• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.749-755
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• 2009

In this paper, we investigate the invariant interval, periodic character, semicycle and global attractivity of all positive solutions of the equation $Y_{n+1}\;=\;\frac{p+qy_{n-k}}{1+y_n+ry_{n-k}}$, n = 0, 1, ..., where the parameters p, q, r and the initial conditions $y_{-k}$, ..., $y_{-1}$, $y_0$ are positive real numbers, k $\in$ {1, 2, 3, ...}. It is worth to mention that our results solve the open problem proposed by Kulenvic and Ladas in their monograph [Dynamics of Second Order Rational Difference Equations: with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2002]

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.531-539
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• 2009

In this paper we first present a structure theorem for an infinite locally finite 3-connected VAP-free planar graph, and in connection with this result we study a possible classification of infinite locally finite planar graphs by reducing modulo finiteness.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.149-153
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• 2004

본 연구에서는 태풍의 천애역 내습시 태풍의 풍역이동과 위험반경내의 풍향 풍속 변화를 해안지형의 특성에 따라 파랑이 충분히 발달할 수 있는 해역을 대상으로 발생가능한 풍향별 취송거리 및 관측된 풍향 풍속으로 천해설계파를 산정하기 위한 한가지 수치해석기법을 소개한다. 이를 통해 구조물 전면에서의 파고계산을 위해서는 구역을 결정할 때 해역의 개방 정도 및 폐쇄성과 태풍중심 이동경로가 천해설계파 산정시 중요함을 강조 할 수 있다. 실시간 해석기법에 대해서 부가적인 재해석 절차가 필요한 상황이지만 본 연구의 해석기법은 연안 해안지역의 천해설계파를 추정함에 있어 태풍의 천해역 통과시 풍역의 변화특성과 이를 고려한 파랑의 불획 정성을 극복하고 보완 할 수 있는 천해설계파 산정을 위한 기초적 연구로서 활용될 수 있을 것이라 판단된다.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.153-164
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• 2010

We study the global asymptotic stability, the character of the semicycles, the periodic nature and oscillation of the positive solutions of the difference equation $x_{n+1}=\frac{p+x_{n-k}}{q+x_n}+\frac{x_{n-k}}{x_n}$, n=0, 1, 2, ${\cdots}$. where p, q ${\in}$ (0, ${\infty}$), q ${\neq}$ 2, k ${\in}$ {1, 2, ${\cdots}$} and the initial values $x_{-k}$, ${\cdots}$, $x_0$ are arbitrary positive real numbers.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.105-115
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• 2003

An infinite locally finite plane graph is called an LV-graph if it is 3-connected and VAP-free. If an LV-graph G contains no unbounded faces, then we say that G is a 3LV-graph. In this paper, a structure theorem for an LV-graph concerning the existence of a sequence of systems of paths exhausting the whole graph is presented. Combining this theorem with the early result of the author, we obtain a necessary and sufficient conditions for an infinite VAP-free planar graph to be a 3LV-graph as well as an LV-graph. These theorems generalize the characterization theorem of Thomassen for infinite triangulations.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.787-797
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• 2007

In this paper, the following fourth-order rational difference equation $$x_{n+1}=\frac{{x_n^b}+x_n-2x_{n-3}^b+a}{{x_n^bx_{n-2}+x_{n-3}^b+a}$$, n=0, 1, 2,..., where a, b ${\in}$ [0, ${\infty}$) and the initial values $X_{-3},\;X_{-2},\;X_{-1},\;X_0\;{\in}\;(0,\;{\infty})$, is considered and the rule of its trajectory structure is described clearly out. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is $1^+,\;1^-,\;1^+,\;4^-,\;3^+,\;1^-,\;2^+,\;2^-$ in a period, by which the positive equilibrium point of the equation is verified to be globally asymptotically stable.