• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.41-52
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• 2016

In the present paper, by generalizing the definition of the zero-difference balanced (ZDB) function to be the G-ZDB function, several classes of G-ZDB functions are constructed based on properties of cyclotomic numbers. Furthermore, some special constant composition codes are obtained directly from G-ZDB functions.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.489-509
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• 2024

In this paper, let q ∈ (0, 1]. We establish the boundedness of intrinsic g-functions from the Hardy-Lorentz spaces with variable exponent H^p(·),q(ℝⁿ) into Lorentz spaces with variable exponent L^p(·),q(ℝⁿ). Then, for any q ∈ (0, 1], via some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function, we obtain several equivalent characterizations of H^p(·),q(ℝⁿ) in terms of wavelets.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.93-106
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• 2005

In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.

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

• 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

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.263-273
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• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.30 no.2
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• pp.51-57
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• 2007

The expected busy period for the controllable M/G/1 queueing model operating under the triadic policy is derived by using the pseudo probability density function which is totally different from the actual probability density function. In order to justify the approach using the pseudo probability density function to derive the expected busy period for the triadic policy, well-known expected busy periods for the dyadic policies are derived from the obtained result as special cases.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2021-2026
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• 2013

Let G = (V,E) be a graph. A function $f:V{\rightarrow}\{-1,+1\}$ defined on the vertices of G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. The signed total domination number of G, ${\gamma}^s_t(G)$, is the minimum weight of a signed total dominating function of G. In this paper, we study the signed total domination number of generalized Petersen graphs P(n, 2) and prove that for any integer $n{\geq}6$, ${\gamma}^s_t(P(n,2))=2[\frac{n}{3}]+2t$, where $t{\equiv}n(mod\;3)$ and $0 {\leq}t{\leq}2$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.697-704
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• 2013

The function $g{\mapsto}{\zeta}^k_G(g)$ which counts the number of solutions of $x^k=g$ in a finite group G, is not necessarily a character of G. We study this function for the case of dihedral groups and generalized quaternion groups.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.343-351
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• 2013

In this paper, the dynamics on a transcendental entire semigroup G is investigated. We show the possible values of any limit function of G in strictly wandering domains and Fatou components, respectively. Moreover, if G is of class $\mathfrak{B}$, for any $z$ in a Fatou domain, there does not exist a sequence $\{g_k\}$ of G such that $g_k(z){\rightarrow}{\infty}$ as $k{\rightarrow}{\infty}$.