• Nuclear Engineering and Technology
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• 제54권11호
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• pp.4253-4264
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• 2022

Since the implementation of the phosphate project in Bled El-Hadba (BEH) deposit, western region of Tébessa, no detailed study has been conducted to assess the natural radioactivity distribution and the associated radiological risk parameter for this open-pit mine. For the sake of determining a credible premining reference database for the region of interest, 21 samples were collected from different geological layers of the above-mentioned deposit. Gamma Spectrometry was applied for measuring radioactivity using a high resolution HPGe semiconductor detector. The obtained activity results have shown a significant broad variation in the radioactive contents for the different phosphate samples. The total average concentrations (in Bq·kg^-1) for ²²⁶Ra, ²³⁸U, ²³⁵U, ²³²Th and ⁴⁰K computed for the different type of phosphate layers were found to be 570 ± 169, 788 ± 280, 52 ± 18, 66 ± 6 and 81 ± 18 respectively. The mean activity concentrations of the measured radionuclides were compared to other regional and worldwide deposits. The ratios between the detected radioisotopes have been calculated for spatial distribution of natural radionuclides in the study area. Based on the aforementioned activity concentrations, the corresponding radiation hazard parameters were assessed. Correlations between the obtained parameters were drawn and a multivariate statistical analysis (Pearson Correlation, Cluster and Factor analysis) was carried out in order to identify the existing relationships.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.419-435
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• 2021

This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N^-1) and for the case 𝜀 ≪ N^-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.153-162
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• 1998

We study limits of sums of fuzzy numbers with different spreads and different shape functions where addition is defined by the sup-t-norm. We show the existence of the limit of the series of fuzzy numbers and prove the uniform continuity of the limit. Finally we investigate a law of large numbers for sequences of fuzzy numbers.

• 대한임베디드공학회논문지
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• 제18권6호
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• pp.267-275
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• 2023

This paper presents the development of specialized software for annotating volume-of-interest on ¹⁸F-FDG PET/CT images with the goal of facilitating the studies and diagnosis of head and neck cancer (HNC). To achieve an efficient annotation process, we employed the SE-Norm-Residual Layer-based U-Net model. This model exhibited outstanding proficiency to segment cancerous regions within ¹⁸F-FDG PET/CT scans of HNC cases. Manual annotation function was also integrated, allowing researchers and clinicians to validate and refine annotations based on dataset characteristics. Workspace has a display with fusion of both PET and CT images, providing enhance user convenience through simultaneous visualization. The performance of deeplearning model was validated using a Hecktor 2021 dataset, and subsequently developed semi-automatic annotation functionalities. We began by performing image preprocessing including resampling, normalization, and co-registration, followed by an evaluation of the deep learning model performance. This model was integrated into the software, serving as an initial automatic segmentation step. Users can manually refine pre-segmented regions to correct false positives and false negatives. Annotation images are subsequently saved along with their corresponding ¹⁸F-FDG PET/CT fusion images, enabling their application across various domains. In this study, we developed a semi-automatic annotation software designed for efficiently generating annotated lesion images, with applications in HNC research and diagnosis. The findings indicated that this software surpasses conventional tools, particularly in the context of HNC-specific annotation with ¹⁸F-FDG PET/CT data. Consequently, developed software offers a robust solution for producing annotated datasets, driving advances in the studies and diagnosis of HNC.

• 대한수학회지
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• 제54권4호
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• pp.1063-1079
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• 2017

Two standard Bessel sequences in a Hilbert $C^*$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^*$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the $C^*$-algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m)-approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.

• 대한수학회지
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• 제43권1호
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• pp.147-157
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• 2006

In this paper, we study complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an antide Sitter space $H_1^4(-1)$. It is proved that complete maximal spacelike hypersurfaces with constant Gauss-Kronecker curvature in an anti-de Sitter space $H_1^4(-1)$ are isometric to the hyperbolic cylinder $H^2(c1){\times}H^1(c2)$ with S = 3 or they satisfy $S{\leq}2$, where S denotes the squared norm of the second fundamental form.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권2호
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• pp.143-159
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• 2020

We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L² and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.

• 호남수학학술지
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• 제27권1호
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• pp.69-76
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• 2005

The aim of this work is to generalize $L_1$-approximation in order to apply them to a discrete approximation. In $L_1$-approximation, we use the norm given by $${\parallel}f{\parallel}_1={\int}{\mid}f{\mid}d{\mu}$$ where ${\mu}$ a non-atomic positive measure. In this paper, we go to the other extreme and consider measure ${\mu}$ which is purely atomic. In fact we shall assume that ${\mu}$ has exactly m atoms. For any ${\ell}$-tuple $b^1,\;{\cdots},\;b^{\ell}{\in}{\mathbb{R}}^m$, we defined the ${\ell}^m_1{w}$-norn, and consider $s^*{\in}S$ such that, for any $b^1,\;{\cdots},\;b^{\ell}{\in}{\mathbb{R}}^m$, $$\array{min&max\\{s{\in}S}&{1{\leq}i{\leq}{\ell}}}\;{\parallel}b^i-s{\parallel}_w$$, where S is a n-dimensional subspace of ${\mathbb{R}}^m$. The $s^*$ is called the Chebyshev center or a discrete simultaneous ${\ell}^m_1$-approximation from the finite dimensional subspace.

• 대한수학회지
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• 제56권1호
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• pp.197-224
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• 2019

Let A be a $JB^*$-triple with Banach dual space $A^*$ and bi-dual the $JBW^*$-triple $A^{**}$. Elements x of $A^*$ of norm one may be regarded as normalised 'Q-measures' defined on the complete ortho-lattice ${\tilde{\mathcal{U}}}(A^{**})$ of tripotents in $A^{**}$. A Q-measure x possesses a support e(x) in ${\tilde{\mathcal{U}}}(A^{**})$ and a compact support $e_c(x)$ in the complete atomic lattice ${\tilde{\mathcal{U}}}_c(A)$ of elements of ${\tilde{\mathcal{U}}}(A^{**})$ compact relative to A. Necessary and sufficient conditions for an element v of ${\tilde{\mathcal{U}}}_c(A)$ to be a compact support tripotent $e_c(x)$ are given, one of which is related to the Q-covering numbers of v by families of elements of ${\tilde{\mathcal{U}}}_c(A)$.

• 대한수학회논문집
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• 제37권2호
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• pp.455-472
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• 2022

For j = 0, 1, 2,…, k - 1; k ≥ 2; and - 1 ≤ B < A ≤ 1, we have introduced the functions classes denoted by ST_[j,k](A, B) and K_[j,k](A, B), respectively, called the generalized (j, k)-symmetric starlike and convex functions. We first proved the sharp bounds on |f(z)| and |f'(z)|. Various radii related problems, such as radius of (j, k)-symmetric starlikeness, convexity, strongly starlikeness and parabolic starlikeness are determined. The quantity |a²₃ - a₅|, which provide the initial bound on Zalcman functional is obtained for the functions in the family ST_[j,k]. Furthermore, the sharp pre-Schwarzian norm is also established for the case when f is a member of K_[j,k](α) for all 0 ≤ α < 1.