• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.55-69
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• 2024

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} && p\;\text{is even} \\ {\frac{p-1}{2}} && p\;\text{is odd,}}$$ and M = {±1, ±2, … ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{s}}_{{\lambda}_1}-\bar{\mathbb{s}}_{{\lambda}^c_1}{\mid}\,{\leq}\,1$ where $\bar{\mathbb{s}}_{{\lambda}_1}$ and $\bar{\mathbb{s}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of some union of graphs.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.36D no.4
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• pp.48-56
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• 1999

In this paper, we have investigated experimentally the effects of initial oxygen concentration on oxygen pileup phenomenon and the diffusion of implanted impurities. 1.2 MeV $^{11}B^{+}$ and 2.2 MeV $^{31}P^{+}$ ions were implanted into p-type (100) Si wafers with a dose of 1${\times}10^{15}$ / $\textrm{cm}^2$. Secondary ion mass spectrometry(SIMS) measurements were carried out to obtain depth distribution profiles for implanted impurities and oxygen atoms after two-step annealing of $700^{\circ}C$(20 hours)+$1000^{\circ}C$(10 hours). Residual secondary defect distribution and annealing behabiour were also studied by cross-sectional transmission electron microscopy(TEM) observations. Oxygen pileup nearly $R_p$(projected range) were observed by SIMS measurements and considerable amount of residual secondary defect layer were observed by TEM observations. It can be seen that oxygen atoms are trapped at the secondary defects by the experimental results. Enhanced diffusions of boron and phosphorus to the bulk direction were observed with the increasing of initial oxygen concentration.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.201-215
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• 2016

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Kirchhoff-type equations $\[a+b\({\int}_{{\mathbb{R}}^N}({\mid}{\nabla}u{\mid}^2+V(x){\mid}u{\mid}^2)dx\)\][-{\Delta}u+V(x)u]=f(x,u)$, in ${\mathbb{R}}^N$. Under certain assumptions on V and f, some new criteria on the existence and multiplicity of nontrivial solutions are established by the Morse theory with local linking and the genus properties in critical point theory. Some results from the previously literature are significantly extended and complemented.

• Journal of the Korean earth science society
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• v.34 no.5
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• pp.415-427
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• 2013

We performed a BVR photometric survey for the entire Small Magellanic Cloud (~26 deg 2 ) with a mosaic system, Wide Field Imager (WFI), covering three seasons: September and October 2001 and November 2002. Through the usual data reduction procedures, we present ~0.73 million catalogue stars brighter than 19 magnitude in B amongst a total of ~1.3 million and compare them with published astrometry and photometry results. We found that the average differences between our and the published data are ~0.7 arcsec in astrometry and 0.065, 0.054, and 0.163 in B, V, and R, respectively, in photometry. In addition, using the 2dF spectroscopic data from Evans et al. (2004), we determined the color excesses in (B-V) and (V-R) to be $0.086{\pm}0.156$, and $0.065{\pm}0.112$, respectively, while for the distance modulus, we obtained $18.55{\pm}1.05$.

• Journal of the Korean Vacuum Society
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• v.22 no.6
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• pp.327-334
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• 2013

Long-wave infrared detectors using the type-II InAs/GaSb strained superlattice (T2SL) material system with the nBn structure were designed and fabricated. The band gap energy of the T2SL material was calculated as a function of the thickness of the InAs and GaSb layers by the Kronig-Penney model. Growth of the barrier material ($Al_{0.2}Ga_{0.8}Sb$) incorporated Te doping to reduce the dark current. The full width at half maximum (FWHM) of the $1^{st}$ satellite superlattice peak from the X-ray diffraction was around 45 arcsec. The cutoff wavelength of the fabricated device was ${\sim}10.2{\mu}m$ (0.12 eV) at 80 K while under an applied bias of -1.4 V. The measured activation energy of the device was ~0.128 eV. The dark current density was shown to be $1.0{\times}10^{-2}A/cm^2$ at 80 K and with a bias -1.5 V. The responsivity was 0.58 A/W at $7.5{\mu}m$ at 80 K and with a bias of -1.5 V.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.273-280
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• 2024

Let I be an ideal of a commutative Noetherian semi-local ring R and M be an R-module. It is shown that if dim M ≤ 2 and Supp_R M ⊆ V (I), then M is I-weakly cofinite if (and only if) the R-modules Hom_R(R/I, M) and Ext¹_R(R/I, M) are weakly Laskerian. As a consequence of this result, it is shown that the category of all I-weakly cofinite modules X with dim X ≤ 2, forms an Abelian subcategory of the category of all R-modules. Finally, it is shown that if dim R/I ≤ 2, then for each pair of finitely generated R-modules M and N and each pair of the integers i, j ≥ 0, the R-modules Tor^R_i(N, H^j_I(M)) and Extⁱ_R(N, H^j_I(M)) are I-weakly cofinite.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.85-97
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• 2022

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}\;=\;\{\array{{\frac{p}{2}}&p\text{ is even}\\{\frac{p-1}{2}}\;&p\text{ is odd,}}$$ and M = {±1, ±2, ⋯ ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{S}}_{{\lambda}_1}-\bar{\mathbb{S}}_{{\lambda}^c_1}{\mid}{\leq}1$ where $\bar{\mathbb{S}}_{{\lambda}_1}$ and $\bar{\mathbb{S}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling of graphs which are obtained from path and cycle.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.237-253
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• 2023

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} & \;\;p\text{ is even} \\ {\frac{p-1}{2}} & \;\;p\text{ is odd,}$$ and M = {±1, ±2, … ± ρ} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling ${\frac{{\lambda}(u)+{\lambda}(v)}{2}}$ if λ(u) + λ(v) is even and ${\frac{{\lambda}(u)+{\lambda}(v)+1}{2}}$ if λ(u) + λ(v) is odd such that ${\mid}{\bar{{\mathbb{S}}}}_{\lambda}{_1}-{\bar{{\mathbb{S}}}}_{{\lambda}^c_1}{\mid}{\leq}1$ where ${\bar{{\mathbb{S}}}}_{\lambda}{_1}$ and ${\bar{{\mathbb{S}}}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of few graphs including the closed helm graph, web graph, jewel graph, sunflower graph, flower graph, tadpole graph, dumbbell graph, umbrella graph, butterfly graph, jelly fish, triangular book graph, quadrilateral book graph.

• Korean Journal of Plant Resources
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• v.18 no.1
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• pp.22-31
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• 2005

To evaluate growth adaptation of the soybean in paddy field, five soybean cultivars were grown in Yeoncheon with two cultivating methods, level row and high ridge. Growth characters of the top plants, such as stem lengths, numbers of branches, diameters of stem, were higher under high ridge than under level row. However, the differences among the cultivars were bigger than those between the cultivation methods in each cultivar. Comparing the growth of top plants, dry matters in level row were higher than those in high ridge in V5 stage, however, via verses as growth progressed with significant differences among the cultivars. Roots were more developed under high ridge than those under level row during whole growth stages, such as V5, R2, and R5 stages. T/R ratio in level row was significantly higher than that in high ridge with significant differences among the cultivars.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.235-251
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• 2021

We consider the Schrödinger type operator ��k = (-∆)k+Vk on ℝn(n ≥ 2k + 1), where k = 1, 2 and the nonnegative potential V belongs to the reverse Hölder class RHs with n/2 < s < n. In this paper, we establish the (Lp, Lq)-boundedness of the higher order Riesz transform T��,�� = V2��∇2��-��2 (0 ≤ �� ≤ 1/2 < �� ≤ 1, �� - �� ≥ 1/2) and its adjoint operator T∗��,�� respectively. We show that T��,�� is bounded from Hardy type space $H^1_{\mathcal{L}_2}({\mathbb{R}}_n)$ into Lp2 (ℝn) and T∗��,�� is bounded from ��p1 (ℝn) into BMO type space $BMO_{\mathcal{L}_1}$ (ℝn) when �� - �� > 1/2, where $p_1={\frac{n}{4({\beta}-{\alpha})-2}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})+2}}$. Moreover, we prove that T��,�� is bounded from $BMO_{\mathcal{L}_1}({\mathbb{R}}_n)$ to itself when �� - �� = 1/2.