• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권3호
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• pp.179-190
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• 2017

In this paper, we introduce and solve the following quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) $$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$ in fuzzy normed spaces, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero real numbers with ${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$ < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) in fuzzy Banach spaces.

• 한국결정학회지
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• 제6권1호
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• pp.27-35
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• 1995

1-tert-butoxycarbonyl-4-[N-(tert-butoxycarbonyl)-N-(ethoxycarbonylmethyl)amino]-3-phenylsulfonylpyrrolidind [C24H36O8N2S;이하 BEP]의 분자 및 결정구조를 X-선 회절법으로 연구하였다. 이 결정의 분자는 C24H36O8N2S, 삼사정계이고 공간군은 P1이다. 단위세포 길이는 a=11.363(8)Å, b=11.589(6)Å, c=11.013(10)Å,α=95.32(6)°,β=98.64(7)°,γ=79.57(5)°,V=1406.8(18)Å3, t=293K, Z=2이다. 구조해석에 사용한 X-선은 CuKα선(λ=1.5418Å)을 사용하였다. 분자구조는 직접법으로 풀었으며 최소자승법으로 정밀화하였다. 최종 신뢰도 R값은 F≥4 σ(F)인 3621개의 회절반점에 대하여 R=9.78% 이었다.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.127-133
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• 2005

An f-coloring of a graph G = (V, E) is a coloring of edge set E such that each color appears at each vertex v $\in$ V at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index $\chi'_f(G)$ of G. Any graph G has f-chromatic index equal to ${\Delta}_f(G)\;or\;{\Delta}_f(G)+1,\;where\;{\Delta}_f(G)\;=\;max\{{\lceil}\frac{d(v)}{f(v)}{\rceil}\}$. If $\chi'_f(G)$= ${\Delta}$f(G), then G is of $C_f$ 1 ; otherwise G is of $C_f$ 2. In this paper, the classification problem of complete graphs on f-coloring is solved completely.

• 한국표면공학회지
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• 제34권5호
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• pp.403-408
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• 2001

In this work, the cyclic perfluorinated ether (c-C$_4$F$_{8}$O) with very high destructive removal efficiency (DRE) than other alternative gases, such as $C_3$F$_{8}$, c-C$_4$F$_{8}$ and NF$_3$ was used as an alternative process chemical. The plasma cleaning of silicon nitride using gas mixtures of c-C$_4$F$_{8}$O/O$_2$ and c-C$_4$F$_{8}$O/O$_2$+ $N_2$ was investigated in order to evaluate the effects of adding $N_2$ to c-C$_4$F$_{8}$O/O$_2$ on the global warming effects. Under optimum condition, the emitted net perfluorocompounds (PFCs) during cleaning of silicon nitride were quantified and then the effects of additive $N_2$ by obtaining the destructive removal efficiency (DRE) and the million metric tons of carbon equivalent (MMT-CE) were calculated. DRE and MMTCE were obtained by evaluating the volumetric emission using. Fourier transform-infrared spectroscopy (FT-IR). During the cleaning using c-C$_4$F$_{8}$O/O$_2$+$N_2$, DRE values as high as (equation omitted) 98% were obtained and MMTCE values were reduced by as high as 70% compared to the case of $C_2$F$_{6}$O$_2$. Recombination characteristics were indirectly investigated by combining the measurements of species in the chamber using optical emission spectroscopy (OES), before and after the cleaning, in order to understand any correlation between plasma and emission characteristics as well as cleaning rate of silicon nitride.silicon nitride.

• 대한수학회지
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• 제44권6호
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• pp.1329-1338
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• 2007

In this paper, we study the location of zeros and Borel direction for the solutions of linear homogeneous differential equations $$f^{(n)}+A_{n-1}(z)f^{(n-1)}+{\cdots}+A_1(z)f#+A_0(z)f=0$$ with entire coefficients. Results are obtained concerning the rays near which the exponent of convergence of zeros of the solutions attains its Borel direction. This paper extends previous results due to S. J. Wu and other authors.

• 대한수학회지
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• 제33권2호
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• pp.381-386
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• 1996

We consider the behavior of positive radial solutions (or, briefly, pp.r.s.) of the equation $$ (1.1) ^\Delta u + \lambda f(u) = 0 in\Omega, _u = 0 on \partial\Omega, $$ where $\Omega = {x \in R^n$\mid$A < $\mid$x$\mid$ < B}$ is an annulus in $R^n, n \geq 2, \lambda > 0 and f \geq 0$ is superlinear in u and satisfies f(0) = 0.

• 충청수학회지
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• 제22권2호
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• pp.211-216
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• 2009

Let G be a Denjoy domain and let G' a Denjoy proper subdomain of G and homeomorphic to G. We consider conformal re-imbeddings of G' into G. Let G and G' are N-connected. We know that if N = 2, there is a re-imbedding f of G' into G such that G - cl(f(G')) has an interior point. In this note, we obtain the following theorem. If $N{\geq}3$, G has a Denjoy proper subdomain G' such that, for any re-imbeddings f of G' into G, G - cl(f(G') has no interior point.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.109-118
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• 2015

In the present paper, a new analytic function valued integral operator is introduced which is defined on n-copies of a subset of the class of normalized analytic functions on the unit disc of the complex plane. This operator, which is denoted here by $\mathfrak{J}^{{\alpha}_i,{\beta}_i}(f_1,{\ldots},f_n)$, unifies and generalizes several integral operators studied earlier. Interesting sufficient conditions are derived for the univalent starlikeness of $\mathfrak{J}^{{\alpha}_i,{\beta}_i}(f_1,{\ldots},f_n)$.

• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.29-36
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• 2011

Some global estimates for the Jacobians of quasiregular mappings f = ($f^1$, $f^2$, ${\cdots}$, $f^n$) of the Sobolev class $W^{1,n}$(${\Omega}$, $R^n$) in $L^{\varphi}({\mu})$-domains and John domains are established.

• 한국의류학회지
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• 제22권1호
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• pp.41-48
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• 1998

An investigation made of the easing contraction ratio according to sewing conditions (eased seam angle; 0$^{\circ}$ 20$^{\circ}$ 30$^{\circ}$ 45$^{\circ}$ 60$^{\circ}$ 70$^{\circ}$ 90$^{\circ}$, stitch density; 38 stitches/3 cm(N1.0), 26 stitches/ 3 cm(N1.5), 19 stitches/3 cm(N2.0), 14 stitches/3 cm(N2.5), 12 stitches/3 cm(N3.0), thread; sp 60' s/2) by lockstitch industrial sewing machine with shirring foot. The results abstained were as follows: 1. The lower the stitch density , the higher the easing contraction ratio. 2. The easing contraction ratio at 0$^{\circ}$ and 90$^{\circ}$ were lower than bias angles (20$^{\circ}$, 30$^{\circ}$, 45$^{\circ}$, 60$^{\circ}$, 70$^{\circ}$). 3. As the results of visual test, the maximum easing conditions were Fl -0$^{\circ}$.20$^{\circ}$.30$^{\circ}$.45$^{\circ}$-12 stitches/3 cm(N3.0), 60$^{\circ}$. 70$^{\circ}$. 90$^{\circ}$-14 stitches/3 cm(N2.5), F2 -0$^{\circ}$. 20$^{\circ}$.30$^{\circ}$.60$^{\circ}$.70$^{\circ}$.90$^{\circ}$-19 stitches/ 3 cm(N2.0), 45$^{\circ}$ -14 stitches/3 cm(N2.5), and F3 -0$^{\circ}$.20$^{\circ}$.30$^{\circ}$.45$^{\circ}$.60$^{\circ}$.70$^{\circ}$.90$^{\circ}$-19 stitches/3 cm (N2.0). 4. Approximately easing contraction ratio was obtained as 2.0% (N1.0)~ 10.2% (N3.0) in F1, 6.7% (N1.0)~ 15.7% (N2.0) in F2, and 5.2% (N1.0)~ 12.1% (N2.0) in F3, according to different angles on the sleeve cap curve line. 5. As a resets of SPSS PC) statistics analysis, it confirmed the relations which were observed between easing contration ratio and stitch density, and easing contraction ratio was correlated with bending properties.