• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.641-652
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• 2015

In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain $D{\subseteq}{\mathbb{C}}$ and n, k be two positive integers such that $n{\geq}k+1$, and let a, b be two finite complex constants such that $a{\neq}0$. Suppose that (1) $f+a(f^{(k)})^n$ and $g+a(g^{(k)})^n$ share b in D for every pair of functions f, $g{\in}F$; (2) All zeros of f have multiplicity at least k + 2 and all poles of f have multiplicity at least 2 for each $f{\in}F$ in D; (3) Zeros of $f^{(k)}(z)$ are not the b points of f(z) for each $f{\in}F$ in D. Then F is normal in D. And some examples are provided to show the result is sharp.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.449-460
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• 2020

In this paper, we investigate the stability of the additive-cubic functional equations f(x+ky)+f(x-ky)-k² f(x+y)-k² f(x-y)+(k²-1)f(x) - (k²-1)f(-x) = 0, f(x+ky)-f(ky-x)-k² f(x+y)+k² f(y-x)+2(k²-1)f(x)= 0, f(kx+y)+f(kx-y)-kf(x+y)-kf(x-y)-2f(kx)+2kf(x)= 0 by using the fixed point theory in the sense of L. Cădariu and V. Radu.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.349-361
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• 2015

A fence is an ordered set that the order forms a path with alternating orientation. Let F = (F;${\leq}$) be a fence and let OT(F) be the semigroup of all order-preserving self-mappings of F. We prove that OT(F) is coregular if and only if ${\mid}F{\mid}{\leq}2$. We characterize all coregular elements in OT(F) when F is finite. For any subfence S of F, we show that the set COTS(F) of all order-preserving self-mappings in OT(F) having S as their range forms a coregular subsemigroup of OT(F). Under some conditions, we show that a union of COTS(F)'s forms a coregular subsemigroup of OT(F).

• Phonetics and Speech Sciences
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• v.10 no.2
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• pp.15-24
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• 2018

Earlier studies reported that the /o/ and /u/ phonemes of Seoul Korean were currently merging in the F1/F2 space. However, studies on perception tests have shown that rates of correctness were high, even in cases where the two vowels overlapped. This study explores whether there is another acoustic parameter that differentiates /o/ from /u/, besides the F1/F2 contrast. Seventy-five native speakers of Seoul Korean, born between 1953 and 1999, participated in a production test. The data collected were analyzed in terms of F1 and F2, H1-H2, and F0. The result shows that the /o/ and /u/ of female speakers almost overlap in the F1/F2 space for all ages, while H1-H2 values are significantly different between the two vowels regardless of age. On the other hand, the /o/ and /u/ of male speakers are largely well separated in the F1/F2 space, while the H1-H2 values between the two vowels are very close at all ages. F0 effect is relatively small for both male and female speakers, even though there is a statistically significant difference. The result of this study provides evidence that female speakers use phonation differences to distinguish /o/ from /u/, and that the F1/F2 contrast has been replaced by H1-H2 values.

• Journal of the Korean Chemical Society
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• v.24 no.2
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• pp.108-114
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• 1980

By using electrostatic model and simple bond additivity scheme a reasonable and simple method was developed for the estimation of standard enthalpy of formation $({\Delta}H_f\;^{\circ})$ of very polar compounds. The bond contributions to the enthalpy of formation for halomethanes were; ${\Delta}H_f\;^{\circ}(C-F)=-36.44\;kcal/mole,\;{\Delta}H_f\;^{\circ}(C-Cl)=-2.57\;kcal/mole,\;{\Delta}H_f\;^{\circ}(C-Br)=5.32\;kcal/mole,\;{\Delta}H_f\;^{\circ}(C-I)=19.18\;kcal/mole,\;and\;{\Delta}H_f\;^{\circ}(C-H)=-3.61\;kcal/mole$, respectively. Using these values and calculated electrostatic energies, the estimated ${\Delta}H_f\;^{\circ}$ values were estimated and found to be in good agreement with observed values.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.36 no.6
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• pp.485-495
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• 1991

This experiment was carried out to obtain the information on the crossability, variation of chromosome number in pollen mother cell (PMC) and somatic cell of the progeny from the cross between hexaploid triticale cv. Sinkihomil and two diploid rye varieties. Seed set was 39.3 to 41.6% (averaged 40.5%) in the cross between triticale (P$_1$) and rye(P$_2$), which resulted in 0.33% in F$_2$(selfed F$_1$), 2.69% in F$_1$/P$_1$ 5.47% in F$_1$/P$_2$ respectively. However, seed set was extremely low in both reciprocal crosses when triticale was used as male. Germination rate of the crossed seed was 94.0% in F$_1$ 40.8% in F$_2$(selfed F$_1$), 59.5% in F$_1$/P$_1$ and 65.9% in F$_1$/P$_2$ from the cross between triticale and rye, respectively. Pollen fertility of F$_1$ plant was averaged 18.7% in the cross between triticale and rye. Number of Uni-, Bi-, and Trivalent in PMC was 12. 6, 6.94, and 0.53, respectively, in the F$_1$ between the triticale and rye. There were 28 chromosomes in F$_1$, 21 to 34 in F$_2$, 34 to 38 in F$_1$/P$_1$ and 19 to 23 in F$_1$/P$_2$ from the cross between the triticale and rye, respectively.

• The Journal of the Acoustical Society of Korea
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• v.19 no.5
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• pp.60-64
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• 2000

This paper studies the relation between the Fundamental Frequency (F0) and the formants of simple vowels in the Korean language sung by sopranos. It is hewn that, in soprano singing, the F0 of a vowel affects its formants. For this reason the formants of simple vowels sung by sopranos must be considered in all over the soprano singing range. We recorded the five simple vowel sounds /a/, /e/, /i/, /o/, and /u/ sung by five professional sopranos from A3 (220.0Hz) to A5 (880.0Hz) in the major scale and compared the formants of the sung vowels with those of spoken vowels. We observed that F1 and F2 of sung vowels were stable in low F0 (lower than B4) but in high F0 (higher than B4), F1 and F2 lost their stabilities. In the case of /a/, /o/, and /u/, the slope of the F1-F2 graph was about 2.6, and those of the F0-F2 and F0-Fl graphs were 2.2-2.5 and 0.7-1.0, respectively. And as the F0 increases, the F1 and F2 of sung vowels /a/, /e/, /i/, /o/, and /u/ were almost the same. At A5, the Fl and F2 of five sung vowels had the same values. This results suggest that the relation between the F0 and the formants be used to synthesize soprano's singing vowels.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.491-503
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• 2011

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation (0.1) f(2x + y) + f(2x - y) = 3f(x + y) + f(-x - y) + 3f(x - y) + f(y - x) + 18f(x) + 6f(-x) - 3f(y) - 3f(-y) in fuzzy Banach spaces.

• 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 $Irr_F(G) = {\chi_1, \chi_2, \cdots, \chi_k}$.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.487-496
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• 1996

Let f(z) be an entire function. Then the order $\rho(f)$ of f is defined by $$ \rho(f) = \overline{lim}_r\to\infty \frac{log r}{log^+ T(r,f)} = \overline{lim}_r\to\infty \frac{log r}{log^+ log^+ M(r,f)}, $$ where T(r,f) is the Nevanlinna characteristic of f (see [4]), $M(r,f) = max_{$\mid$z$\mid$=r} $\mid$f(z)$\mid$$ and $log^+ t = max(log t, 0)$.