• Honam Mathematical Journal
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• v.37 no.4
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• pp.473-486
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• 2015

In this paper, we investigate a stability problem for a functional equation f(-x - y - z) - f(x + y) - f(y + z) - f(x + z) + 2f(x) + 2f(y) + 2f(z) - f(-x) - f(-y) - f(-z) = 0 by applying the direct method.

• 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.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.451-457
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• 2011

The function f(z) = $e^{p(z)}$ where p(z) is a polynomial of degree n has 2n Julia lines. Julia lines of $e^{p(z)}$ divide the complex plane into 2n equal sectors with the same vertex at the origin. In each sector, $e^{p(z)}$ has radial limits of 0 or innity. Main results of the paper are concerned with maximum curves of $e^{p(z)}$. We deal with some properties of maximum curves of $e^{p(z)}$ and we give some examples of the maximum curves of functions of the form $e^{p(z)}$.

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.57-63
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• 2005

Let ∑(p)(p ∈ N) be the class of functions f(z) = z/sup -p/ + α/sub 1-p/ z/sup 1-p/ + α/sub 2-p/z/sup 2-p/ + ... analytic in 0 < ｜z｜ < 1 and let M(p, λ, μ)(0 < λ≤ 2 and 2λ(λ - 1) ≤ μ ≤ λ²) denote the class of functions f(z) ∈ ∑(p) which satisfy (equation omitted). The object of the present paper is to derive some properties of functions in the class M(p, λ, μ).

• Bulletin of the Korean Mathematical Society
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• v.21 no.1
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• pp.1-5
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• 1984

The notion of linear 2-normed spaces was introduced by S. Gahler ([8,9,10,11]), and these space have been extensively studied by C. Diminnie, R. Ehret, S. Gahler, K. Iseki, A. White, Jr, and others. For nonzero vectors x,y in X, let V(x,y) denote the subspace of X generated by x and y. A linear 2-normed space (X,v) is said to be strictly convex ([3]) if v(x+y,z)=v(x,z)+v(y+z) and z not.mem.V(x,y) imply that y=ax for some a>0. Some characterizations of strict convexity for linear 2-normed spaces are given in [1,3,4,5,12]. Also, a linear 2-normed space (X,v) is said to be strictly 2-convex ([6]) if v(x,y)=v(x,z)=v(y,z)=1/3v(x+z, y+z)=1 implies that z=x+y. These space have been studied in [2,4,6,13]. It is easy to see that every strictly convex linear 2-normed space is always strictly 2-convex but the converse is not necessarily true. Throughout this paper, let (X,v) denote a linear 2-normed space.

• Korean Journal of Medicinal Crop Science
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• v.10 no.3
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• pp.162-166
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• 2002

(Z)-ocimene+limonene, $(E)-{\beta}-ocimene$ and citronellal showed seasonal variation in the leaves of Z. schinifolium. Especially estragole was detected at fruiting stage regardless of collection sites. Common variation components in the leaves of Z. piperitum at all collection sites were (Z)-3-hexenol, ${\alpha}-pinene$, limonene and citronellal. The compositions with monthly variation in Z. schinifolium at arboretum were ${\alpha}-pinene$, myrcene, (Z)-3-hexenyl acetate, ${\alpha}-phellandrene$, (Z)-ocimene+limonene, ${\beta}-phellandrene$, linalool, geranyl acetate while in Z. piperitum were hexanal, (Z)-3-hexenol, (E)-2-hexenal, hexanol, ${\alpha}-pinene$, (Z)-ocimene, limonene, citronellal, geranyl acetate, ${\beta}-caryophyllene$. Estragole was not detected in Z. schinifolium leaves at arboretum due to too young tree to bearing fruit on it.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.521-534
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• 2022

In this paper, we introduce a new class 𝓡^k_λ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ^∞_n=2 a_nzⁿ (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡^k_λ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a₃-𝜇a²₂| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.103-110
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• 2008

In this paper, we obtain the general solution and the stability of the cubic functional equation f(2x + y, 2z + w) + f(2x - y, 2z - w) = 2f(x + y, z + w) + 2f(x - y, z - w) + 12f(x, z). The cubic form $f(x,\;y)\;=\;ax^3\;+\;bx^2y\;+\;cxy^2\;+\;dy^3$ is a solution of the above functional equation.

• Bulletin of the Korean Chemical Society
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• v.29 no.3
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• pp.627-640
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• 2008

The geometrical structures, atomic charges, and relative energies of tetracoordinated Pd complexes [PdCl3Z (Z = Cl-, Br-, OH?-, H2O, NH3, PH3), PdCl2Z2 (Z = Br-, OH?-, H2O, NH3, PH3), PdZ?2X (Z = Cl-, OH?-, H2O, NH3, PH3; X = oxalate, O2-?CCO2-), and PdZ2Y (Z = Cl?-, OH?-, H2O, NH3, PH3; Y = succinate, CO2-?CHCHCO2-?)] and the ligand exchange reactions of the Pd complexes were investigated using the ab initio second order Mller-Plesset perturbation (MP2) and Density Functional Theory (DFT) methods. The geometrical characteristics of the tetracoordinated Pd(II) complexes with mono- and bidentate ligands, the effects of the atomic charges for the charged and uncharged ligands, the (dz2-p ) interactions between the dz2-orbital of Pd(II) and the p -orbital of bidentates, and the relative stabilities between the isomers of PdCl2Z2 and PdZ2Y were investigated in detail. The potential energy surfaces for the ligand exchange reactions used for the conversions of {[PdCl2(NH3)2] + H2O} to {[PdCl(NH3)2(H2O)]+ + Cl?-?} and {[PdCl2(PH3)2] + H2O} to {[PdCl(PH3)2(H2O)]+ + Cl?-?]} were investigated. The geometrical structure variations, molecular orbital variations (HOMO and LUMO), and relative stabilities for the ligand exchange processes were also examined quantitatively.

• Applied Biological Chemistry
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• v.29 no.2
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• pp.182-189
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• 1986

Alachlor, 2-chloro-2',6'-diethyl-N-(methoxymethyl) acetanilide produced four major degradation products, when incubated under an upland soil condition for 80 days. They include 8-ethyl-2-hydroxy-N-(methoxymethyl)-1,2,3,4-tetrahydroquinoline (m/z 221), N-hydroxyacetyl-2,3-dihydro-7-ethylindole (m/z 205), 2-hydroxy-2',6'-diethyl-N-(methoxymethyl) acetanilide (m/z 251), and 9-ethyl-1,5-dihydrol-(methoxymethyl)-5-methyl-4,1-benzoxazepin-2 (3H)-one (m/z 249). The products turned out to be a little different from those obtained under the flooded paddy soil condition used in the previous paper. The plausible pathways for the degradation were proposed.