• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.315-327
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• 2022

In this paper, we investigate the transferred superstability for the p-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from the p-radical functional equations: $$f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)g(y),\;\\f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)h(y),$$ where p is an odd positive integer, λ is a positive real number, and f is a complex valued function. Furthermore, the results are extended to Banach algebras. Therefore, the obtained result will be forced to the pre-results(p=1) for this type's equations, and will serve as a sample to apply it to the extension of the other known equations.

• Publications of The Korean Astronomical Society
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• v.25 no.4
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• pp.113-118
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• 2010

The Henyey-Greenstein (H-G) phase function, which is characterized by a single parameter, has been generally used to approximate the realistic dust-scattering phase function in investigating scattering properties of the interstellar dust. Draine (2003) proposed a new analytic phase function with two parameters and showed that the realistic phase function is better represented by his phase function. If the H-G and Draine's phase functions are significantly different, using the H-G phase function in radiative transfer models may lead to wrong conclusions about the dust-scattering properties. Here, we investigate whether the H-G and Draine's phase functions would indeed produce significant differences in radiative transfer calculations for two simple configurations. For the uniformly distributed dust with an illuminating star at the center, no significant difference is found. However, up to ~ 20% of difference is found when the central star is surrounded by a spherical-shell dust medium and the radiation of $\lambda$ < $2000\;{\AA}$ is considered. It would mean that the investigation of dust-scattering properties using the H-G phase function may produce errors of up to ~ 20% depending on the geometry of dust medium and the radiation wavelength. This amount of uncertainty would be, however, unavoidable since the configurations of dust density and radiation sources are only approximately available.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.285-295
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• 2024

In this work, we consider the function $${\Psi}(z)=\frac{z}{\ln(1+z)}=1+\sum\limits_{n=1}^{\infty}\,G_nz^n$$ whose coefficients G_n are the Gregory coefficients related to Stirling numbers of the first kind and introduce a new subclass ${\mathcal{G}}^{{\lambda},{\mu}}_{\Sigma}(\Psi)$ of analytic bi-univalent functions subordinate to the function Ψ. For functions belong to this class, we investigate the estimates for the general Taylor-Maclaurin coefficients by using the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.3
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• pp.179-186
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• 1993

We derive the arbitrary time point system size distribution of M/ $G^{B}$1 queue in which late arrivals are not allowed to join the on-going service. The distribution is given by P(z) = $P_{4}$(z) $S^{*}$ (.lambda.-.lambda.z) where $P_{4}$ (z) is the probability generating function of the queue size and $S^{*}$(.theta.) is the Laplace-Stieltjes transform of the service time distribution function. We also derive the distribution of the service siez at arbitrary point of time. time.

• Korean Journal of Optics and Photonics
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• v.8 no.2
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• pp.111-115
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• 1997

Vertical-cavity surface-emitting laser(VCSEL)s operating at 1.3-micron wavelength for optical communication are fabricated by using Si/SiO$_2$dielectric quater-wave pairs on both sides of the InGaAsP(${\lambda}_g$=1.3 ${\mu}{\textrm}{m}$) gain material. VCSELs are optically pumped with a Nd-YAG laser in a pulsed mode and lasing around 1.3 microns is observed. Lasing characteristics such as threshold pump intensity as a function of mirror-reflectivity, polarization, and threshold pump density with pump spot size are investigated.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-69
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• 2023

Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝⁿ → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

• Journal of The Korean Astronomical Society
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• v.37 no.4
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• pp.269-272
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• 2004

We present the first results of a wide field survey for planetary nebulae throughout M31 undertaken at the KPNO 0.9m telescope with the Mosaic camera. So far, images in [O III]$\lambda$5007 and its continuum filter have been analyzed. Our survey appears to be at least $90\%$ complete to about 2 mag below the peak of the planetary nebula luminosity function. Over 900 planetary nebulae candidates have been found within a 12 square degree area.

• The KIPS Transactions:PartB
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• v.15B no.2
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• pp.131-136
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• 2008

L(2,1)-labeling of a graph G is a function f: V(G) $\rightarrow$ {0, 1, 2, ...} such that $|f(u)\;-\;f(\upsilon)|\;{\geq}\;2$ when d(u, v) = 1 and $|f(u)\;-\;f(\upsilon)|\;{\geq}\;1$ when d(u, $\upsilon$) = 2. L(2,1)-labeling number of G, denoted by ${\lambda}(G)$, is the smallest number m such that G has an L(2,1)-labeling with no label greater than m. Since this problem has been proved to be NP-complete, in this article, we develop genetic algorithms for L(2,1)-labeling problem and show that the suggested genetic algorithm peforms very efficiently by applying the algorithms to the class of graphs with known optimum values.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.597-610
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• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.