• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1143-1156
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• 2010

In this paper, we study the following p&q-Laplacian problem with critical Sobolev and Hardy exponents {$-{\Delta}_pu-{\Delta}_qu={\mu}\frac{{\mid}u{\mid}^{p^*(s)-2}u}{{\mid}x{\mid}^s}+{\lambda}f(x,\;u)$, in $\Omega$, u=0, on $\Omega$, where ${\Omega}\;{\subset}\;\mathbb{R}^{\mathbb{N}}$ is a bounded domain and ${\Delta}_ru=div({\mid}{\nabla}u{\mid}^{r-2}{\nabla}u)$ is the r-Laplacian of u. By using the variational method and concentration-compactness principle, we obtain the existence of infinitely many small solutions for above problem which are the complement of previously known results.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.653-659
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• 2003

Let $1{\;}\leq{\;}p{\;}\infty{\;}and{\;}{\alpha}{\;}>{\;}-1$. If f is a holomorphic self-map of the open unit disc U of C with f(0) = 0, then the quantity $\int_U\;\{\frac{$\mid$f'(z)$\mid$}{1\;-\;$\mid$f(z)$\mid$^2}\}^p\;(1\;-\;$\mid$z$\mid$)^{\alpha+p}dxdy$ is equivalent to the operator norm of the composition operator $C_f{\;}:{\;}B{\;}\rightarrow{\;}A^{p,{\alpha}$ defined by $C_fh{\;}={\;}h{\;}\circ{\;}f{\;}-{\;}h(0)$, where B and $A^{p,{\alpha}$ are the Bloch space and the weighted Bergman space on U respectively.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.247-256
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• 2021

Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent: $$(\mathcal{P}_{\lambda})\;\{\begin{array}{lll}{\Delta}^2u-(a{\int}_{\Omega}{\mid}{\nabla}u{\mid}^2dx+b){\Delta}u+cu=f(x){\mid}u{\mid}^{-{\gamma}}-{\lambda}{\mid}u{\mid}^{p-2}u&&\text{ in }{\Omega},\\{\Delta}u=u=0&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω is a smooth bounded domain of ℝⁿ (n ≥ 5), ∆² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0 < γ < 1, λ > 0, 0 < p ≤ 2^# and a, b, c are three positive constants with a + b > 0 and f belongs to a given Lebesgue space.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.757-780
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• 2022

In this article, we study the weak and extra-weak type integral inequalities for the modified integral Hardy operators. We provide suitable conditions on the weights ω, ρ, φ and ψ to hold the following weak type modular inequality $${\mathcal{U}}^{-1}\({\int_{{\mid}{\mathcal{I}}f{\mid}>{\gamma}}}\;{\mathcal{U}}({\gamma}{\omega}){\rho}\){\leq}{\mathcal{V}}^{-1}\({\int}_{0}^{\infty}{\mathcal{V}}(C{\mid}f{\mid}{\phi}){\psi}\),$$ where ${\mathcal{I}}$ is the modified integral Hardy operators. We also obtain a necesary and sufficient condition for the following extra-weak type integral inequality $${\omega}\(\{{\left|{\mathcal{I}}f\right|}>{\gamma}\}\){\leq}{\mathcal{U}}{\circ}{\mathcal{V}}^{-1}\({\int}_{0}^{\infty}{\mathcal{V}}\(\frac{C{\mid}f{\mid}{\phi}}{{\gamma}}\){\psi}\).$$ Further, we discuss the above two inequalities for the conjugate of the modified integral Hardy operators. It will extend the existing results for the Hardy operator and its integral version.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.68.4-68.4
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• 2019

In this poster, we present a relation between the Galactic foregrounds and Galactic latitude to study the structure of the Galactic foregrounds. We propose that the standard deviation of observed values along a line of sight with Galactic latitude b ('σ_l.o.s') is inversely proportional to ${\sqrt{sin{\mid}b{\mid}}}$. To confirm this, we use synchrotron intensity data from the Planck archive and rotation measure (RM) data from the NVSS. We divided the sphere of the Galactic coordinate into bins with a constant surface area and calculated the average of standard deviation along Galactic latitude ('σ_lat'). We compared σ_lat ${\sqrt{sin{\mid}b{\mid}}}$ with σ_lat along Galactic latitude and found that σ_lat ${\sqrt{sin{\mid}b{\mid}}}$ is the most constant. These results support that the relation is reasonable.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2013.05a
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• pp.479-480
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• 2013

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.14 no.9
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• pp.43-51
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• 1996

• Journal of Families and Better Life
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• v.9 no.1 s.17
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• pp.65-80
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• 1991

The purpose of this study is to search a tendency of adjustment of mid-life women and to identify the variables that influence the adjustment of mid-life women. For this purpose, attitudes toward the menopause(ATM) scale, Korean Sex-Role Inventory(KSRI) scale, General Well-Being(GWB) scale, and Center for Epidemiological Studies Depression(CESD) scale were developed. The sample was selected from the 331 women living in Seoul, whose age was from 40-59, and whose last child was older than 13 years of age. The main results were as follows : 1) The level of well-being that the mid-life women was average and the level of depression was above average. 2) the attitudes of the mid-life women about menopause were a litte negative in both physical and psychological sides. 3) As for the related variables, frequency of leasure activies was significant to the well-being level of the mid-life women. And age, Socio-Economic Status(SES), status of last child have a significant influence on the depression level of them. 4) The attitudes toward menopause had insignificant influence on their adjustment and menopause status was irrelevant to it. 5) In the case that the mid-life women have high sex-role identity, that they have androgyny or masculinity, they appeared well adjusted. 6) In the result of mulitiple regressing analysis, the influence that the variables had on the mid-life women's well-being will be presented as fallows in order of importance: Sex-role identity, frequency of leasure activies and age. Above 3 variables explain 24% of adjustment of mid-life.

• Journal of the Korean Ceramic Society
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• v.32 no.11
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• pp.1292-1300
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• 1995

The ionic conductivity of NASICON solid electrolytes was simulated by using Monte Carlo Method (MCM). There were included two conduction paths: (1) Na1-Na2 and (2) Na1-Na2 including Na2-Na2. We assumed that mid-Na ions provde an additional driving force for Na mobile ions due to the interionic repulsion between Na1 and Na2 ions. The inflection point of vacancy availability factor, V has been shown at nearby x=2, the maximum mid-Na ions. The inflection point of vacancy availability factor, V has been shown at nearby x=2, the maximum mid-Na sites are occupied. The effective jump frequency factor, V has been shown at nearby x=2, the maximum mid-Na sites are occupied. The effective jump frequency factor, W increased rapidly with the composition at low temperature, but decreased at high temperature region. On Na1-Na2 conduction path, the minimum of charge correlation factor, fc and the maximum of $\sigma$T were appeared at x=2.0. this indicated that mid-Na ions affect on the high ionic conductivity behavior. At the whole range of NASICON composition, 1n $\sigma$T vs. 1/T* plots have been shown Arrhenius behavior but 1n (VWFc) vs. 1/T* have been shown the Arrhenius type tendency at x=2, which mid-Na is being the maximum. The results of MCM agreed with the experimental one when the chosen saddle point value was 6$\varepsilon$ : 3$\varepsilon$. Here the calculated characteristic parameter of materials, K and the phase transition temperature were -4.001$\times$103 and 178$^{\circ}C$ (1/T*=1.92, 1000/T=2.22), respectively.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1133-1143
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• 1999

Chaterji strengthened version of a theorem for martin-gales which is a generalization of a theorem of Marcinkiewicz proving that if $X_n$ is a sequence of independent, identically distributed random variables with $E{\mid}X_n{\mid}^p\;<\;{\infty}$, 0 < P < 2 and $EX_1\;=\;1{\leq}\;p\;<\;2$ then $n^{-1/p}{\sum^n}_{i=1}X_i\;\rightarrow\;0$ a,s, and in $L^p$. In this paper, we probe a version of law of large numbers for double arrays. If ${X_{ij}}$ is a double sequence of random variables with $E{\mid}X_{11}\mid^log^+\mid X_{11}\mid^p\;<\infty$, 0 < P <2, then $lim_{m{\vee}n{\rightarrow}\infty}\frac{{\sum^m}_{i=1}{\sum^n}_{j=1}(X_{ij-a_{ij}}}{(mn)^\frac{1}{p}}\;=0$ a.s. and in $L^p$, where $a_{ij}$ = 0 if 0 < p < 1, and $a_{ij}\;=\;E[X_{ij}\midF_[ij}]$ if $1{\leq}p{\leq}2$, which is a generalization of Etemadi's marcinkiewicz-type SLLN for double arrays. this also generalize earlier results of Smythe, and Gut for double arrays of i.i.d. r.v's.