• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.383-398
• /
• 2009

In this paper, we study the generalized Hyers-Ulam stability of a bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,w)+f(y,\;z)+f(y,w)$$. Moreover, we establish stability results on the punctured domain.

• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.261-265
• /
• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.195-209
• /
• 2010

In this paper, we prove the generalized Hyers-Ulam stability of bi-homomorphisms in $C^*$-ternary algebras and of bi-derivations on $C^*$-ternary algebras for the following bi-additive functional equation f(x + y, z - w) + f(x - y, z + w) = 2f(x, z) - 2f(y, w). This is applied to investigate bi-isomorphisms between $C^*$-ternary algebras.

• Kyungpook Mathematical Journal
• /
• v.54 no.4
• /
• pp.531-543
• /
• 2014

The object of the present paper is to discuss some interesting properties of analytic functions f(z) associated with the subclasses $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$. Also, radius problems of $\frac{1}{\delta}f({\delta}z)$ for f(z) in the class $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$ are considered.

• Kyungpook Mathematical Journal
• /
• v.48 no.4
• /
• pp.705-720
• /
• 2008

In this paper, we obtain the Hyers-Ulam-Rassias stability of a bi-Jensen functional equation $4f(\frac {x+y}{2},\;\frac {z+w}{2})=f(x,z)+f(x,w)+f(y,z)+f(y,w)$.

• Journal of Integrative Natural Science
• /
• v.7 no.2
• /
• pp.145-147
• /
• 2014

Let $T_n(x)$ be the Chebyshev polynomials of first kind of degree n. In this paper, we show that for a > 1, the polynomial with integer coefficients $\frac{T_n(z)-T_n(a)}{z-a}$ has all its roots in $|z|{\leq}a$.

• Kyungpook Mathematical Journal
• /
• v.56 no.2
• /
• pp.577-582
• /
• 2016

In this paper we consider all orientation-preserving ${\mathbb{Z}}_4$-actions on 3-dimensional handlebodies $V_g$ of genus g > 0. We study the graph of groups (${\Gamma}(v)$, G(v)), which determines a handlebody orbifold $V({\Gamma}(v),G(v)){\simeq}V_g/{\mathbb{Z}}_4$. This algebraic characterization is used to enumerate the total number of ${\mathbb{Z}}_4$ group actions on such handlebodies, up to equivalence.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.2
• /
• pp.179-189
• /
• 2019

In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.

• Korean Journal of Mathematics
• /
• v.29 no.2
• /
• pp.387-393
• /
• 2021

In this paper, we introduce the notion of symmetric bi-derivations on subtraction algebra and investigated some related properties. We prove that a map D : X × X → X is a symmetric bi-derivation on X if and only if D is a symmetric map and it satisfies D(x - y, z) = D(x, z) - y for all x, y, z ∈ X.

• Journal of Sericultural and Entomological Science
• /
• v.51 no.2
• /
• pp.185-190
• /
• 2013

The superworm, as known the larva of Zophobas morio, has been officially imported from 2011 and bred commercially in Korea. But it is named as the corrected scientific name, Zophobas atratus by junior synonym throughout traditional taxonomy in this study and newly designated Korean name as 'a-me-ri-ca-wang-geo-jeo-ri' in terms of resource management. Z. atratus was compared with wild native tenebrionids, Promethis valgipes and a commercial reared Tenebrio molitor on the basis of DNA barcode analysis. As the results, the average genetic divergence was 21.4% between Z. atratus and P. valgipes, and 20.9% between Z. atratus and T. molitor. These large divergences imply these tenebrionids species can be easily identified by DNA barcodes. The results of genetic divergences within species also suggest that Korean populations of Z. atratus, having the same haplotype, might be introduced from the same area of foreign country. On the other hand, a population of T. molitor was separated into two distinct intra-specific groups with DNA barcoding gaps ranged from 1.17- 2.19%. We suppose that domestic breeding entities of T. molitor might be introduced and mixed from two different local groups. Through this study, we expect that classification for two tenebrionid introduced from foreign countries can be used for the management of insect resources in Korea.