• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.689-695
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• 1995

Let G be a finite group with k distinct conjugacy classes $C_1, C_2, \cdots, C_k$ and F an algebraically closed field such that char$(F){\dag}\left$\mid$ G \right$\mid$$. We denoted by $Irr_F$(G) the set of all irreducible F-characters of G and $Cf_F$(G) the set of all class functions of G into F. Then $Cf_F$(G) is a commutative F-algebra with an F-basis $Irr_F(G) = {\chi_1, \chi_2, \cdots, \chi_k}$.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.315-330
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• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quadratic functional equation $$(0.1)\;\frac{1}{2}(f(2x+y)+f(2x-y)-f(-2x-y)-f(y- 2x))\\{\hspace{35}}=2f(x+y)+2f(x-y)+4f(x)-8f(-x)-2f(y)-2f(-y)$$ in fuzzy Banach spaces.

• Journal of the Korea Furniture Society
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• v.11 no.2
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• pp.73-78
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• 2000

This study was carried out to measure formaldehyde emission with the passing of two years from plywood, sliver-board and strand-board bonded with urea resins which were made of 6 f/U molar ratios. The urea resins were manufactured by six kinds of formaldehyde/urea molar ratio of 1.0, 1.2, 1.4, 1.6, 1.8 and 2.0. 1. The plywood with molar ratio of 1.0 satisfied the KS F3101 $F_2$ directly after manufacture. The plywood with molar ratio of 1.2 satisfied m 3 days. The plywood with molar ratio of 1.4 satisfied the $F_3$ in 3 days and the $F_2$ in 600 days. And the plywood with molar ratio of 1.8 and 2.0 satisfied the $F_3$ in 365 days, but didn't satisfy the $F_2$ in 730 days. 2. Sliver-board with molar ratio of 1.0 and 1.2 satisfied the KS F3104 $E_2$ right after manufacture. Sliver-board with molar ratio of 1.4 and 1.6 satisfied in 150 and 360 days, respectively. Sliver-board with molar ratio of 1.8 and 2.0 satisfied in 730 days. 3. Strand-board with molar ratio of 1.0 and 1.2 satisfied the KS F3104$ E_2$ directly after manufacture. Strand-board with molar ratio of 1.4 and 1.6 satisfied in 150 days. But Strand-board with molar ratio of 1.8 and 2.0 didn't satisfied in 730 days.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.519-525
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• 2008

Let f be a diffeomorphisms of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper, we prove that if generically, f is tame diffeomorphims then the following conditions are equivalent: (i) f is ${\Omega}$-stable, (ii) f has the $C^1$-stable shadowing property (iii) f has the $C^1$-stable inverse shadowing property.

• Journal of Plant Biology
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• v.4 no.1
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• pp.1-7
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• 1961

Harn, Chang Yawl (Chonpuk U., Iri, Korea)-Studies on the interspecific crossing of FORSYTHIA genus. Kor. Jour. Bot. 4(1)1~8 1961: Interspecific crossing of two species, F. saxatilis and F. Koreana, was carried out in order to make clear the segregation ratio of style length, mode of fertility, the fertility of F1 generation, dioecism, and other taxonomic question, the result of which being summarized as follows: 1) Style length is segregated into 1:1 ratio. 2) The behaviro of fertility in the legitimate and illegitimate unions between the different species is exactly like that in the two dimorphic forms of the same species. 3) The mode of fertility between the long and short style of the F1 generation also follows that of the heterostyle plants. 4) No difficulties or irregularities are observed in the interspecific crossing and the F1's fertility. 5) In F1 generation exceedingly high morphological and physiological variations are observed. 6) The short style individual is well fertilized and sets seed when legitimately combined. The insistence that the short style is male, this genus being dioecious, is groundless. 7) Among F1 individuals, are observed a few dwarf-types with tiny and weak vegetative and reproductive organs. 8) The two species used behave in many ways like the different styles of the same species.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.1-16
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• 1996

Earlier in 1935[12], M. S. Robertson introduced the class of quadrant preserving functions. More precisely, let Q be the class of all functions f(z) analytic in the unit disk $D = {z : $\mid$z$\mid$ < 1}$ such that f(0) = 0, f'(0) = 1, and the range f(z) is in the j-th quadrant whenever z is in the j-th quadrant of D, j = 1,2,3,4. This class Q contains the subclass of normalized, odd univalent functions which have real coefficients. On the other hand, this class Q is contained in the class T of odd typically real functions which was introduced by W. Rogosinski [13]. Clearly, if $f \in Q$, then f(z) is real when z is real and therefore the coefficients of f are all real. Recently, it was observed by Y. Abu-Muhanna and T. H. MacGregor [1] that any function $f \in Q$ is odd. Instead of functions "preserving quadrants", the authors [1] have introduced the notion of "preserving sectors".

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.13-17
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• 1987

Let S denote the class of nivalent functions normalized so that f(0)=f'(0)-1=0 in vertical bar z vertical bar <1. Let $S_{\alpha}$$^{*}$, -.pi./2<.alpha.<.pi./2, denote the subclass of S that satisfies Re $e^{i{\alpha}}$zf'(z)/f(z).geq.0 in vertical bar z vertical bar <1; then f is called .alpha.-spiral-like and the case .alpha.=0 is the class of normalized starlike functions [6, pp.52]. Let T denote the class of functions f normalized as above and satisfying Im z[Im f(z)]..geq.0 in vertical bar z vertical bar <1; then f is called typically real and T contains those functions of S whose coefficients are real [6, pp.55]. Also, in view of [6, pp.231], let B(.lambda.) be the class of function normalized as above and map vertical bar z vertical bar <1 onto the complement of an arc with radial angle .lambda.(0<.lambda.<.pi./2). The radial angle is meant to be the angle between the tangent and radial vectors to the arc. This note includes a sharp version for Corollary 1 of [2] when f.mem. $S_{\alpha}$$^{*}$ as well as a logarithmic coefficient estimate.nt estimate.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.105-115
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• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• Food Science and Biotechnology
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• v.15 no.5
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• pp.672-676
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• 2006

The aim of this study is to evaluate the antioxidant, antimicrobial, and antitumor activities of various concentrations of partially purified substance(s) from green tea seed (Camellia sinensis L.). The total polyphenol contents of each fraction (non-adsorption fraction: F-1, fraction eluted with 40% methanol: F-2, and fraction eluted with 100% methanol: F-3) purified by Diaion HP-20 column chromatography were, in the increasing order: F-1 (3.7 mg tannic acid equivalents, TAB/g) < F-3 (23.2 mg TAB/g) < seed extracts (26.2 mg TAB/g) < F-2 (42.7 mg TAB/g). The scavenging activities toward the 1,1-diphenyl-2-picyrylhydrazyl (DPPH) radical were, in decreasing order: F-2 (93.3%) > butylated hydroxytoluene (BHT; 89.8%) > ascorbic acid (89.3%) > leaf extracts (70.3%) > F-3 (15.9%) > seed extracts (15.8%) > F-1 (14.8%) at a 0.1% concentration. In studies on antimicrobial activities, the results indicate that the growth of yeast (Candida albicans KCCM 11282 and Cryptococcus neoformans KCCM 50544) was inhibited more so than that of other fungi (Alternaria alternate KCTC 6005 and Rhizoctonia solani). In addition, it appears that the antitumor activities of the F-1, F-2, and F-3 fractions at a concentration of $50\;{\mu}g/mL$ showed 6, 7, and 23% growth inhibition of the HEC-1B cell line, 14, 11, 82% inhibition of the HEP-2 cell line, and 8, 16, and 81% inhibition of the SK-OV-3 cell line, respectively. Overall these results indicate that the antioxidant activity is greatest in the F-2 fraction, and the antimicrobial and antitumor activities are greatest in the F-3 fraction.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.219-227
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• 2018

In this paper, we solve the additive ${\rho}$-functional equations $$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < 1, and $$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ${\rho}$-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.