• Journal of the Korean Mathematical Society
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• v.48 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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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.

• Honam Mathematical Journal
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• v.42 no.2
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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.

• Honam Mathematical Journal
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• v.45 no.3
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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.

• Honam Mathematical Journal
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• v.41 no.1
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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.

• Journal of the Korean Chemical Society
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• v.34 no.1
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• pp.63-68
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• 1990

The chemical ingredients such as $SiO_2,\;Al_2O_3,\;MgO,\;Fe_2O_3,\;CaO$ and $TiO_2$in silica minerals were determined by X-ray fluorescence spectrometry using a matrix correction method. The synthesized standards mixed with reagent grade oxides and the sample were diluted by fusing with 16 times $Li_2B_4O_7$. The matrix effects correlated among the ingredients were corrected by the empirical coefficient method based on the Lucas-Tooth and Pyne model. The analytical results showed relatively good agreement between the different sets of coefficients but were improved with increasing the number of standard. The accuracy of this method was also examined with the standard reference material of NIST.

• Analytical Science and Technology
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• v.9 no.4
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• pp.382-391
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• 1996

In this study, 12 different chemical species of fine ceramic($BaTiO_3$) were synthesized as the standard materials for the fast and accurate measurements of X-ray fluorescence spectrometry. Samples were diluted to sixteen times with the filling compound ($Li_2B_4O_7+LiBO_2$) in order to remove the matrix effect, and to get the convenient storage and homogeneity of ingredients. The matrix effects among the ingredients were corrected by the empirical coefficient method based on the Lucas-Tooth and Price model. The standard curve on 12 standard materials containing 15 elements were obtained by using X-ray fluorescence spectrometry at three different laboratories. The correlation factors of BaO, PbO, SrO, $Fe_2O_3$, $La_2O_3$, $SnO_2$, ZnO, $ZrO_2$, CaO indicated the relati vely good agreement over 0.995 among the three different laboratories. $SiO_2$ and $Al_2O_3$ showed the poor linearity because of their low fluorescence intensities.

• Journal of Adhesion and Interface
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• v.7 no.4
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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.