• 대한수학회보
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• 제56권3호
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• pp.597-607
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• 2019

In this article, we consider properties of transcendental meromorphic solutions of the complex differential-difference equation $$P_n(z)f^{(n)}(2+{\eta}_n)+{\cdots}+P_1(z)f^{\prime}(z+{\eta}_1)+P_0(z)f(z+{\eta}_0)=0$$, and its non-homogeneous equation. Our results extend earlier results by Liu et al. [9].

• 대한수학회지
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• 제42권6호
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• pp.1121-1136
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• 2005

Nonstandard finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with periodic boundary conditions, which are of the type $$U_t\;+\;\frac{{\partial}^2}{{\partial}x^2} g(u,\;U_x,\;U_{xx})\;=\;\frac{{\partial}^{\alpha}}{{\partial}x^{\alpha}}f(u,\;u_x),\;{\alpha}\;=\;0,\;1,\;2$$. Stability and error estimate of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem. Three examples are provided to apply the nonstandard finite difference schemes.

• 대한수학회지
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• 제44권6호
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• pp.1429-1440
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• 2007

Let ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ be a multiple Kravchuk polynomial with respect to r discrete Kravchuk weights. We first find a lowering operator for multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ in which the orthogonalizing weights are not involved. Combining the lowering operator and the raising operator by Rodrigues# formula, we find a (r+1)-th order difference equation which has the multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ as solutions. Lastly we give an explicit difference equation for ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ for the case of r=2.

• 정보보호학회논문지
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• 제12권1호
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• pp.21-32
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• 2002

본 논문에서는 소수 p의 멱승인 q에 대해서 주기 $q_n$-1인 q진 시퀸스(d-동차함수)로부터 Singer 파라미터 equation omitted를 갖는 새로운 순회차집합을 생성하였다. q가 3의 멱승일 때, Helleseth, Kumar, Martinsen의 주기가 $q_n$-1이고, 이상적인 자기상관성질을 갖는 3진 시퀸스로부터 Singer 파라미터 equation omitted를 갖는 새로운 순회 차집합을 생성시킨다.

• 대한수학회보
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• 제40권3호
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• pp.489-501
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• 2003

In this paper we shall consider the nonlinear delay difference equation $\Delta({p_n}{\Deltax_N})\;+\;q_nf(x_{n-\sigma})\;=\;0,\;n\;=\;0,\;1,\;2,\;...$ when (equation omitted). We will establish some sufficient conditions which guarantee that every solution is oscillatory or converges to zero.

• 대한수학회논문집
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• 제29권1호
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• pp.195-204
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• 2014

We consider a functional difference equation and use fixed point theory to analyze the stability of its zero solution. In particular, our study focuses on the nonlinear delay functional difference equation x(t + 1) = a(t)g(x(t - r)).

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.201-216
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• 2007

In this paper we consider the difference equation $$x_{n+1}=\frac{a+bx_{n-k}\;-\;cx_{n-m}}{1+g(x_{n-l})}$$ where a, b, c are nonegative real numbers, k, l, m are nonnegative integers and g(x) is a nonegative real function. The oscillatory and periodic character, the boundedness and the stability of positive solutions of the equation is investigated. The existence and nonexistence of two-period positive solutions are investigated in details. In the last section of the paper we consider a generalization of the equation.

• 한국소음진동공학회논문집
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• 제12권8호
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• pp.626-631
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• 2002

A modified equation for the evaluation of discomfort of a seated human body exposed to differential vibration at the seat and the floor was proposed in this paper. Through the review and analysis of the preceding studies, effect of phase difference between the seat and the floor vibration on discomfort were quantitatively identified. The phase effect was shown to be governed by not only phase difference between the two vibrations but both their frequency and the magnitude, which means the present equation for the evaluation of perceptual amount of vibration provided by ISO 2631-1 should be modified. The proposed equation was developed such that the correction function was multiplied to the present equation. The correction function consisted of three parts, each of them represented the effect by phase difference, frequency and vibration magnitude on discomfort respectively.

• 대한수학회논문집
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• 제30권4호
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• pp.447-456
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• 2015

In this paper, we investigate the differential-difference equation $(f(z+c)-f(z))^2+P(z)^2(f^{(k)}(z))^2=Q(z)$, where P(z), Q(z) are nonzero polynomials. In addition, we also investigate Fermat type q-difference differential equations $f(qz)^2+(f^{(k)}(z))^2=1$ and $(f(qz)-f(z))^2+(f^{(k)}(z))^2=1$. If the above equations admit a transcendental entire solution of finite order, then we can obtain the precise expression of the solution.

• 대한수학회보
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• 제43권2호
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• pp.253-263
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• 2006

In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.