• Honam Mathematical Journal
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• v.44 no.1
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• pp.135-145
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• 2022

This paper aims to investigate characterizations on parameters k₁, k₂, k₃, k₄, k₅, l₁, l₂, l₃, and l₄ to find relation between the class of 𝓗(k, l, m, n, o) hypergeometric functions defined by $$5_F_4\[{\array{k_1,\;k_2,\;k_3,\;k_4,\;k_5\\l_1,\;l_2,\;l_3,\;l_4}}\;:\;z\]=\sum\limits_{n=2}^{\infty}\frac{(k_1)_n(k_2)_n(k_3)_n(k_4)_n(k_5)_n}{(l_1)_n(l_2)_n(l_3)_n(l_4)_n(1)_n}z^n$$. We need to find k, l, m and n that lead to the necessary and sufficient condition for the function zF([W]), G = z(2 - F([W])) and $H_1[W]=z^2{\frac{d}{dz}}(ln(z)-h(z))$ to be in 𝓢^*(2^-r), r is a positive integer in the open unit disc 𝒟 = {z : |z| < 1, z ∈ ℂ} with $$h(z)=\sum\limits_{n=0}^{\infty}\frac{(k)_n(l)_n(m)_n(n)_n(1+\frac{k}{2})_n}{(\frac{k}{2})_n(1+k-l)_n(1+k-m)_n(1+k-n)_nn(1)_n}z^n$$ and $$[W]=\[{\array{k,\;1+{\frac{k}{2}},\;l,\;m,\;n\\{\frac{k}{2}},\;1+k-l,\;1+k-m,\;1+k-n}}\;:\;z\]$$.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.71.1-71.1
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• 2012

We have identified local analogs of strong $H{\alpha}$ Emitters (HAEs) that dominate the z~4 Lyman-break galaxy population using the Sloan Digital Sky Survey (SDSS). At z<0.4, only 0.04% of galaxies are classified as HAEs with $H{\alpha}$ equivalent width larger than $500{\AA}$, comparable to that of z~4 HAEs. The $H{\alpha}$-to-UV luminosity ratio of local HAEs is consistent with that of z~4 HAEs, indicating relatively large specific star formation rate in these galaxies compared to traditionally studied UV-selected Lyman break analogs. Local HAEs are young, less evolved galaxies with low metallicity. It is still difficult to constrain whether the star formation in local HAEs is powered by minor mergers or by cosmological cold gas accretion. However, the stacked optical spectrum of local HAEs shows several strong ionization lines, for example HeII 4686 emission line, which are shown in Wolf-Rayet galaxies. Thus it is highly likely that local HAEs are galaxies with an elevated ionization parameter, either due to a high electron density or large escape fraction of hydrogen ionizing photons.

• Transactions of the Korean hydrogen and new energy society
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• v.18 no.3
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• pp.325-333
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• 2007

[ $LiNi_{0.995}Al_{0.005}O_2$ ], $LiNi_{0.990}Ti_{0.010}O_2$ and $LiNi_{0.0990}Al_{0.005}Ti_{0.005}O_2$ were synthesized with a combustion method by calcining in an $O_2$ stream at $750^{\circ}C$ for 36 h. The X-ray diffraction patterns of these synthesized samples showed $-NaFeO_2$ structure of rhombohedral system(space group; $R{\bar{3}}\;m$) with no evidence of impurities. Among these samples, $LiNi_{0.995}Al_{0.005}O_2$ exhibited comparatively high first discharge capacity and discharge capacity, and the best cycling performance. $LiNi_{0.995}Al_{0.005}O_2$ had the first discharge capacity of 165.2 mA h/g and a discharge capacity of 116.7 mA h/g at the 50th cycle at 0.1C rate. It showed the first discharge capacity of 141.0 mA h/g and a discharge capacity of 93.5 mA h/g at the 50th cycle at 0.5C rate.

• Progress in Superconductivity
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• v.6 no.1
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• pp.37-40
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• 2004

We investigated the effects of impurity doping on the electrical transport and magnetic properties of TEX>$(Ru, Sn)(Sr, La)<_2$$EuCeCu_2$$O_{z}$ samples. We found that Sn substitution fur Ru causes a significant decrease of the volume fraction of ferromagnetic phase, as well as a decrease of the temperature where the ferromagnetic component is observed. La substitution for Sr leads to an increase of the magnetic ordering temperature with a moderate change of ferromagnetic component. The experimental results are discussed in conjunction with the structural data, transport properties and a possible change of oxygen content.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1025-1039
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• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.839-850
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• 2020

For functions f(z) = z + a₂z² + a₃z³ + ⋯ belonging to particular classes, this paper finds sharp bounds for the initial coefficients a₂, a₃, a₄, as well as the sharp estimate for the second order Hankel determinant H₂(2) = a₂a₄ - a₂³. Two classes are treated: first is the class consisting of f(z) = z + a₂z² + a₃z³ + ⋯ in the unit disk 𝔻 satisfying $$\|\(\frac{z}{f(z)}\)^{1+{\alpha}}\;f^{\prime}(z)-1\|<{\lambda},\;0<{\alpha}<1,\;0<{\lambda}{\leq}1.$$ The second class consists of Bazilevič functions f(z) = z+a₂z²+a₃z³+⋯ in 𝔻 satisfying $$Re\{\(\frac{f(z)}{z}\)^{{\alpha}-1}\;f^{\prime}(z)\}>0,\;{\alpha}>0.$$

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1461-1484
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• 2021

We deal with the following elliptic equations: $\{-div({\varphi}^{\prime}(\left|{\nabla}z\right|^2){\nabla}z)+V(x)\left|z\right|^{{\alpha}-2}z={\lambda}{\rho}(x)\left|z\right|^{r-2}z+h(x,z),\\z(x){\rightarrow}0,\;as\;\left|x\right|{\rightarrow}{\infty},$ in ℝ^N , where N ≥ 2, 1 < p < q < N, 1 < α ≤ p^*q'/p', α < q, 1 < r < min{p, α}, φ(t) behaves like t^q/2 for small t and t^p/2 for large t, and p' and q' the conjugate exponents of p and q, respectively. Here, V : ℝ^N → (0, ∞) is a potential function and h : ℝ^N × ℝ → ℝ is a Carathéodory function. The present paper is devoted to the existence of at least two distinct nontrivial solutions to quasilinear elliptic problems of Schrödinger type, which provides a concave-convex nature to the problem. The primary tools are the well-known mountain pass theorem and a variant of Ekeland's variational principle.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.579-591
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• 2006

In this paper we obtain a sufficient and necessary condition for an analytic function f on the unit ball B with Hadamard gaps, that is, for $f(z)\;=\;{\sum}^{\infty}_{k=1}\;P_{nk}(z)$ (the homogeneous polynomial expansion of f) satisfying $n_{k+1}/n_{k}{\ge}{\lambda}>1$ for all $k\;{\in}\;N$, to belong to the weighted Bergman space $$A^p_{\alpha}(B)\;=\;\{f{\mid}{\int}_{B}{\mid}f(z){\mid}^{p}(1-{\mid}z{\mid}^2)^{\alpha}dV(z) < {\infty},\;f{\in}H(B)\}$$. We find a growth estimate for the integral mean $$\({\int}_{{\partial}B}{\mid}f(r{\zeta}){\mid}^pd{\sigma}({\zeta})\)^{1/p}$$, and an estimate for the point evaluations in this class of functions. Similar results on the mixed norm space $H_{p,q,{\alpha}$(B) and weighted Bergman space on polydisc $A^p_{^{\to}_{\alpha}}(U^n)$ are also given.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.36.1-36.1
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• 2019

We present the observed relationship between Eddington ratio (${\lambda}Edd$) and optical narrow-emission-line ratio ([NII] ${\lambda}6583/H{\alpha}$) of X-ray-selected unobscured active galactic nuclei (AGN) at 0.6 < z < 1.7 using 27 near-infrared spectra from the Fiber Multi-Object Spectrograph mounted on the Subaru telescope along with 26 additional sources from the literature. We show that the ${\lambda}Edd$ and [NII] ${\lambda}6583/H{\alpha}$ ratio at 0.6 < z < 1.7 exhibits a similar distribution of ${\lambda}Edd$-[NII] ${\lambda}6583/H{\alpha}$ anti-correlation that has been found for local ( = 0.036), hard X-ray selected AGN. The observed anti-correlation suggests that [N II] ${\lambda}6583/H{\alpha}$ optical narrow-line ratio in the AGN host galaxy may carry important information about the accretion state of the central supermassive black hole, suggesting the observational hint of consistent relationship from local to z ~ 1.7. Further study is necessary to determine whether the ${\lambda}Edd$-[N II] ${\lambda}6583/H{\alpha}$ correlation in high-redshift still holds at ${\log}{\lambda}Edd$ < -2 compared to local AGN.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.819-835
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• 2018

Let $f=h+{\bar{g}}$ be a normalized harmonic mapping in the unit disk $\mathbb{D}$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D^{\epsilon}{_f}=zf_z-{\epsilon}{\bar{z}}f_{\bar{z}}({\mid}{\epsilon}{\mid}=1)$ and $F_{\lambda}(z)=(1-{\lambda)f+{\lambda}D^{\epsilon}{_f}(0{\leq}{\lambda}{\leq}1)$ when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function $f=h+{\bar{g}}$. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].