• 대한수학회논문집
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• 제24권1호
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• pp.127-144
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• 2009

Let f be a diffeomorphism of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of $C^1$-stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set $\cal{R}(f)$ of f has $C^1$-stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) $C^1$-generically, the chain component $C_f(p)$ of f associated to p is hyperbolic if and only if $C_f(p)$ has the $C^1$-stable inverse shadowing property.

• 대한수학회보
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• 제49권1호
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• pp.175-195
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• 2012

Representing planar Pythagorean hodograph (PH) curves by the complex roots of their hodographs, we standardize Farouki's double cubic method to become the undetermined junction point (UJP) method, and then prove the generic existence of solutions for general $C^1$ Hermite interpolation problems. We also extend the UJP method to solve $C^2$ Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with $C^1$ junction points. Further generalizing the UJP method, we go on to solve $C^2$ Hermite interpolation problems using two PH quintics with a $C^1$ junction point, and we also show the possibility of applying the modi e UJP method to $G^2[C^1]$ Hermite interpolation.

• 충청수학회지
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• 제30권2호
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• pp.177-181
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• 2017

Let $f:M{\rightarrow}M$ be a diffeomorphism of a compact smooth manifold M. In this paper, we show that $C^1$ generically, if a chain transitive set ${\Lambda}$ is locally maximal then it admits a dominated splitting. Moreover, $C^1$ generically if a chain transitive set ${\Lambda}$ of f is locally maximal then it has zero entropy.

• 대한수학회논문집
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• 제34권2호
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• pp.615-632
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• 2019

We study generic lightlike submanifolds M of an indefinite trans-Sasakian manifold ${\bar{M}}$ or an indefinite generalized Sasakian space form ${\bar{M}}(f_1,f_2,f_3)$ endowed with an $({\ell},m)$-type metric connection subject such that the structure vector field ${\zeta}$ of ${\bar{M}}$ is tangent to M.

• 대한수학회논문집
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• 제38권1호
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• pp.243-256
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• 2023

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C¹ generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.

• Journal of Communications and Networks
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• 제2권1호
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• pp.35-45
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• 2000

this paper presents the concept of "mobile ATM', a proposal for third-generation (3G) mobile communication network infrastructure capable of supporting flexible evolution of radio technologies from today's cellular and data services towards future wireless multimedia services. Mobile ATM provides generic mobility management and QoS-based transport capabilities suitable for integration of multiple radio access technologies including cellular voice. wireless data, and future broadband wireless services. The architecture of a mobile ATM network is outlined in terms of the newly-defined "W-UNI" interface at the radio link and "M-UNI"and "M-UNI" interface which supports unified access for WATM and non-ATM mobile terminals through corresponding interworking functions (IWF) is explained. leading to an understanding of how different radio access technologies are supported by the same ATM-based core network infrastructure. Generic mechanisms for handoff and location management within the core mobile network are discussed. and related protocol extensions over the "W-UNI" and "M-UNI/NNI"interfaces are proposed. the issue of "crossover switch (COS)" selection in mobile ATM is considered, and a unified handoff signaling syntax which supports flexibility in COS selection is described. Typical signaling sequences for call connection and handoff using the proposed protocols are outlined. Experimental results form a proof-of-concept mobile ATM network prototype are presented in conclusion.

• 충청수학회지
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• 제25권4호
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• pp.725-730
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• 2012

Let $f$ be a diffeomorphism of a closed $C^{\infty}$ manifold M. We show that $C^1$-generically, if $f$ has the shadowing property on a robustly transitive set, then it is hyperbolic.

• 대한수학회논문집
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• 제31권4호
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• pp.683-693
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• 2016

In [1], the authors proved that the finite union of linear star-configurations in $\mathbb{P}^2$ has a generic Hilbert function. In this paper, we find the minimal graded free resolution of the union of two linear star-configurations in $\mathbb{P}^2$ of type $s{\times}t$ with $\(^t_2\){\leq}s$ and $3{\leq}t$.

• 충청수학회지
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• 제21권4호
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• pp.519-525
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• 2008

Let f be a diffeomorphisms of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper, we prove that if generically, f is tame diffeomorphims then the following conditions are equivalent: (i) f is ${\Omega}$-stable, (ii) f has the $C^1$-stable shadowing property (iii) f has the $C^1$-stable inverse shadowing property.

• 충청수학회지
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• 제24권4호
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• pp.631-638
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• 2011

In this paper, we prove that for $C^1$ generically, if every hyperbolic periodic point in a chain component is uniformly far away from being nonhyperbolic, and it is $C^1$-robustly average shadowable, then the chain component is hyperbolic.