• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.285-293
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• 2014

Let M be a closed, symplectic connected Riemannian manifold and f a symplectomorphism on M. We prove that if f is $C^1$-stably weak shadowable on M, then the whole manifold M admits a partially hyperbolic splitting.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.581-587
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• 2013

Let ${\Lambda}$ be a robustly transitive set of a diffeomorphism $f$ on a closed $C^{\infty}$ manifold. In this paper, we characterize hyperbolicity of ${\Lambda}$ in $C^1$-generic sense.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.961-969
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• 2021

In this paper, we study the ∆-convergence and strong convergence of SP-iteration scheme involving a nonexpansive mapping in partially ordered hyperbolic metric spaces. Also, we give an example to support our main result and compare SP-iteration scheme with the Mann iteration and Ishikawa iteration scheme. Thus, we generalize many previous results.

• Journal of the Korean Institute of Navigation
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• v.13 no.1
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• pp.1-10
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• 1989

Nowadays Hyperbolic Navigation System-LORAN, DECCA, OMEGA, OMEGA-is available on the ocean, and Spherical Navigation System, GPS (Global Positioning System) is operated partially. Hyperbolic Navigation System has the blind area near the base line extention because divergence rate of hyperbola is infinite theoretically. The Position Accuracy is differ from the cross angle of LOP although each LOP has the same error of quantity. GDOP(Geometric Dilution of Precisoin) is used to estimate the position accuracy according to the cross angle of LOP and LOP error. Hyperbola and ellipse are crossed at right angle everywhere. Hyperbola and ellipse are used to LOP in Rectangular Navigation System. The equation calculating the GDOP of rectangular Navigation System is induced and GDOP diagram is completed in this paper. A scheme that can improve the position accuracy in the blind area of Hyperboic Navigation System using the Rectangular Navigation System is proposed through the computer simulation.

• Journal of Advanced Marine Engineering and Technology
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• v.40 no.5
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• pp.389-396
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• 2016

The theory of Fourier heat conduction predicts accurately the temperature profiles of a system in a non-equilibrium steady state. However, in the case of transient states at the nanoscale, its applicability is significantly limited. The limitation of the classical Fourier's theory was overcome by C. Cattaneo and P. Vernotte who developed the theory of non-Fourier heat conduction in 1958. Although this new theory has been used in various thermal science areas, it requires considerable mathematical skills for calculating analytical solutions. The aim of this study was the identification of a newer and a simpler type of solution for the hyperbolic partial differential equations of the non-Fourier heat conduction. This constitutes the first trial in a series of planned studies. By inspecting each term included in the proposed solution, the theoretical feasibility of the solution was achieved. The new analytical solution for the non-Fourier heat conduction is a simple exponential function that is compared to the existing data for justification. Although the proposed solution partially satisfies the Cattaneo-Vernotte equation, it cannot simulate a thermal wave behavior. However, the results of this study indicate that it is possible to obtain the theoretical solution of the Cattaneo-Vernotte equation by improving the form of the proposed solution.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.185-190
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• 1989

In [4], J. Leray introduced the notion of partial hyperbolicity to characterize the operators for which the non-characteristic Cauchy problem is solvable in the Geverey class for any data which are holomorphic in a part of variables x"=(x$_{2}$,..,x$_{l}$ ) in the initial hyperplane x$_{1}$=0. A linear partial differential operator is called partially hyperbolic modulo the linear subvarieties S:x"=constant if the equation P$_{m}$(x, .zeta.$_{1}$, .xi.')=0 for .zeta.$_{1}$ has only real roots when .xi.'is real and .xi."=0, where P$_{m}$ is the principal symbol of pp. Limiting to the case of operators with constant coefficients, A. Kaneko proposed a new sharper condition when S is a hyperplane [3]. In this paper, we generalize this condition to the case of general linear subvariety S and show that it is sufficient for the solvability of Cauchy problem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.blem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.239-250
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• 2018

A knot complement admits a pseudo-hyperbolic structure by solving Thurston's gluing equations for an octahedral decomposition. It is known that a solution to these equations can be described in terms of region variables, also called w-variables. In this paper, we consider the case when pinched octahedra appear as a boundary parabolic solution in this decomposition. The w-solution with pinched octahedra induces a solution for a new knot obtained by changing the crossing or inserting a tangle at the pinched place. We discuss this phenomenon with corresponding holonomy representations and give some examples including ones obtained from connected sum.

• Science of Emotion and Sensibility
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• v.20 no.1
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• pp.83-94
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• 2017

In this study, we figured out that music modes and item types could affect people's urged decision making through a k-value which results from a delay discounting's hyperbolic function. Generally, high k-value is related to impulsive decision making. Concretely, there was a significant interaction between items and music. For the luxury item, the k-value was higher while listening to major music than minor. However, for the non-luxury item condition the k-value difference was not significant between two pieces of music. Moreover, we expected mood could be manipulated after listening to the music and mediate a difference of tendency. We used first movement as an allegro and second as an andante of Mozart piano concerto No.5 D-major and No.20 D-minor for stimuli. As a result, mode and tempo's main effects were not significant. Nevertheless, there was a significant two-way interaction. To put it concretely, the k-value of major condition was marginally higher than minor condition on allegro. However, the k-value of major condition was significantly lower than minor condition on andante. Also, depressed degree difference was significant but it was not significant as a mediator. Set depressed degree as a predict variable and future time span as a mediator, further research found future time perception partially mediated the effect that depressed degree affects impulsivity.