• The Pure and Applied Mathematics
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• v.24 no.3
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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.

• Korean Journal of Crystallography
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• v.6 no.1
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• pp.27-35
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• 1995

The crystal structure of 1-tert-butoxycarbonyl-4-[N-(tert-butoxycarbonyl)-N-(ethoxycarbonylmethyl)amino]-3-phenylsulfonylpyrrolidind [C24H36O8N2S] has been from single crystal x-ray diffraction study ; C24H36O8N2S triclinic, p1, 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=2, CuKα(λ=1.5418Å). The molecular structure was solved by diredt method and refined by full-matrix least squares to a final R=9.78% for 3621 unique observed [F≥4σ(F)] reflections and 703 paramenters.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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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.

• Journal of the Korean institute of surface engineering
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• v.34 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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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.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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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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• v.55 no.1
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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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• v.51 no.1
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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.

• Journal of the Korean Society of Clothing and Textiles
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• v.22 no.1
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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.