• Journal of the Korean Mathematical Society
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• v.54 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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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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• v.24 no.2
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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.

• Honam Mathematical Journal
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• v.27 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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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 ${\tilde{\mathcal{U}}}_c(A)$.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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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.

• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1007-1023
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• 2024

In this paper we are able to define a standard fractional vector cross product(SFVCP) of two vectors in a Euclidean 3-space where it satisfies all the conditions of geometrical reality. For γ = 1 this definition satisfies the conditions of standard vector cross product(SVCP). The formulae for euclidean norm and fractional triple vector cross product of two vectors with standard fractional vector cross product are presented. Fractional curl and divergence of an electromagnetic vector field are presented using the new definition. All the properties are further supported with particular cases at γ = 0, γ = 1 and examples on standard orthogonal basis in R³. This concept has application in electrodynamics, elastodynamics, fluid flow etc.

• The Journal of the Korea Contents Association
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• v.20 no.10
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• pp.395-400
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• 2020

Between October 2019 and January 2020, 120EA of a syringe that was equipped with a 3-way injection material and administered ^99mTc labeled compound among inpatients for SPECT examination at the Department of Nuclear Medicine at Daegu P Hospital. When using a plastic syringe, the average dosing rate according to the number of dilutions was ^99mTc-ECD the highest at 90.87±11.08, and ^99mTc-DMSA the lowest at 75.28±7.43. The average dose rate according to the number of dilutions was the highest at 93.58±7.96, and the lowest at ^99mTc-DMSA at 91.60±6.07. The independent sample t-test showed whether the difference between the ^99mTc-DMSA plastic syringe and the normjek syringe was statistically significant(p<0.01). The ^99mTc-DMSA used for radiopharmaceuticals is a radiopharmaceutical that is mainly used for pediatric patients, and it is considered that it is necessary to use a normjek syringe rather than a general plastic syringe because the precise dosage is important.

• Nuclear Engineering and Technology
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• v.55 no.10
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• pp.3913-3923
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• 2023

Todays, medium energy resolution detectors are preferably used in radioisotope identification devices(RID) in nuclear and radioactive material categorization. However, there is still a need to develop or enhance « automated identifiers » for the useful RID algorithms. To decide whether any material is SNM or NORM, a key parameter is the better energy resolution of the detector. Although masking, shielding and gain shift/stabilization and other affecting parameters on site are also important for successful operations, the suitability of the RID algorithm is also a critical point to enhance the identification reliability while extracting the features from the spectral analysis. In this study, a RID algorithm based on Bayesian statistical method has been modified for medium energy resolution detectors and applied to the uranium gamma-ray spectra taken by a LaBr3:Ce detector. The present Bayesian RID algorithm covers up to 2000 keV energy range. It uses the peak centroids, the peak areas from the measured gamma-ray spectra. The extraction features are derived from the peak-based Bayesian classifiers to estimate a posterior probability for each isotope in the ANSI library. The program operations were tested under a MATLAB platform. The present peak based Bayesian RID algorithm was validated by using single isotopes(²⁴¹Am, ⁵⁷Co, ¹³⁷Cs, ⁵⁴Mn, ⁶⁰Co), and then applied to five standard nuclear materials(0.32-4.51% at.²³⁵U), as well as natural U- and Th-ores. The ID performance of the RID algorithm was quantified in terms of F-score for each isotope. The posterior probability is calculated to be 54.5-74.4% for ²³⁸U and 4.7-10.5% for ²³⁵U in EC-NRM171 uranium materials. For the case of the more complex gamma-ray spectra from CRMs, the total scoring (ST) method was preferred for its ID performance evaluation. It was shown that the present peak based Bayesian RID algorithm can be applied to identify ²³⁵U and ²³⁸U isotopes in LEU or natural U-Th samples if a medium energy resolution detector is was in the measurements.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.161-173
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• 2013

This paper is concerned with the space $\mathcal{K}_{w^*}(X^*,Y)$ of $weak^*$ to weak continuous compact operators from the dual space $X^*$ of a Banach space X to a Banach space Y. We show that if $X^*$ or $Y^*$ has the Radon-Nikod$\acute{y}$m property, $\mathcal{C}$ is a convex subset of $\mathcal{K}_{w^*}(X^*,Y)$ with $0{\in}\mathcal{C}$ and T is a bounded linear operator from $X^*$ into Y, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\{S{\in}\mathcal{C}:{\parallel}S{\parallel}{\leq}{\parallel}T{\parallel}\}}^{{\tau}_{\mathcal{c}}}$, where ${\tau}_{\mathcal{c}}$ is the topology of uniform convergence on each compact subset of X, moreover, if $T{\in}\mathcal{K}_{w^*}(X^*, Y)$, here $\mathcal{C}$ need not to contain 0, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\mathcal{C}}$ in the topology of the operator norm. Some properties of $\mathcal{K}_{w^*}(X^*,Y)$ are presented.