• 대한수학회논문집
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• 제31권1호
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• pp.101-113
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• 2016

In this article, we considered the stability of the following (${\alpha}$, ${\beta}$, ${\gamma}$)-derivation $${\alpha}D[x,y]={\beta}[D(x),y]+{\gamma}[x,D(y)]$$ and homomorphisms associated to the quadratic type functional equation $$f(kx+y)+f(kx+{\sigma}(y))=2kg(x)+2g(y),\;x,y{\in}A$$, where ${\sigma}$ is an involution of the Lie $C^*$-algebra A and k is a fixed positive integer. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.

• 대한수학회지
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• 제57권1호
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• pp.145-169
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• 2020

Let k be a field of characteristic 0. Let ${\mathfrak{C}}=Spec(k[x,y]/{\langle}f{\rangle})$ be a weighted homogeneous plane curve singularity with tangent space ${\pi}_{\mathfrak{C}}:T_{{\mathfrak{C}}/k}{\rightarrow}{\mathfrak{C}$. In this article, we study, from a computational point of view, the Zariski closure ${\mathfrak{G}}({\mathfrak{C}})$ of the set of the 1-jets on ${\mathfrak{C}}$ which define formal solutions (in F[[t]]² for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal ${\mathcal{N}}_1({\mathfrak{C}})$ defining ${\mathfrak{G}}({\mathfrak{C}})$ as a reduced closed subscheme of $T_{{\mathfrak{C}}/k}$ and obtain applications in terms of logarithmic differential operators (in the plane) along ${\mathfrak{C}}$.

• 대한수학회보
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• 제46권1호
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• pp.45-60
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• 2009

In this paper, we investigate homomorphisms in proper $JCQ^*$-triples and derivations on proper $JCQ^*$-triples associated to the following Pexiderized functional equation $$f(x+y+z)=f_0(x)+f_1(y)+f_2(z)$$. This is applied to investigate homomorphisms and derivations in proper $JCQ^*$-triples.

• 대한수학회논문집
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• 제24권1호
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• pp.5-16
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• 2009

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $$\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)$$ for a fixed positive integer m with $m\;{\geq}\;2$. This is applied to investigate derivations and their stability on proper Lie $CQ^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.603-615
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• 2019

Let R be an associative unital ring with an endomorphism α and α-derivation δ. The constant products of elements in Ore extension rings, when the coefficient ring is reversible, is investigated. We show that if f(x) = ∑ⁿ_i=0 a_ixⁱ and g(x) = ∑^m_j=0 b_jx^j be nonzero elements in Ore extension ring R[x; α, δ] such that g(x)f(x) = c ∈ R, then there exist non-zero elements r, a ∈ R such that rf(x) = ac, when R is an (α, δ)-compatible ring which is reversible. Among applications, we give an exact characterization of the unit elements in R[x; α, δ], when the coeficient ring R is (α, δ)-compatible. Furthermore, it is shown that if R is a weakly 2-primal ring which is (α, δ)-compatible, then J(R[x; α, δ]) = N iℓ(R)[x; α, δ]. Some other applications and examples of rings with this property are given, with an emphasis on certain classes of NI rings. As a consequence we obtain generalizations of the many results in the literature. As the final part of the paper we construct examples of rings that explain the limitations of the results obtained and support our main results.

• 한국산림과학회지
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• 제112권2호
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• pp.188-194
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• 2023

본 연구는 우리나라의 대나무림에 대한 탄소계정을 위하여 탄소배출계수 중 하나인 목재기본밀도를 도출하기 위하여 수행되어 졌다. 대나무는 전라남도와 경상남도에 주로 분포해 있으며, 계수 도출을 위한 표준목은 솜대, 왕대, 맹종죽 등 3수종별로 각각 101본씩을 선정하여 활용하였다. 목재기본밀도 도출은 KS F 2098 방법을 따랐다. 측정결과, 솜대의 목재기본밀도는 0.83 g/cm³, 왕대는 0.81 g/cm³, 맹종죽은 0.72 g/cm³로 각각 나타났다. 그렇지만, 우리나라는 대나무 분포 면적이 많지 않고, 맹종죽의 경우 일정 지역에 국한되어 생육하고 있다. 따라서 대나무에 적용할 수 있는 목재기본밀도는 하나로 통합하여 0.79 g/cm³로 확정하였다. 그리고 도출된 목재기본밀도에 대한 불확도를 평가한 결과, 1.61%로 낮은 불확도 값을 가져, 본 분석에서의 측정값에 대한 신뢰도를 확인할 수 있었다. 본 연구에서는 이번에 개발한 목재기본밀도와 기존의 바이오매스확장계수, 뿌리함량비 등을 이용하여 대나무 표준목에 대한 탄소저장량을 계산하고, 이를 확장시켜 ha단위까지 계산해 보았다. 이번 연구로 대나무의 재적을 이용하여 목재기본밀도 등 탄소배출계수 적용으로 탄소저장 및 흡수량 계산이 가능하게 되었다. 본 결과가 우리나라 탄소중립 정책 및 산림관리 방향에 도움이 되기를 기대한다.

• Advances in aircraft and spacecraft science
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• 제4권6호
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• pp.613-637
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• 2017

The development systems for the Structural Health Monitoring has attracted considerable interest from several engineering fields during the last decades and more specifically in the aerospace one. In fact, the introduction of those systems could allow the transition of the maintenance strategy from a scheduled basis to a condition-based approach providing cost benefits for the companies. The research presented in this paper consists of a definition and next comparison of four methods applied to numerical measurements for the extraction of damage features. The first method is based on the determination of the Structural Intensity field at the on-resonance condition in order to acquire information about the dissipation of vibrational energy throughout the structure. The Damage Quantification Indicator and the Average Integrated Global Amplitude Criterion methods need the evaluation of the Frequency Response Function for a healthy plate and a damaged one. The main difference between these two parameters is their mathematical definition and therefore the accuracy of the scalar values provided as output. The fourth and last method is based on the Mode-shape Curvature, a FRF-based technique which requires the application of particular finite-difference schemes for the derivation of the curvature of the plate. All the methods have been assessed for several damage conditions (the shape, the extension and the intensity of the damage) on two test plates: an isotropic (steel) plate and a 4-plies composite plate.