• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.367-370
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• 2016

In this paper, we consider the generalized Lucas sequence which is the (p, q) - Lucas sequence. Then we used the Binet's formula to show some properties of the (p, q) - Lucas number. We get some generalized identities of the (p, q) - Lucas number.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.447-450
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• 2016

Let $F_n$ and $L_n$ be the nth Fibonacci number and Lucas number, respectively. The order of appearance of m in the Fibonacci sequence, denoted by z(m), is the smallest positive integer k such that m divides $F_k$. Marques obtained the formula of $z(L^k_n)$ in some cases. In this article, we obtain the formula of $z(L^k_n)$ for all $n,k{\geq}1$.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.135-151
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• 2005

In this paper, we obtain some properties of the sequences $U^{q}_n\;and\;V^{q}_n$ introduced in [6]. We find polynomial representations and formulas of them. For q = 5, $U^{5}_n$ is the Fibonacci sequence $F_n\;and\;V^{5}_n$ is the Lucas sequence $L_n$.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.511-522
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• 2017

We explicitly solve the diophantine equations of the form $$A_{n_1}A_{n_2}{\cdots}A_{n_k}{\pm}1=B^2_m$$, where $(A_n)_{n{\geq}0}$ and $(B_m)_{m{\geq}0}$ are either the Fibonacci sequence or Lucas sequence. This extends the result of D. Marques [9] and L. Szalay [13] concerning a variant of Brocard-Ramanujan equation.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1439-1443
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• 2010

For a positive integer k $\geq$ 2, the k-bonacci sequence {$g^{(k)}_n$} is defined as: $g^{(k)}_1=\cdots=g^{(k)}_{k-2}=0$, $g^{(k)}_{k-1}=g^{(k)}_k=1$ and for n > k $\geq$ 2, $g^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n-2}+{\cdots}+g^{(k)}_{n-k}$. And the k-Lucas sequence {$l^{(k)}_n$} is defined as $l^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n+k-1}$ for $n{\geq}1$. In this paper, we give a representation of nth k-Lucas $l^{(k)}_n$ by using determinant.

• 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.

• Journal of Convergence for Information Technology
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• v.9 no.11
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• pp.227-233
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• 2019

The purpose of this study is to evaluate the quality of chest compression by conducting comparison research between mechanical chest compressor(LUCAS) and manuale cardiopulmonary resuscitation(CPR) in a out-of-hospital environment and suggest effective advanced cardiac life support using mechanical chest compressors. For this, a out-of-hospital cardiac arrest was simulated with a team of 3 ambulance workers, and manuale CPR and CPR using LUCAS were performed on site and during transport in an ambulance. The research results are as follows: the comparison of manuale CPR between on site and in an ambulance revealed that on-site manuale CPR showed significant differences in the average compression depth, compression rate, and relaxation rate. Second, the comparison between manuale CPR and LUCAS in an ambulance showed significant differences in the average compression depth, compression rate, the number of compression per minute.

• 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.

• Smart Structures and Systems
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• v.31 no.4
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• pp.409-419
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• 2023

Structural integrity can be accessed from dynamic deformations of structures. Moreover, dynamic deformations can be acquired from non-contact sensors such as video cameras. Kanade-Lucas-Tomasi (KLT) algorithm is one of the commonly used methods for motion tracking. However, averaging throughout the extracted features would induce bias in the measurement. In addition, pixel-wise measurements can be converted to physical units through camera intrinsic. Still, the depth information is unreachable without prior knowledge of the space information. The assigned homogeneous coordinates would then mismatch manually selected feature points, resulting in measurement errors during coordinate transformation. In this study, a two-stage optimization method for video-based measurements is proposed. The manually selected feature points are first optimized by minimizing the errors compared with the homogeneous coordinate. Then, the optimized points are utilized for the KLT algorithm to extract displacements through inverse projection. Two additional criteria are employed to eliminate outliers from KLT, resulting in more reliable displacement responses. The second-stage optimization subsequently fine-tunes the geometry of the selected coordinates. The optimization process also considers the number of interpolation points at different depths of an image to reduce the effect of out-of-plane motions. As a result, the proposed method is numerically investigated by using a truss bridge as a physics-based graphic model (PBGM) to extract high-accuracy displacements from recorded videos under various capturing angles and structural conditions.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.1103-1113
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• 2009

We know that the first digits sequence of fibonacci numbers obey Benford's law. For the sequence in which the first two numbers are the arbitrary integers and the recurrence relation $a_{n+2}=a_{n+1}+a_n$ is satisfied, we can find that the first digits sequence of this sequence obey Benford's law. Also, we can find the stucture of the first digits sequence of this sequence with the exploratory data analysis tools.