• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.209-219
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• 2021

A set {a₁, a₂, ⋯ , a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. Let F_n be the nth Fibonacci number which is defined by F₀ = 0, F₁ = 1 and F_n+2 = F_n+1 + F_n. In this paper, we find the extendibility of Diophantine pairs {F_2k, b} with some conditions.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.247-254
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation f(x + ky) - k²f(x + y) + 2(k² - 1)f(x) - k²f(x - y) + f(x - ky) - k²(k² - 1)(f(y) + f(-y)) = 0, where k is a fixed real number with |k| ≠ 0, 1.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.393-402
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• 2013

For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• 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.

• Journal of the Korean Ceramic Society
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• v.21 no.3
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• pp.231-238
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• 1984

Heavy metal fluoride glasses exhibit considerable promise as high transparency materials from the UV to the IR. These glasses are prepared by fusion of the mixture of metal fulorides($ZrF_4$, $BaF_2$, $LaF_3$ etc) at 800-1, 00$0^{\circ}C$ under the inert$(N_2)$ or reactive ($CCl_4$, $Cl_2$) atmosphere following the casting into glass on cooling. Infrared absorption at the 3, 400 cm-1 -OH peak has been measured as a function of thickness for several ZrF-$BaF_2$-LaF and $HfF_4$-$BaF_2$-$LaF_3$ glasses to separate contributions from bulk and surface -OH. For glasses melted under $CCl_4$ reactive atmosphere the peak is due almost entirely to surface-OH. and melting in a closed reactor was best for removing -OH. In ambient atmosphere the -OH peak exhibited no time dependence over a 30 d period indicating a very small rate of surface attack by atmospheric H2O. Removal of -OH absorption processing was generally easier and more complete for the $BaF_2$/ThF4-glasses than for the $ZrF_4$-or $HfF_4$-based glasses.

• The Korean Nurse
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• v.31 no.1
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• pp.68-87
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• 1992

The purpose of this study is to develop a patient care standard which is the basis of unit based quality assurance. The subjects were 570 nurses of 6 hospitals is Seoul. Patient Care Standards were developed from 3 times of clinical Nurses Association's workshop & the joint meeting of Clinical Nurses Association & the Korean Nurses Academic Socity of Nursing Administration. Respondents were instructed to rate of the 2 types of 5 - point Likert type questionnaire(one is the level of perceived importance, the other is the level of actual performance) Findings of this study were as follows 1. As a results of reliability analysis, each questionnaire ranged from $\alpha$=0.79 to 0.94