• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.327-329
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• 1994

The Dirichlet problem (DP) on the upper half plane {z = x ＋ iy : y > 0} is to find a real-valued harmonic function u(x, y) satisfying u(x, 0) = g(x) almost everywhere for some reasonably nice function g defined on the real line, which is called the data on the boundary for (DP).(omitted)

• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.265-269
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• 2012

In this paper, we prove the following theorem which gives a characterization of $M_1$-spaces by g-function.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.277-287
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• 2007

We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends($1) in which every bounded energy finite p-harmonic function is asymptotically constant for almost every path, then the set $\mathcal{HBD}_p(G)$ of all bounded energy finite p-harmonic functions on G is in one to one corresponding to $\mathbf{R}^l$, where $l$ is the number of p-hyperbolic ends of G. Furthermore, we prove that if a graph G' is roughly isometric to G, then $\mathcal{HBD}_p(G')$ is also in an one to one correspondence with $\mathbf{R}^l$.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.39-49
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• 2010

This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, $\infty$) with the boundary conditions $$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$ where $g\;{\in}\;L^1[0,{\infty})$ with g(t) > 0 on [0, $\infty$) and ${\int}^{\infty}_0g(s)ds\;=\;1$, f is a g-Carath$\acute{e}$odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.31-48
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• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.105-120
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• 2021

In this paper, we extend some results related to the growth rates of entire functions by introducing the relative logarithmic order ����g(f) of a nonconstant entire function f with respect to another nonconstant entire function g. Next we investigate some theorems related the behavior of ����g(f). We also define the relative logarithmic proximate order of f with respect to g and give some theorems on it.

• Bulletin of the Korean Chemical Society
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• v.27 no.7
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• pp.1048-1052
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• 2006

Ab initio calculations of the structure, atomic charges and natural bond orbital (NBO) have been performed at HF/6-311G** and B3LYP/6-311G** levels for the title compound of dibenzothiazyl-disulfide. The calculated results show that the two nitrogen atoms have the biggest negative charges and they are the potential sites to react with the metallic ions, which make the title compound become a di-dentate ligand. Vibrational frequencies of the title compound have been obtained and compared with the experimental value and the comparison indicates that B3LYP/6-311G** level is better than HF/6-311G** level to predict the vibrational frequencies for the system studied here. For the title compound, electronic absorption spectra calculated by time?ependent density functional theory (TD-DFT) are more accurate than Hartree-Focksingle-excitation CI (CI-Singles) method. NBO analyses show that the electronic transitions are mainly derived from the contribution of bands $\pi\rightarrow\pi^{*}$. Thermodynamic calculated results show that the formation of the title compound from 2-mercaptobenzothiazole is a spontaneous process at room temperature with the change of free Gibbs being negative value.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.375-379
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• 2012

We find a general solution $f:G{\rightarrow}G$ of the symmetric functional equation $$x+f(y+f(x))=y+f(x+f(y)),\;f(0)=0$$ where G is a 2-divisible abelian group. We also prove that there exists no measurable solution $f:\mathbb{R}{\rightarrow}\mathbb{R}$ of the equation. We also find the continuous solutions $f:\mathbb{C}{\rightarrow}\mathbb{C}$ of the equation.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.525-539
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• 2007

Consider the regression model $Y_i=g(x_i)+e_i\;for\;i=1,\;2,\;{\ldots},\;n$, where: (1) $x_i$ are fixed design points, (2) $e_i$ are independent random errors with mean zero, (3) g($\cdot$) is unknown regression function defined on [0, 1]. Under $Y_i$ are censored randomly, we discuss the asymptotic normality of the weighted kernel estimators of g when the censored distribution function is known or unknown.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.31-34
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• 1995

Let R$^n$be n-th Euclidean space. Let be the n-th spere embeded as a subspace in R$\^$n+1/ centered at the origin. In this paper, we are going to consider the function space F = {f│f : S$^n$\longrightarrow S$^n$} metrized by as follow D(f,g)=d(f($\chi$), g($\chi$)) where f, g $\in$ F and d is the metric in S$^n$. Finally we want to find certain relation these spaces.(omitted)