• 대한수학회지
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• 제48권1호
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• pp.33-48
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• 2011

The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.

• 대한수학회논문집
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• 제33권3호
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• pp.695-704
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• 2018

In this paper, firstly we compute the spectral norm of g-circulant matrices $C_{n,g}=g-Circ(c_0,c_1,{\cdots},c{_{n-1}})$, where $c_i{\geq}0$ or $c_i{\leq}0$ (equivalently $c_i{\cdot}c_j{\geq}0$). After, we compute the spectral norms, determinants and inverses of the g-circulant matrices with the Fibonacci and Lucas numbers.

• 호남수학학술지
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• 제42권2호
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• pp.235-249
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• 2020

Let Q and R be the well-known matrices associated with Fibonacci and Lucas numbers, and k, m, and n be any integers. It is mainly established all solutions of the matrix equations c₁Qⁿ + c₂Q^m = Q^k, c₁Qⁿ + c₂Q^m = RQ^k, and c₁Qⁿ + c₂RQ^m = Q^k with unknowns c₁, c₂ ∈ ℂ*. Moreover, using the obtained results, it is presented many identities, some of them are available in the literature, and the others are new, related to the Fibonacci and Lucas numbers.

• 호남수학학술지
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• 제45권3호
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• pp.418-432
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• 2023

In this study, we consider the Hankel and Gram matrices which are defined by the elements of special number sequences. Firstly, the eigenvalues, determinant, and norms of the Hankel matrix defined by special number sequences are obtained. Afterwards, using the relationship between the Gram and Hankel matrices, the eigenvalues, determinants, and norms of the Gram matrices defined by number sequences are given.

• 호남수학학술지
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• 제41권1호
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• pp.197-206
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• 2019

We consider the extended generalized Hecke groups ${\bar{H}}_{3,q}$ generated by $X(z)=-(z-1)^{-1}$, $Y(z)=-(z+{\lambda}_q)^{-1}$ with ${\lambda}_q=2\;cos({\frac{\pi}{q}})$ where $q{\geq}3$ an integer. In this work, we study the generalized Pell sequences in ${\bar{H}}_{3,q}$. Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group ${\bar{H}}_{3,3}$ can be written by using Pell, Pell-Lucas and modified-Pell numbers.

• 대한화학회지
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• 제34권1호
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• pp.63-68
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• 1990

규산질 광물 중 화학성분 원소인 $SiO_2,\;Al_2O_3,\;MgO,\;Fe_2O_3,\;CaO$ 및 $TiO_2$를 매트릭스 보정법을 이용한 X-선 형광분광법으로 분석하였다. 순수한 금속산화물을 혼합하여 만든 합성표준시료와 분석시료를 $Li_2B_4O_7$로 16배 희석, 용융하여 glass bead로 만들고 Lucas-Tooth와 Pyne 보정식을 사용한 실험계수법으로 성분간의 매트릭스 효과를 보정하였다. 각각 다른 세트의 매트릭스 계수를 사용하여 분석한 결과를 비교적 잘 일치하였으며 표준시료의 수가 많은 세트를 사용할 때 좋은 분석결과를 얻었다. 또한 NIST의 표준시료를 사용하여 이 방법에 의한 정확도를 검토하였다.

• 분석과학
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• 제9권4호
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• pp.382-391
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• 1996

세라믹스 분야, 전자요업 분야 등에서 폭넓게 사용되고 있는 티탄산바륨 소재에 대하여 신속하고 정확하게 분석할 수 있는 X-선 형광분석용 표준물질 12종을 제작하였다. 특히 매질효과 제거, 보관성, 균질성 등을 고려하면서 융제 ($Li_2B_4O_7+LiBO_2$)로 시료를 16배 희석하여 제작 하였다. 티타늄을 비롯한 몇 원소는 매트릭스의 영향을 받는 것으로 보여 실험 계수법을 사용하고 Lucas Tooth와 Price의 식을 이용해 매트릭스의 영향을 보정해 주었다. 세 곳의 분석기관에서 X-선 형광분광기로 12개의 표준물질에 포함된 15 원소에 대하여 검정곡선을 작성해 본 결과 BaO, PbO, SrO, $Fe_2O_3$, $La_2O_3$, $SnO_2$, ZnO, $ZrO_2$, CaO들은 correlation factor가 0.995를 넘는 아주 좋은 곡선을 얻었다. $SiO_2$와 $Al_2O_3$는 X-선 형광세기도 약하고 correlation factor가 낮은 검정 곡선을 보였다.

• 접착 및 계면
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• 제7권4호
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• pp.1-9
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• 2006

The single lap joint is the most studied joint in the literature in terms of both theory and practice. It is easy to manufacture and the lap shear strength is a useful value for strength assessment and quality control. Simple design rules exist such as the one present in standard ASTM 1002 or in a recent paper by Adams and Davies. The main factors that have an influence on the lap shear strength are the type of adhesive, i.e. ductile or brittle, the adherend yield strength and the overlap length. The overlap increases the shear strength almost linearly if the adhesive is sufficiently ductile and the adherend does not yield. For substrates that yield, a plateau is reached for a certain value of overlap corresponding to the yielding of the adherend. For intermediate or brittle adhesives, the analysis is more complex and needs further investigation. In order to quantify the influence of the adhesive, the adherend and the overlap on the lap shear strength, the experimental design technique of Taguchi was used. An experimental matrix of 27 tests was designed and each test was repeated three times. The influence of each variable could be assessed as well as the interactions between them using the statistical software Statview. The results show that the most important variable on the lap shear strength is the overlap length followed by the type of adherend.