• 대한수학회논문집
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• 제34권2호
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• pp.465-475
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• 2019

Let X be a Banach space and $X^*$ be its dual. In this paper, we give relationships among some parameters in $X^*$: ${\varepsilon}$-nonsquareness parameter, $J({\varepsilon},X^*)$; ${\varepsilon}$-boundary parameter, $Q({\varepsilon},X^*)$; the modulus of smoothness, ${\rho}_{X^*}({\varepsilon})$; and ${\varepsilon}$-Pythagorean parameter, $E({\varepsilon},X^*)$, and weak orthogonality parameter, ${\omega}(X)$ in X that imply uniform norm structure in X. Some existing results are extended or approved.

• IEIE Transactions on Smart Processing and Computing
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• 제6권1호
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• pp.66-70
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• 2017

Radioactive materials are used in medicine, non-destructive testing, and nuclear plants. Source localization is especially important during nuclear decommissioning and decontamination because the actual location of the radioactive source within nuclear waste is often unknown. The coded-aperture imaging technique started with space exploration and moved into X-ray and gamma ray imaging, which have imaging process characteristics similar to each other. In this study, we simulated $21{\times}21$ and $37{\times}37$ coded aperture collimators based on a modified uniformly redundant array (MURA) pattern to make a gamma imaging system that can localize a gamma-ray source. We designed a $21{\times}21$ coded aperture collimator that matches our gamma imaging detector and did feasibility experiments with the coded aperture imaging system. We evaluated the performance of each collimator, from 2 mm to 10 mm thicknesses (at 2 mm intervals) using root mean square error (RMSE) and sensitivity in a simulation. In experimental results, the full width half maximum (FWHM) of the point source was $5.09^{\circ}$ at the center and $4.82^{\circ}$ at the location of the source was $9^{\circ}$. We will continue to improve the decoding algorithm and optimize the collimator for high-energy gamma rays emitted from a nuclear power plant.