• Kyungpook Mathematical Journal
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• 제27권1호
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• pp.7-13
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• 1987

This paper is a study of the oscillatory and asymptotic behaviour of solutions of the second order nonhomogeneous linear differential equation y"+P(x)y=f(x), and the associated homogeneous equation. Conditions are determined, under which the nonhomogeneous equation is oscillatory if and only if the homogeneous equation is oscillatory.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.87-99
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• 2002

We consider the problem of oscillation and nonoscillation solutions for unstable type second-order neutral difference equation : $\Delta^2(x(n))-p(n)x(n-\tau))=q(n)x(g(n))$. (1) In this paper, we obtain some conditions for the bounded solutions of Eq(1) to be oscillatory and for the existence of the nonoscillatory solutions.

• 대한기계학회논문집B
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• 제25권6호
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• pp.804-810
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• 2001

Transition of flows in natural convection in a horizontal cylindrical annulus is investigated for the fluid with Pr=0.2. The unsteady streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady crescent-shaped eddy flow bifurcates to a time-periodic flow with like-rotating eddies. After the first Hopf bifurcation, however, a reverse transition from oscillatory to a steady flow occurs by the flow pattern variation. Hysteresis phenomenon occurs between the solution branches of up-scan and down-scan stages, and dual solutions with one steady and one oscillatory flow are found. Overall Nusselt of the flows at the flows at the down-scan stage is greater than that at the up-scan stage.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권1호
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• pp.53-59
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• 1995

Consider a solution y(t) of the nonlinear equation (E) y" ＋ f(t, y) = 0. A solution y(t) is said to be oscillatory if for every T ＞ 0 there exists $t_{0}$ ＞ T such that y($t_{0}$) = 0. Let F be the class of solutions of (E) which are indefinitely continuable to the right, i.e. y $\in$ F implies y(t) exists as a solution to (E) on some interval of the form [t$\sub$y/, $\infty$). Equation (E) is said to be oscillatory if each solution from F is oscillatory.(omitted)

• 한국식품저장유통학회지
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• 제30권5호
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• pp.785-796
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• 2023

The aim of this study was to elucidate chemical structures and rheological properties of arabinogalactans (AGs) isolated from three legumes including black gram (BG), great northern bean (GNB), and California small white bean (CSWB). The ratio of galactose to arabinose (G/A) in three legumes increased in the order of BG > GNB > CSWB. The rheological measurements of 1-5% (w/v) AG solutions revealed Newtonian and non-Newtonian flow behaviors. BG exhibited yield stress, indicating plastic behavior. Small-amplitude oscillatory tests indicated viscoelastic properties of BG, GNB, and CSWB ranging from solid-like, paste-like, and liquid-like behaviors, respectively. Small-strain oscillatory tests were conducted to assess the structure recovery of the AGs after pre-shearing. G" values of BG and GNB increased, but those of CSWB remained constant after shearing. These results suggest that the chemical structures of the AGs, particularly their G/A ratios, influence their rheological properties.

• 한국전산유체공학회지
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• 제5권3호
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• pp.40-46
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• 2000

Natural convection in a wide-gap horizontal annulus is considered, and the transition of flows from steady to oscillatory convection is investigated for the fluid with Pr=0.1. The unsteady streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady crescent-shaped flow bifurcates to a time-periodic flow with like-rotating eddies. And afterwards, a transition to an oscillatory multicellular flow with a counter-rotating eddy on the top of the annulus occurs. A transition from steady to an oscillatory flow occurs, but dual solutions and hysteresis phenomena are not observed.

• 융합신호처리학회논문지
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• 제9권1호
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• pp.82-88
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• 2008

본 논문은 주기적 진동 문제를 연구하기 위해 Runge-Kutta(RK)-Butcher 알고리듬이 소개되었다. RK-Butcher 알고리듬을 사용하여 얻어진 시뮬레이션 결과와 고전적인 4차 RK(4) 방법을 통해 얻은 결과들을 제안한 알고리듬의 성능을 확인하기 위하여 몇몇 주기적 진동 문제들의 정확한 해와 비교하였다. RK-Butcher 알고리듬의 시뮬레이션 결과는 항상 문제의 정확한 해 RK(4) 방법보다 더 근접한 결과를 줌이 확인되었다. 정확도 측면에서 RK-Butcher 알고리듬이 RK(4) 방법과 비교해볼 때 우수함을 알 수 있다. 제안한 RK-Butcher 알고리듬은 프로그램 언어로 쉽게 구현할 수 있으며 임의 시간에 종료해도 훌륭한 근사적인 해를 얻을 수 있다. RK-Butcher 알고리듬은 짧은 시간내에 이상적인 정확한 해에 근접한 결과를 주기 때문에 궤도 와 두 물체의 문제를 연구하는데 훌륭한 수치 알고리듬으로 적용 가능하다.

• Journal of Biosystems Engineering
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• 제18권3호
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• pp.275-287
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• 1993

The flow characteristics of the transitional oscillatory flows are investigated analytically and experimentally in the entrance region of a square duct. The systems of conservation equations are analytically solved by linearizing the non-linear convective terms for the developing transitional oscillatory flows in a square duct. The analytical solutions are obtained in the form of infinite series for the velocity profiles. The experimental study for the air flow in a square duct is carried out to measure the velocity profiles and waveforms by using a hot-wire anemometer with the data acquisition and processing systems. The theoretical and experimental results provide the major characteristics of the developing transitional oscillatory flows, such as velocity profiles, velocity waveforms, and entrance length. The velocity profiles in the decelerating phase are larger than those in the accelerating phase for the developing transitional oscillatory flows. The correlations of the entrance length of the transitional oscillatory flows in a square duct are found to be $Le/Dh=K{\cdot}Re_{os}/2({\omega}^+)^2$, where K is 1.23 of an experimental constant.

• Korean Journal of Mathematics
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• 제12권2호
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• pp.155-163
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• 2004

In this paper, we study oscillation and nonoscillation criteria of solutions for the following nonlinear differential equation $$\[\frac{1}{p(t)}(x^{\prime}(t))^{{\mu}}\]^{\prime}+q(t)x(t)^{{\mu}}=0$$ where ${\mu}$ with ${\mu}{\geq}1$ is a quotient of odd integers.

• 대한수학회논문집
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• 제18권4호
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• pp.755-765
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• 2003

Krylov-Bogoliubov-Mitropolskii method has been extended to obtain asymptotic solution of n-th order nonlinear differential system characterized by certain non-oscillatory processes. The damping force is considered in such a manner that one of the characteristic roots of the linear system becomes small and others are in integral multiple. The method is illustrated by an example. The solutions for different initial conditions show a good agreement with those obtained by numerical method.