• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권2호
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• pp.153-161
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• 2008

In the present paper we introduce a Jensen type quartic functional equation and then investigate the generalized Hyers-Ulam stability problem for the equation.

• 대한수학회논문집
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• 제26권2호
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• pp.237-251
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• 2011

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w) in intuitionistic fuzzy normed spaces (IFNS). We dene the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately 2-dimensional vector variable quadratic mapping implies the completeness of IFNS.

• 대한수학회논문집
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• 제25권3호
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• pp.405-417
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• 2010

We prove the generalized Hyers-Ulam stability of the generalized quadratic functional equation $$f(rx\;+\;sy)\;=\;r^2f(x)\;+\;s^2f(y)\;+\;\frac{rs}{2}[f(x\;+\;y)\;-\;f(x\;-\;y)]$$ in fuzzy Banach spaces, where r, s are non-zero rational numbers with $r^2\;+\;s^2\;{\neq}\;1$.

• 충청수학회지
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• 제24권2호
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• pp.147-162
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• 2011

In this paper, we investigate the Ulam-Hyers stability of $C^{\star}$-ternary algebra 3-homomorphisms for the functional equation $$f(x_1+x_2,y_1+y_2,z_1+z_2)=\;\displaystyle\sum_{1{\leq}i,j,k{\leq}2}\;f(x_i,y_j,z_k)$$ in $C^{\star}$-ternary algebras.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.295-301
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• 2006

We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.

• 대한수학회논문집
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• 제23권2호
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• pp.191-199
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• 2008

We investigate the relation between the vector variable bi-additive functional equation $f(\sum\limits^n_{i=1} xi,\;\sum\limits^n_{i=1} yj)={\sum\limits^n_{i=1}\sum\limits^n_ {j=1}f(x_i,y_j)$ and the multi-variable quadratic functional equation $$g(\sum\limits^n_{i=1}xi)\;+\;\sum\limits_{1{\leq}i<j{\leq}n}\;g(x_i-x_j)=n\sum\limits^n_{i=1}\;g(x_i)$$. Furthermore, we find out the general solution of the above two functional equations.

• 대한수학회논문집
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• 제36권2호
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• pp.343-359
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• 2021

The aim of this paper is to obtain the general solution of the 2-variable radical functional equations $f({\sqrt[k]{x^k+z^k}},\;{\sqrt[{\ell}]{y^{\ell}+w^{\ell}}})=f(x,y)+f(z,w)$, x, y, z, w ∈ ℝ, for f a mapping from the set of all real numbers ℝ into a vector space, where k and ℓ are fixed positive integers. Also using the fixed point result of Brzdęk and Ciepliński [11, Theorem 1] in (2, 𝛽)-Banach spaces, we prove the generalized hyperstability results of the 2-variable radical functional equations. In the end of this paper we derive some consequences from our main results.

• 한국전기전자재료학회논문지
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• 제37권5호
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• pp.476-485
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• 2024

Understanding the structure-property relationship in functional materials is crucial as microstructural features such as nano-precipitates, phase boundary, grain boundary segregation, and grain boundary phases play a key role in their functional properties. Atom probe tomography (APT) is an advanced analytical technique that allows for the three-dimensional (3D) mapping of atomic distributions and the precise determination of local chemical compositions in materials. Moreover, it offers sub-nanometer spatial resolution and chemical sensitivity at the tens of parts per million (ppm) level. Owing to its unique capabilities, this technique has been employed to uncover the 3D elemental distributions in a wide range of materials, including alloys, semiconductors, nanomaterials, and even biomaterials. In this paper, various kinds of examples are introduced for elucidating structure-property relationships on functional materials by utilizing the atom probe tomography.

• 한국작물학회지
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• 제51권6호
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• pp.565-570
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• 2006

The viviparous germination (VG) with lodging caused the yield reduction and quality deterioration in rice. We carried out the evaluation of VG tolerance (on the 40th day after heading) and mapping QTLs associated with VG tolerance using the recombinant inbred lines (M/G RILs) from a cross between Milyang 23 (japonica/indica) and Gihobyeo (japonica). The VG rates of Milyang 23 and Gihobyeo were 0.0 and 7.0%, respectively. The averaged VG rate of 162 M/G RILs was 7.7%, and their range was from 0.0 to 50.9%. Of the 162 RILs, 144 lines were tolerant less than 10%, and 18 lines were susceptible more than 10%. Using the M/G RIL Map, three QTLs associated with the viviparous trait were detected on chromosome 2 (qVG 2-1 and qVG 2-2) and 8 (qVG 8). qVG 2-1 was linked to RM 32D and RZ 166, and had LOD score of 2.97. qVG 2-2 was tightly linked to E13M59.119-Pl and E13M59.M003-P2, and showed higher LOD score of 3.41. qVG 8 was linked to RM33 and TCT116, and had LOD score of 2.67. The total phenotypic variance explained by the three QTLs was about 24.4% of the total variance in the population. The detection of new QTLs associated with VG tolerance will provide important informations for the seed dormancy, low temperature germination, or comparative genetics.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.17.2-17
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• 2003

The purpose of this paper is to solve the generalized Hyers-Ulam stability problem for a cubic functional equation 8f(x-y/2)＋8f(y-x/2)＋2f(x＋y)=9f(x)＋9f(y) on the basis of a direct method.