• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1453-1467
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• 2007

By means of a Riccati transform some oscillation or nonoscillation criteria are established for nonlinear differential equations of second order $$(E_1)\;[p(t)|x#(t)|^{\alpha}sgn\;x#(t)]#+q(t)|x(\tau(t)|^{\alpha}sgn\;x(\tau(t))=0$$. $$(E_2),\;(E_3)\;and\;(E_4)\;where\;0<{\alpha}$$ and $${\tau}(t){\leq}t,\;{\tau}#(t)>0,\;{\tau}(t){\rightarrow}{\infty}\;as\;t{\rightarrow}{\infty}$$. In this paper we improve some previous results.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.245-256
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• 2005

We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.405-417
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• 2005

In this paper, the oscillation and asymptotic stability behavior of a third order linear impulsive equation are investigated. A lemma is presented to deal with the sign relation of the nonoscillatory solutions and their derived functions. By the lemma explicit sufficient conditions are obtained for all solutions either oscillating or asymptotically tending to zero. Two illustrative examples are proposed to demonstrate the effectiveness of the conditions.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.945-949
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• 2003

In this paper, we present that now and heat transfer characteristics of oscillatory impinging jet which have been numerically investigated using parallel computations. Numerical value were obtained for dimensionless distance H=4, dimensionless outlet length L=45 and Reynolds number Re= 1500. It was found that the oscillatory impinging jet generated the regular heat transfer area even though the maximum heat transfer is lower than nonoscillatory impinging jet. We also found that heat transfer depends on the period of nozzle for the oscillatory impinging jet.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.477-488
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• 2006

In this paper, the authors first classify all nonoscillatory solutions of equation (1) $${\Delta}^2|{\Delta}^2{_{y_n}}|^{{\alpha}-1}{\Delta}^2{_{y_n}}+q_n|y_{{\sigma}(n)}|^{{\beta}-1}y_{{\sigma}(n)}=o,\;n{\in}\mathbb{N}$$ into six disjoint classes according to their asymptotic behavior, and then they obtain necessary and sufficient conditions for the existence of solutions in these classes. Examples are inserted to illustrate the results.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.49-62
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• 2007

In this paper, the oscillation and existence of nonoscillatory solutions of odd order difference equations with nonlinear neutral terms are studied respectively. Some new criteria are established. Furthermore, some examples are given to illustrate the advance of our results.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.103-120
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• 2002

A second order upwind method for linear hyperbolic systems is studied in this paper. The method approximates solutions as piecewise linear functions, and state variables and slopes of the linear functions for next time step are computed separately. We present a new method for the computation of slopes, derived from an upwinding difference for a derivative. For nonoscillatory solutions, a monotonicity algorithm is also proposed by modifying an existing algorithm. To validate our second order upwind method, numerical results for linear advection equations and linear systems for elastic and acoustic waves are given.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.3
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• pp.131-137
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• 1996

The existing digital governors are in the beginning stage. Placing the focus on the marine site, most of the digital governors developed are still using the simple PID algorithm. But, the performance of a diesel engine is widely changed according to the parameters of the PID controller. So, this article describes a new method to adjust the parameters of the PID controller in a marine digital governor. In this paper, the diesel engine is considered as a nonoscillatory second order system. A new method to adjust the parameters of the PID controller for speed control of a diesel engine is proposed by means of the model matching method. Also, the simulations by numerical methods are carried out in cases of the exact understanding or out of the parameters of a diesel engine respectively. And this paper confirms that the proposed new method here is superior to Ziegler & Nichols's method through the comparisons and analysis of the characteristics of indicial responses.