• Kyungpook Mathematical Journal
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• 제56권2호
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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.

• 대한수학회논문집
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• 제31권3호
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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 $n,k{\geq}1$.

• 대한수학회지
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• 제42권1호
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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 $L_n$.

• 대한수학회논문집
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• 제32권3호
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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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• 제28권5_6호
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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.

• 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.

• 융합정보논문지
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• 제9권11호
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• pp.227-233
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• 2019

본 연구는 병원 전 환경에서 기계식 가슴압박기(LUCAS)와 수기심폐소생술의 비교실험을 통해 가슴압박의 질을 평가하고 기계적 가슴압박기를 사용한 효과적인 전문심장소생술을 제안하는데 그 목적이 있다. 병원 전 심정지상황을 가정하고 구급대원이 3인 1조로 현장에서 수기심폐소생술과 LUCAS를 이용한 심폐소생술을 적용하고, 구급차로 이송하며 수기심폐소생술과 LUCAS를 이용한 심폐소생술을 시행하였다. 연구결과는 다음과 같다. 첫째, 현장과 이송중의 수기심폐소생술의 비교결과 현장에서 수기심폐소생술이 평균압박깊이와 압박률, 이완율에서 유의한 차이가 나타났다(p<.001). 둘째, 현장에서 수기심폐소생술과 LUCAS를 비교한 결과 LUCAS가 압박률, 이완율에서 유의한 차이가 나타났다(p<.001). 셋째, 구급차로 이송중 수기심폐소생술과 LUCAS를 비교한 결과 평균압박깊이, 압박률, 분당압박횟수에서 유의한 차이를 보였다(p<.001). 위와 같은 결과로 보아 LUCAS는 적절한 압력으로 가슴압박을 수행할 수 있고, 그 동안 구급대원의 전문기도기 삽입, 정맥로 확보 등의 전문심장소생술을 추가적으로 수행할 수 있으며 환자의 소생률을 높이는데 기여할 것이다.

• 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.

• Smart Structures and Systems
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• 제31권4호
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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.

• 응용통계연구
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• 제22권5호
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• pp.1103-1113
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• 2009

피보나치수열의 첫 숫자수열이 벤포드법칙을 따름은 알려진 사실이다. 이러한 피보나치수열을 확장하여 임의의 두개의 자연수를 정하고 재귀식 $a_{n+2}=a_{n+1}+a_n$을 만족하는 수열을 만들었을 때 이 수열의 첫 숫자수열이 벤포드법칙을 만족하는 지를 확인하고 이러한 수열의 첫 숫자수열의 구조를 탐색적 자료분석의 입장에서 살펴보았다.