• 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 $n,k{\geq}1$.

• 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.

• 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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• 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.

• 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.

• Journal of Microbiology and Biotechnology
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• 제20권9호
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• pp.1259-1265
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• 2010

The filamentous cyanobacterium Arthrospira platensis strain MMG-9 was isolated from a rice field. The ability of this strain to synthesize the bioactive compound indole-3-acetic acid (IAA) was demonstrated. IAA was extracted from the culture of A. platensis strain MMG-9 and its identity was confirmed by thin-layer chromatography (TLC) as well as by high-performance liquid chromatography (HPLC). The IAA precursor L-tryptophan was required for IAA biosynthesis. Released IAA increased with the increase of the initial concentration of L-tryptophan in the medium and with the incubation time. A. platensis strain MMG-9 accumulated more IAA than it released into the medium. The bioactivity of the secreted IAA was shown by its effect on the formation of roots by Pisum sativum. There was a significant positive effect of the supernatant of cultures of A. platensis strain MMG-9 on the number of lateral roots of P. sativum, whereas a negative effect on root length was observed.

• Journal of Microbiology and Biotechnology
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• 제24권8호
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• pp.1015-1025
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• 2014

Microorganisms that live in the rhizosphere play a pivotal role in the functioning and maintenance of soil ecosystems. The study of rhizospheric cyanobacteria has been hampered by the difficulty to culture and maintain them in the laboratory. The present work investigated the production of the plant hormone indole-3-acetic acid (IAA) and the potential of biofilm formation on the rhizoplane of pea plants by two cyanobacterial strains, isolated from rice rhizosphere. The unicellular cyanobacteria Chroococcidiopsis sp. MMG-5 and Synechocystis sp. MMG-8 that were isolated from a rice rhizosphere, were investigated. Production of IAA by Chroococcidiopsis sp. MMG-5 and Synechocystis sp. MMG-8 was measured under experimental conditions (pH and light). The bioactivity of the cyanobacterial auxin was demonstrated through the alteration of the rooting pattern of Pisum sativum seedlings. The increase in the concentration of L-tryptophan and the time that this amino acid was present in the medium resulted in a significant enhancement of the synthesis of IAA (r > 0.900 at p = 0.01). There was also a significant correlation between the concentration of IAA in the supernatant of the cyanobacteria cultures and the root length and number of the pea seedlings. Observations made by confocal laser scanning microscopy revealed the presence of cyanobacteria on the surface of the roots and also provided evidence for the penetration of the cyanobacteria in the endorhizosphere. We show that the synthesis of IAA by Chroococcidiopsis sp. MMG-5 and Synechocystis sp. MMG-8 occurs under different environmental conditions and that the auxin is important for the development of the seedling roots and for establishing an intimate symbiosis between cyanobacteria and host plants.

• Parasites, Hosts and Diseases
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• 제49권4호
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• pp.427-430
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• 2011

The aim of this study was to test the susceptibility of mice to Trypanosoma evansi treated with human plasma containing different concentrations of apolipoprotein L-1 (APOL1). For this experiment, a strain of T. evansi and human plasma (plasmas 1, 2, and 3) from 3 adult males clinically healthy were used. In vivo test used 50 mice divided in 5 groups (A to E) with 10 animals in each group. Animals of groups B to E were infected, and then treated with 0.2 ml of human plasma in the following outline: negative control (A), positive control (B), treatment with plasma 1 (C), treatment with plasma 2(D), and treatment with plasma 3 (E). Mice treated with human plasma showed an increase in longevity of $40.9{\pm}0.3$ (C), $20{\pm}9.0$ (D) and $35.6{\pm}9.3$ (E) days compared to the control group (B) which was $4.3{\pm}0.5$ days. The number of surviving mice and free of the parasite (blood smear and PCR negative) at the end of the experiment was 90%, 0%, and 60% for groups C, D, and E, respectively. The quantification of APOL1 was performed due to the large difference in the treatments that differed in the source plasma. In plasmas 1, 2, and 3 was detected the concentration of 194, 99, and 115 mg/dl of APOL1, respectively. However, we believe that this difference in the treatment efficiency is related to the level of APOL1 in plasmas.