• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.235-239
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• 2012

Let $f$ be an Axiom A difeomorphism of a closed 2- dimensional smooth manifold M: We show that $f$ has the limit shadowing property if and only if $f$ satisfies the $C^0$ transversality condition.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.257-262
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• 2010

Let f be a $C^2$-diffeomorphism on a closed surface which satisfies the Axiom A. Then f is in the $C^2$-interior of the set of all diffeomorphisms having the inverse shadowing property with respect to the class of the continuous methods if and only if f satisfies the strong transversality condition.

• Structural Engineering and Mechanics
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• v.71 no.2
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• pp.119-129
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• 2019

Optimum shape and length of laterally loaded piles can be obtained with different optimization techniques. In particular, the Fully Stress Design method (FSD) is an optimality condition that allows to obtain the optimum shape of the pile, while the optimum length can be obtained through a transversality condition at the pile lower end. Using this technique, the structure is analysed by finite elements and shaped through the FSD method by contemporarily checking that the transversality condition is satisfied. In this paper it is noted that laterally loaded piles with optimum shape and length have some peculiar characteristics, depending on the type of cross-section, that allow to design them with simple calculations without using finite element analysis. Some examples illustrating the proposed simplified design method of laterally loaded piles with optimum shape and length are introduced.

• 전기의세계
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• v.19 no.2
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• pp.21-23
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• 1970

Necessary conditions of optimal distributed parameter control systems, Hamiltons coanonical equations, welerstress condition, transversality condition and boundary condition are obtained, when the control function is constrained and the performance index takes on the general form. Also it is concluded that the lumped parameter system is the special case of the distributed parameter system.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.193-201
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• 1997

The paper presens results on the perturbation problem of invariant manifolds of differential equations. It is well-known that if there is a pseudohyperbollic structure on an invariant manifold then one is strongly indestructible. The set of strongly inderstructible invariant manifolds is wider than the set of persistent (normally hyperbolic) manifolds. The following theorem is main result of the paper: if the condition of transversality holds on an invariant manifold, except, possibly, for the non-degenerate strong sources and non-degenerate strong sinks, then there is the pseudohyperbolic structure on the invariant manifold. From this it follows the conditions for the indestructibility of locally non-unique invariant manifolds. An example is considered.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.201-205
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• 2015

We show that if a regular map belongs to the $C^1$-interior of the set of all Kupka-Smale differentiable maps then it satisfis Axiom A and the strong transverality condition.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.61-73
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• 2002

We consider the inverse shadowing property of a dynamical system which is an "inverse" form of the shadowing property of the system. In particular, we show that every Morse-Smale system f on a compact smooth manifold has the inverse shadowing property with respect to the class $\mathcal{T}_h(f)$ of continuous methods generated by homeomorphisms, but the system f does not have the inverse\mathrm{T} shadowing property with respect to the class $\mathcal{T}_c(f)$ of continuous methods.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.563-571
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• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.121-130
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• 2018

This study deals with optimum geometry design of laterally loaded piles in a Winkler's medium through the Fully Stressed Design (FSD) method. A numerical algorithm distributing the mass by means of the FSD method and updating the moment by finite elements is implemented. The FSD method is implemented here using a simple procedure to optimise the beam length using an approach based on the calculus of variations. For this aim two conditions are imposed, one transversality condition at the bottom end, and a one sided constraint for moment and mass distribution in the lower part of the beam. With this approach we derive a simple condition to optimise the beam length. Some examples referred to different fields are reported. In particular, the case of laterally loaded piles in Geotechnics is faced.

• Journal of Electrical Engineering and Technology
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• v.8 no.4
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• pp.719-728
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• 2013

Probabilistic assessment of voltage stability margin (VSM) with existence of correlated wind speeds is investigated. Nataf transformation is adopted to establish wind speed correlation (WSC) model. Based on the saddle-node bifurcation transversality condition equations and Monte Carlo simulation technique, probability distribution of VSM is determined. With correlation coefficients range low to high value, the effect of WSC on VSM is studied. In addition, two risk indexes are proposed and the possible threat caused by WSC is evaluated from the viewpoint of risk analysis. Experimental results show that the presence of correlated wind speeds is harmful to safe and stable operation of a power system as far as voltage stability is concerned. The achievement of this paper gives a detailed elaboration about the influence of WSC on voltage stability and provides a potentially effective analytical tool for modern power system with large-scale wind power sources integration.