• Structural Engineering and Mechanics
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• 제26권4호
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• pp.377-392
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• 2007

A discrete sliding mode control (SMC) method based on hybrid model of neural network and nominal model is proposed to reduce the vibration of flexible structures, which is a robust active controller developed by using a sliding manifold approach. Since the thick boundary layer will reduce the virtue of SMC, the multilayer feed-forward neural network is adopted to model the uncertainty part. The neural network is trained by Levenberg-Marquardt backpropagation. The design objective of the sliding mode surface is based on the quadratic optimal cost function. In course of running, the input signal of SMC come from the hybrid model of the nominal model and the neural network. The simulation shows that the proposed control scheme is very effective for large uncertainty systems.

• 대한수학회보
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• 제20권1호
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• pp.51-54
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• 1983

Let M be a n-dimensional compact Riemannian manifold with sectional curvature bounded below by one. Then Li and Zhong[3], and Li and Treibergs [4] proved that if the first eigenvalue of the Laplacian .lambda.$_{1}$ is less than some universal constant and if n.leq.4, then M is diffeomorphic to the n-sphere S$^{n}$ . The purpose of this paper is to prove this pinching theorem for all n with some extra condition.

• 대한수학회보
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• 제46권2호
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• pp.311-319
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• 2009

Let H be a Hilbert space which is the direct sum of five closed subspaces $X_0,\;X_1,\;X_2,\;X_3$ and $X_4$ with $X_1,\;X_2,\;X_3$ of finite dimension. Let J be a $C^{1,1}$ functional defined on H with J(0) = 0. We show the existence of at least four nontrivial critical points when the sublevels of J (the torus with three holes and sphere) link and the functional J satisfies sup-inf variational inequality on the linking subspaces, and the functional J satisfies $(P.S.)^*_c$ condition and $f|X_0{\otimes}X_4$ has no critical point with level c. For the proof of main theorem we use the nonsmooth version of the classical deformation lemma and the limit relative category theory.

• 대한기계학회논문집
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• 제19권2호
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• pp.537-547
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• 1995

Numerical study on the chaotic stirring of viscous flow in an alternately driven cavity has been performed. Even under the Stokes-flow assumption, the inherent singularity at the corners made the problem not so easily accessible. With some special treatments to the region near the corners, the biharmonic equation was solved numerically by using the fully implicit method. The velocity field was then used in obtaining the trajectories of passive particles for studying the stirring effect. The three tools developed in the field of the nonlinear dynamics and chaos, that are the Poincare sections, the unstable manifolds, and the Lyapunov exponents, were used in analysing the stirring effect. It was shown that the unstable manifolds obtained in this study well fit the experimental results given by the previous investigators. It is predicted that the best stirring can be obtained when the aspect ratio a is near 0.8 and the dimensionless period T is in the range 4.3 - 4.7.

• 호남수학학술지
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• 제26권4호
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• pp.509-532
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• 2004

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6, 7. This paper is the first part of the following series of two papers, in which we obtain a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor, with main emphasis on the derivation of powerful and useful recurrence relations which hold in 8-dimensional Einstein's unified field theory(i.e., 8-g-UFT): I. The recurrence relations in 8-g-UFT II. The Einstein's connection in 8-g-UFT All considerations in these papers are restricted to the second class only, since the case of the first class are done in [1], [2] and the case of the third class, the simplest case, was already studied by many authors.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.781-802
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• 2011

Of concern in the paper is a Holling-Tanner predator-prey model with modified version of the Leslie-Gower functional response. Dynamical behaviours such as stability, permanence and Hopf bifurcation have been carried out deterministically. Using the normal form theory and center manifold theorem, the explicit formulae determining the stability and direction of Hopf bifurcation have been derived. The deterministic model is extended to a stochastic one by perturbing the growth equation of prey and predator by white and colored noises and finally the mean square stability of the stochastic model systems is investigated analytically. An extensive quantitative analysis has been performed based on numerical computation so as to validate the applicability of the proposed mathematical model.

• 한국전산유체공학회지
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• 제20권4호
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• pp.58-62
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• 2015

Recent studies on wall-bounded shear flow have emphasized the significance of the stable manifold of simple nonlinear invariant solutions to the Navier-Stokes equation in the formation of the boundary between the laminar and turbulent regions in state space. In this paper we present newly discovered homoclinic orbits of the Kawahara and Kida(2001) periodic solution in plane Couette flow. We show that as the Reynolds number decreases a pair of homoclinic orbits move closer to each other until they disappear to exhibit homoclinic tangency.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.605-618
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• 2009

A stage-structured predator-prey system with time delay and Beddington-DeAngelis functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.

• 한국자동차공학회논문집
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• 제4권4호
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• pp.140-146
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• 1996

A large portion(above 70%) fo the hydrocorbon and NOx emissions for a typical vehicle occur mainly before the conventional underbody catalyst reaches activation temperature. To meet the stringent regulation as EC stage 2, the emissions produced during this period must be reduced. One of alternative techniques is to place CCC(Close-Coupled Catalyst) near the exhaust manifold. In this study, the characteristics of CCC are observed through EEC mode.

• 약학회지
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• 제37권4호
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• pp.356-361
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• 1993

A sensitive method for the determination of methamphetamine(MA) and amphetamine(AM) in hair was developed by gas chromatography/mass spectrometry using stable isotope-labeled internal standards, amphetamine-d$_{5}$ and methamphetamine-d$_{5}$. Hair sample was washed with MeOH, incubated with MeOH(I% HCI) overnight at $37^{\circ}C$ while stirring and extracted using solid phase extraction column on a vacuum manifold. The extract obtained was pentafluoropropionated, and applied to GC/MS. The calibration curves of MA and AM were linear from 2.5 to 250 ng (r>0.99 for both). The limit of detection was 0.1 ng/mg in hair and cut-off level was set at 0.25 ng/mg for both. Hair samples of 27 MA abusers showed positive results in the range 0.7 to 106.8 ng/mg. AM, its metabolite, was detected in 20 out of 27 samples. The ratio of MA versus AM was 4.6~38.3 in specimens. Hair analysis for methamphetamine by GC/MS is an effective method for identifying long-term drug abusers.