• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.423-435
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• 2014

In this paper, the fractional Hardy-type operator of variable order ${\beta}(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)$ with variable exponent $q_1(x)$ into the weighted space $M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})$, where ${\omega}=(1+|x|)^{-{\gamma}(x)}$ with some ${\gamma}(x)$ > 0 and $1/q_1(x)-1/q_2(x)={\beta}(x)/n$ when $q_1(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_1(x)$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.387-398
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• 2016

Let X be a vector space over a field K of real or complex numbers and $k{\in}{\mathbb{N}}$. We prove the superstability of the following generalized Golab-Schinzel type equation $f(x_1+{\limits\sum_{i=2}^p}x_if(x_1)^kf(x_2)^k{\cdots}f(x_{i-1})^k)={\limits\prod_{i=1}^pf(x_i),x_1,x_2,{\cdots},x_p{\in}X$, where $f:X{\rightarrow}K$ is an unknown function which is hemicontinuous at the origin.

• Journal of Korean Academy of Nursing
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• v.31 no.6
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• pp.1119-1128
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• 2001

This study was designed to identify degrees of self-esteem, health status, and life satisfaction in elderly women and investigate the relationship between these factors. The results will contribute to effective nursing intervention for promoting the quality of life for elderly women. Method: The subjects of this study included 129 elderly women. The data was collected through personal interviews using questionnaires from Nov. to Dec. of 2000. The measurement tools were the self-esteem scale developed by Rosenberg and translated by Byong-Je Jong (1974), the health status scale developed by Young Ja Lee(1989), and the life satisfaction scale developed by Jin Youn(1982). The data was analyzed by the SPSS computer program, and it included descriptive statistics, x2-test, t-test and the pearson correlation coefficient. Result: The conclusions of this study are summarized as follows: 1. There was a significant difference in age (x2=12.952, p=.000), religion (x2=6.140, p=.000), spending money (x2=.7.511, p= .000), living expenses load (x2=16.189, p= .000), and the major support provider (x2=6.539, p=.000), according to general characteristics in the existence elderly women. 2. There was a significant difference in self-esteem (t=7.05, P=.000), Health status (t=-10.09, P=.000), and life satisfaction (t=6.62, P=.000) between the two groups. 3. There was a significant positive correlation between self-esteem and health status (r=.406, P=.000), self-esteem and life satisfaction (r=.524, P=.000), and health status and life satisfaction (r=.504, P= .0000) in elderly women.

• Asian-Australasian Journal of Animal Sciences
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• v.15 no.9
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• pp.1263-1266
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• 2002

The objective of this study was to evaluate the effects of some production factors on commercial production of Etawah Crossbred Goats (ECG) of Inpres Desa Tertinggal member groups (AKIDT) at Krasak, Pandansari, Brajan, and Kragilan villages in Boyolali regency, Central Java, Indonesia. The study was from February to April 2000. Eighty respondents of AKIDT were selected by simple random sampling and the data were analyzed using Cobb Douglas Production Function. The results showed that ECG production simultaneously were highly significant (p<0.01) influenced by amount of feed consumed (kg TDN/year, $x_1$), number of does of ECG (Animal Unit/year, $x_2$), number of kids and does/ barn/year (Animal Unit/year, $x_3$), labor use (man-days/year, $x_4$) and work capital (US$/year, $x_5$) with $R^2= 0.6568$. In addition, ECG production was partially influenced by $x_2$, $x_3$ and $x_5$ (p<0.01) and $x_1$ (p<0.05), but not significant (p>0.05) by $x_4$. Technically, production factors of $x_1$, $x_2$, $x_3$, $x_4$, $x_5$ had reached technique efficiency (0$x_1$, $x_3$, $x_4$, $x_5$ did not showed efficiency (Ep<1) and $x_2$ was not efficient yet.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.187-213
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• 2009

For a positive integer k and an arbitrary integer h, the classical Dedekind sums s(h,k) is defined by $$S(h,\;k)=\sum\limits_{j=1}^k\(\(\frac{j}{k}\)\)\(\(\frac{hj}{k}\)\),$$ where $$((x))=\{{x-[x]-\frac{1}{2},\;if\;x\;is\;not\;an\;integer; \atop \;0,\;\;\;\;\;\;\;\;\;\;if\;x\;is\;an\;integer.}\$$ J. B. Conrey et al proved that $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^{2m}(h,\;k)=fm(k)\;\(\frac{k}{12}\)^{2m}+O\(\(k^{\frac{9}{5}}+k^{{2m-1}+\frac{1}{m+1}}\)\;\log^3k\).$$ For $m\;{\geq}\;2$, C. Jia reduced the error terms to $O(k^{2m-1})$. While for m = 1, W. Zhang showed $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^2(h,\;k)=\frac{5}{144}k{\phi}(k)\prod_{p^{\alpha}{\parallel}k}\[\frac{\(1+\frac{1}{p}\)^2-\frac{1}{p^{3\alpha+1}}}{1+\frac{1}{p}+\frac{1}{p^2}}\]\;+\;O\(k\;{\exp}\;\(\frac{4{\log}k}{\log\log{k}}\)\).$$. In this paper we give some formulae on the mean value of the Dedekind sums and and Hardy sums, and generalize the above results.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1169-1182
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• 2011

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $$-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2$$ in an unbounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, with sufficiently smooth bounded boundary ${\partial}{\Omega}$, where $h(x){\in}L_{loc}^1(\overline{\Omega})$, $\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}$, $h(x){\geq}1$ for all $x{\in}{\Omega}$. The proof of main results rely essentially on the arguments of variational method.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.81-93
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• 2020

Let m ∈ ℕ₀, p > 1 and $${\alpha}^{[m,p]}(x)\;:\;{\sqrt{x}},\;\{{\sqrt{\frac{(m+n-1)p-(m+n-2)}{(m+n)p-(m+n-1)}}}\}^{\infty}_{n=1}$$. In this paper, we consider the backward extensions of Bergman-type weighted shift W_α^[m,p](x). We consider its subnormality, k-hyponormality and positive quadratic hyponormality. Our results include all the results on Bergman weighted shift W_α(x) with m ∈ ℕ and $${\alpha}(x)\;:\;{\sqrt{x}},\;{\sqrt{\frac{m}{m+1}},\;{\sqrt{\frac{m}{m+2}},\;{\sqrt{\frac{m+2}{m+3}},{\cdots}$$.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.349-361
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• 2022

In this paper, we study the following nonlinear problem: $$\{-\Delta_{p}^{3}(x)u\;=\;{\lambda}V_{1}(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u\;=\;{\Delta}u\;{\Delta}^{2}u\;=\;0\;on\;{\partial}\Omega, $$ under adequate conditions on the exponent functions p, q and the weight function V₁. We prove the existence and nonexistence of eigenvalues for p(x)-triharmonic problem with Navier boundary value conditions on a bounded domain in ℝ^N. Our technique is based on variational approaches and the theory of variable exponent Lebesgue spaces.

• Korean Journal of Environmental Biology
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• v.17 no.1
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• pp.27-34
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• 1999

In order to obtain necessary data for the use of hydrophytes to improve water quality of artificial lakes, production and nutrients absorption by some macrohydrophytes were investigated in a small water course at Woongcheon, Chungnam Province. The maximum above-ground standing biomass of Phragmites communis, Typha angustifolia and Zizania latifolia stand were 3,504 g/m$x^2$, 2,834 g/m$x^2$ and 3,125 g/m$x^2$, respectively. Estimated below-ground standing biomass of each stand were 9,671 g/m$x^2$,5,158 g/m$x^2$ and 5,813 g/m$x^2$, respectively. Concentration of nutrients in each organ was different among plant species. Maximum amount of standing nitrogen was the highest in the reed stand and that of standing phosphorus was the highest in the cattail stand. Amount of maximum standing nutrients are 2795.6 kgN/ha and 42.5 kgP/ha for the reed stand, 1,413 kg N/ha and 24.8 kgP/ha for the cattail stand and 1.901.1 kgN/ha and 38.4 kgP/ha for the wild rice stand, respectively. According to our investigation, it is concluded that reed, cattail and wild rice are suitable for water quality improvement of artificial lakes through nutrients absorption.

• Kyungpook Mathematical Journal
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• v.33 no.1
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• pp.61-67
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• 1993