• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.67-80
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• 2019

For positive integers a, b, c, and an integer n, the number of integer solutions $(x,y,z){\in}{\mathbb{Z}}^3$ of $a{\frac{x(x-1)}{2}}+b{\frac{y(y-1)}{2}}+c{\frac{z(z-1)}{2}}=n$ is denoted by t(a, b, c; n). In this article, we prove some relations between t(a, b, c; n) and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in [6].

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.335-348
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• 2010

In this paper, we study the Hyers-Ulam-Rassias stability of a bi-Pexider functional equation $$f(x+y,z)-f_1(x,z)-f_2(y,z)=0$$, $$f(x,y+z)-f_3(x,y)-f_4(x,z)=0$$. Moreover, we establish stability results on the punctured domain.

• Proceedings of the Korean Society for Bio-Environment Control Conference
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• 2002.11a
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• pp.253-261
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• 2002

칼라(Zantedeschia spp.)는 남아프리카가 원산인 구근식물로 천남성과에 속하며 7개의 원종과 2개의 아종이 있다. 원예학적으로는 두 그룹으로 분류되며 Z. aethiopica 종이 속한 그룹은 습지생육형으로서 보통 백색칼라로 불리고, Z. albomaculata, Z. rehmannii, Z. jucunda, Z. ellittiana 및 Z. pentlandii 5종이 포함된 건지생육형 그룹은 유색칼라로 불린다. 그 외에 두 그룹의 중간 형태인 Z. ordorata 종이 있다(Funnell, 1993). (중략)

• East Asian mathematical journal
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• v.14 no.1
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• pp.107-116
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• 1998

This paper deals with functions of the form $f(z)=a_1z-{\sum}{\limits}_{n=2}^{\infty}a_nz^n(a_1>0,\;a_n{\geqslant}0)$ with $(1-{\mu})f(z_0)/z_0+{\mu}f'(z_0)=1(-1. We introduce the class $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$ with generalized fractional derivatives. Also we have obtained coefficient inequalities, distortion theorem and radious problem of functions belonging to the calss $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$.

• Restorative Dentistry and Endodontics
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• v.34 no.2
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• pp.145-153
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• 2009

The purpose of this study was to evaluate the effect of instrument compliance on the polymerization shrinkage stress measurements of dental composites. The contraction strain and stress of composites during light curing were measured by a custom made stress-strain analyzer, which consisted of a displacement sensor, a cantilever load cell and a negative feedback mechanism. The instrument can measure the polymerization stress by two modes: with compliance mode in which the instrument compliance is allowed, or without compliance mode in which the instrument compliance is not allowed. A flowable (Filtek Flow: FF) and two universal hybrid (Z100: Z1 and Z250: Z2) composites were studied. A silane treated metal rod with a diameter of 3.0 mm was fixed at free end of the load cell, and other metal rod was fixed on the base plate. Composite of 1.0 mm thickness was placed between the two rods and light cured. The axial shrinkage strain and stress of the composite were recorded for 10 minutes during polymerization. and the tensile modulus of the materials was also determined with the instrument. The statistical analysis was conducted by ANOVA. paired t-test and Tukey's test (${\alpha}<0.05$). There were significant differences between the two measurement modes and among materials. With compliance mode, the contraction stress of FF was the highest: 3.11 (0.13). followed by Z1: 2.91 (0.10) and Z2: 1.94 (0.09) MPa. When the instrument compliance is not allowed, the contraction stress of Z1 was the highest: 17.08 (0.89), followed by FF: 10.11 (0.29) and Z2: 9.46 (1.63) MPa. The tensile modulus for Z1, Z2 and FF was 2.31 (0.18), 2.05 (0.20), 1.41 (0.11) GPa, respectively. With compliance mode. the measured stress correlated with the axial shrinkage strain of composite: while without compliance the elastic modulus of materials played a significant role in the stress measurement.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1139-1148
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• 2015

The estimate of third Hankel determinant $$H_{3,1}(f)=\left|a_1\;a_2\;a_3\\a_2\;a_3\;a_4\\a_3\;a_4\;a_5\right|$$ of the analytic function $f(z)=z+a2z^2+a3z^3+{\cdots}$, for which ${\Re}(1+zf^{{\prime}{\prime}}(z)/f^{\prime}(z))>-1/2$ are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.795-814
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• 2021

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: fⁿ + P(f) = R(z)e^α(z) and fⁿ + P_*(f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z) in the complex plane, where P(f) and P_*(f) are differential polynomials in f of degree n - 1 with coefficients being small functions and rational functions respectively, R is a non-vanishing small function of f, α is a nonconstant entire function, p₁, p₂ are non-vanishing rational functions, and α₁, α₂ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when p₁, p₂ are nonzero constants, and deg α₁ = deg α₂ = 1. Our results are improvements and complements of Liao ([9]), and Rong-Xu ([11]), etc., which partially answer a question proposed by Li ([7]).

• East Asian mathematical journal
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• v.5 no.1
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• pp.35-47
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• 1989

Let $S_o*({\alpha},{\beta},{\mu})$ denote the class of functions $f(z)=a_1z-{\sum}{\limit}^{\infty}_{n=2}\;a_nz^n$ analytic in the unit disc $U=\{z:{\mid}z{\mid}<1\}$ and satisfying the condition $${\mid}\frac{\frac{zf'(z)}{f(z)}-1}{(1+\mu)\;\beta(\frac{zf'(z)}{f(z)}-\alpha)-(\frac{zf'(z)}{f(z)}-1)}\mid<1$$ for some $\alpha(0{\leq}{\alpha}<1),\;{\beta}(0<{\beta}{\leq}1),\;{\mu}(0{\leq}{\mu}{\leq}1)$ and for all $z{\in}U$. And it is the purpose of this paper to show a necessary and sufficient condition for the class $S_o*({\alpha},{\beta},{\mu})$, some results for the Hadamard products of two functions f(z) and g(z) in the class $S_o*({\alpha},{\beta},{\mu})$, the distortion theorem and the distortion theorems for the fractional calculus.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.31 no.5
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• pp.197-202
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• 2021

Synthesis of Z-type hexaferrite Ba₃Co₂Fe₂₄O₄₁ (Ba₃Z) and Ba_1.5La_1.5Co₂Fe₂₄O₄₁ (Ba_1.5La_1.5Z) powders were tried using molten salt synthesis after primary calcination. Ba₃Z calcined at 1000℃ was formed with both M-type and Y-type hexaferrite, and then Z-type was obtained when sintered with molten salt at 1150℃ and 1200℃. In the case of Ba_1.5La_1.5Z calcined at 1000℃, however, M-type hexaferrite, CoFe₂O₄ (Spinel phase), and LaFeO₃ were synthesized. As a result, Z-type hexaferrite was not synthesized after sintering with molten salt. In addition, the aspect ratio of the particles decreased as the sintering temperature increased with molten salt synthesis. To obtain a single-phase Ba_1.5La_1.5Z with a high aspect ratio, it is expected the raw materials have to calcine below the temperature of a spinel phase formation before sintering with molten salt.

• The Journal of Korean Academic Society of Nursing Education
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• v.5 no.2
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• pp.300-314
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• 1999

This study is an attempt to evaluate the effect of the medication and symptoms self-care education on the psychiatric patients' quality of life. This exploratory study was designed to a quasi-experiment of pretest-postest with a non equivalent control group. Subjects of 40 patients who were discharged from a mental hospital in Pusan were selected to be experiment and control group, with each group consisting of 20. The research period was from March, 6 to May, 29, 1999 and the pre-post test was given before and after implementing MSSE to the both experiment and control group. The results finding were summarized as follows ; 1. subjects who attended self-care education scored significantly higher than control group in quality of life.(Z=-2.06, P=0.034) 2. Those who were in the experiment group reported more significant higher scores than control group in item of quality of life, living situation(A=-2.62 P=0.012), relations with spouse (Z=-2.31 P=0.038) and children (Z=3.37, P=0.008), fear (Z=-1 95, P=0.049) and anger(Z=-2.07 P=0.041), work functioning (Z=-2.34, P=0.021), environmental adjustment. (Z=-2.05, P=0.039)