• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.395-404
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• 2005

Let α be a complex number with 𝕽α > 0. Let the functions f and g be analytic in the unit disc E = {z : |z| < 1} and normalized by the conditions f(0) = g(0) = 0, f'(0) = g'(0) = 1. In the present article, we study the differential subordinations of the forms $${\alpha}{\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}+{\frac{zf^{\prime}(z)}{f(z)}}{\prec}{\alpha}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}}+{\frac{zg^{\prime}(z)}{g(z)}},\;z{\in}E,$$ and $${\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}{\prec}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}},\;z{\in}E.$$ As consequences, we obtain a number of sufficient conditions for star likeness of analytic maps in the unit disc. Here, the symbol ' ${\prec}$ ' stands for subordination

• Korean Journal of Food Science and Technology
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• v.31 no.2
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• pp.322-328
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• 1999

Volatile flavor components of watermelon (Citrullus vulgaris S.) and oriental melon (Cucumis melo L.) obtained by simultaneous steam distillation and extraction apparatus were separated by gas chromatography (GC) and gas chromatography-mass spectrometry (GC/MS). Thirty seven and fifty five volatile flavor components were identified in watermelon and oriental melon, respectively. (Z)-3-Nonen-1-ol, (Z,Z)-3,6-nonadien-1-ol, (E,Z)-2,6-nonadienal and (E)-2-nonenal containing unsaturated nine carbon atoms were the characteristic flavor components of watermelon. $C_{9}-Unsaturated$ esters including (Z)-3-nonenyl acetate, (Z)-6-nonenyl acetate, (Z,Z)-3,6-nonadienyl acetate and thioester were important components in the flavor profile of oriental melon.

• Archives of Pharmacal Research
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• v.28 no.12
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• pp.1381-1385
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• 2005

Further investigation of Lycium chinense fruits gave a mixture of (6'-O-palmitoyl)- and (6'-O­stearoyl)-$\beta$-sitosterol-3-O-$\beta$-D-glucopyranoside (1) and two glycolipids, 1-O-(9Z, 12Z, 15Z-octa­decatrienoyl)-2-O-(9Z, 12Z, 15Z-octadecatrienoyl)-3-O-$\beta$-D-galactopyranosyl glycerol (2) and 1-O-(9Z, 12Z-octadecadienoyl)-2-O-(9Z, 12Z, 15Z-octadecatrienoyl)-3-O-$\beta$-D-galactopyranosyl glycerol (3). These compounds were newly isolated as constituents of L. chinense.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.543-555
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• 2019

In this paper, we give some results on ${\frac{zf^{\prime}(z)}{f(z)}}$ for the certain classes of holomorphic functions in the unit disc $E=\{z:{\mid}z{\mid}<1\}$ and on ${\partial}E=\{z:{\mid}z{\mid}=1\}$. For the function $f(z)=z^2+c_3z^3+c_4z^4+{\cdots}$ defined in the unit disc E such that $f(z){\in}{\mathcal{A}}_{\alpha}$, we estimate a modulus of the angular derivative of ${\frac{zf^{\prime}(z)}{f(z)}}$ function at the boundary point b with ${\frac{bf^{\prime}(b)}{f(b)}}=1+{\alpha}$. Moreover, Schwarz lemma for class ${\mathcal{A}}_{\alpha}$ is given. The sharpness of these inequalities is also proved.

• Applied Science and Convergence Technology
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• v.27 no.3
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• pp.56-60
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• 2018

The optical properties of the digital-alloy $(In_{0.53}Ga_{0.47}As)_{1-z}/(In_{0.52}Al_{0.48}As)_z$ grown by molecular beam epitaxy as a function of composition z (z = 0.4, 0.6, and 0.8) have been studied using temperature-dependent photoluminescence (PL) and time-resolved PL (TRPL) spectroscopy. As the composition z increases from 0.4 to 0.8, the PL peak energy of the digital-alloy $In(Ga_{1-z}Al_z)As$ is blueshifted, which is explained by the enhanced quantization energy due to the reduced well width. The decrease in the PL intensity and the broaden FWHM with increasing z are interpreted as being due to the increased Al contents in the digital-alloy $In(Ga_{1-z}Al_z)As$ because of the intermixing of Ga and Al in interface of InGaAs well and InAlAs barrier. The PL decay time at 10 K decreases with increasing z, which can be explained by the easier carrier escape from InGaAs wells due to the enhanced quantized energies because of the decreased InGaAs well width as z increases. The emission energy and luminescence properties of the digitalalloy $(InGaAs)_{1-z}/(InAlAs)_z$ can be controlled by adjusting composition z.

• Korean Journal of Materials Research
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• v.21 no.12
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• pp.644-649
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• 2011

[ $A_{3-2x/3}Al_{1-z}In_{z}O_4F:Eu_x^{3+}$ ](A = Ca, Sr, Ba, x = -0.15, z = 0, 0.1) oxyfluoride phosphors were simply prepared by the solid-state method at $1050^{\circ}C$ in air. The phosphors had the bright red photoluminescence (PL) spectra of an $A_{3-2x/3}Al_{1-z}In_{z}O_4F$ for $Eu^{3+}$ activator. X-ray diffraction (XRD) patterns of the obtained red phosphors were exhibited for indexing peak positions and calculating unit-cell parameters. Dynamic excitation and emission spectra of $Eu^{3+}$ activated red oxyfluoride phosphors were clearly monitored. Red and blue shifts gradually occurred in the emission spectra of $Eu^{3+}$ activated $A_3AlO_4F$ oxyfluoride phosphors when $Sr^{2+}$ by $Ca^{2+}$ and $Ba^{2+}$ ions were substituted, respectively. The concentration quenching as a function of $Eu^{3+}$ contents in $A_{3-2x/3}AlO_4F:Eu^{3+}$ (A = Ca, Sr, Ba) was measured. The interesting behaviors of defect-induced $A_{3-2x/3}Al_{1-z}In_{z}O_{4-{\alpha}}F_{1-{\delta}}$ phosphors with $Eu^{3+}$ activator are discussed based on PL spectra and CIE coordinates. Substituting $In^{3+}$ into the $Al^{3+}$ position in the $A_{3-2x/3}AlO_4F:Eu^{3+}$ oxyfluorides resulted in the relative intensity of the red emitted phosphors noticeably increasing by seven times.

• Korean Journal of Food Science and Technology
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• v.52 no.6
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• pp.587-594
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• 2020

In this study, we analyzed glucosinolates and their metabolites in the inner and outer parts of napa cabbage (NC; Brassica rapa subsp. pekinensis) and napa cabbage kimchi (NKC) using UPLC-ESI-MS/MS. In the extracts from NC and NKC, glucobrassicanapin (m/z 386), glucoalyssin (m/z 450), glucobrassicin (m/z 447), 4-methoxyglucobrassicin (m/z 477), and neoglucobrassicin (m/z 477) were detected using the MS scan mode ([M-H]-), and gluconapin (m/z 372→97), progoitrin (m/z 388→97), glucoiberin (m/z 422→97), 4-methoxyglucobrassicin (m/z 477→97), and neoglucobrassicin (m/z 477→447) were detected using the MS/MS MRM mode ([M-H]-). Ascorbigen (m/z 306→130) and indole-3-carboxaldehyde (I3A; m/z 146→118), which were metabolites of glucobrassicins, were detected using the MS/MS MRM ([M+H]+) mode. The peak intensities of ascorbigen in the extract from the inner and outer parts of NC were significantly higher than those of the NKC extract (p<0.05); however, there was no significant difference in I3A peak intensity between the NC and NKC extracts.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.109-116
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• 2004

In this paper, we study the uniqueness of entire functions and prove the following result: Let f(z) and g(z) be two nonconstant entire functions, $n\;{\geq}\;7$ a positive integer, and let a be a nonzero finite complex number. If $f^{n}(z)(f(z)\;-\;1)f'(z)\;and\;g^{n}(z)(g(z)\;-\;1)g'(z)$ share a CM, then $f(z)\;{\equiv}\;g(z)$. The result improves the theorem due to ref. [3].

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.601-607
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• 1996

For functions $f(z) = \sum_{n = 0}^{\infty}a_n z^n$ and $g(z) = \sum_{n = 0}^{\infty} b_n z^n$ analytic in the unit disk $\Delta = {z : $\mid$z$\mid$ < 1}$, the convolution $f * g$ is defined by $(f * g)(z) = \sum_{n = 0}^{\infty}a_n b_n z^n$. Let S denote the family of functions $f(z) = z + \cdots$ analytic and univalent in $\Delta$ and K, St, C the subfamilies that are respectively convex, starlike, and close-to-convex.