the solutions between the problem with Neumann boundary conditions and the problem with no boundary conditions (on the whole real line) by using the extension method. Numerical experiments are done for the inverse problem with the boundary conditions.
Highly stable N-doped carbon dots as the sensitive probe for the detection of Fe3+
Zhao Youjun,Yu Lixin,Deng Yakun,Peng Kangliang,Huang Shuai 한국물리학회 2023 Current Applied Physics Vol.50 No.-
The nitrogen-doped carbon dots (NCDs) are facilely fabricated by a one-step hydrothermal strategy using citric acid and o-phenylenediamine as start ingredient. The as-synthesized NCDs with a high quantum yield of 38.63% at 370 nm excitation maintain significant fluorescence stability in various complex environments, indicating that NCDs have the possibility of application in harsh environments. Moreover, after adding the Fe3+ to this as-synthesized NCDs, the emission intensity at 446 nm is remarkably reduced and exhibits line-dependent relationship in the range of 0.5–90 μM with a detection limit of 0.37 μM. Meanwhile, the fluorescence lifetime and absorption characteristics are compared respectively, and Stern-Volmer is calculated. These results illustrate that the quenched fluorescence is attributed to the synergistic effect of internal filtration effect (IFE) and static quenching. Moreover, this carbon-based sensing material has elevated efficiency in detecting Fe3+ in practical samples, implying that the sensing probe provides a fast and accurate new technique for the detection of Fe3+.