• 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.

• 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.

• 대한수학회논문집
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• 제33권3호
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• pp.935-942
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• 2018

In this paper, we prove that any stable f-harmonic map from sphere ${\mathbb{S}}^n$ to Riemannian manifold (N, h) is constant, where f is a smooth positive function on ${\mathbb{S}}^n{\times}N$ satisfying one condition with n > 2. We also prove that any stable f-harmonic map ${\varphi}$ from a compact Riemannian manifold (M, g) to ${\mathbb{S}}^n$ (n > 2) is constant where, in this case, f is a smooth positive function on $M{\times}{\mathbb{S}}^n$ satisfying ${\Delta}^{{\mathbb{S}}^n}(f){\circ}{\varphi}{\leq}0$.

• 전력전자학회논문지
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• 제25권5호
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• pp.395-403
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• 2020

This study presents a stable start-up strategy for v/f scalar-controlled permanent magnet synchronous motors (PMSMs). The v/f-controlled PMSMs easily lose synchronism under low-speed conditions if an insufficient stator voltage is applied to the machine due to errors in measured motor parameters and inverter nonlinearity, such as inverter dead time and on-state voltage drop. The proposed method adopts the I/f control method to ensure a stable start at low speeds and then switches to the v/f control method at medium speeds. A smooth transition method from I/f control to v/f control is proposed to minimize the oscillation of the stator current and rotor speed during transition. Moreover, the stability of the I/f and v/f control methods is analyzed using a small-signal model. Simulation and experimental results are provided to verify the performance of the proposed control strategy.

• 대한수학회논문집
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• 제30권4호
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• pp.471-479
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• 2015

In this paper, we prove that any stable f-harmonic map ${\psi}$ from ${\mathbb{S}}^2$ to N is a holomorphic or anti-holomorphic map, where N is a $K{\ddot{a}}hlerian$ manifold with non-positive holomorphic bisectional curvature and f is a smooth positive function on the sphere ${\mathbb{S}}^2$with Hess $f{\leq}0$. We also prove that any stable f-harmonic map ${\psi}$ from sphere ${\mathbb{S}}^n$ (n > 2) to Riemannian manifold N is constant.

• 충청수학회지
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• 제16권1호
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• pp.113-121
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• 2003

This paper is concerned with some properties of stable domains and limit functions. Using the relationship between cycles of periodic stable domains and orbits of critical points and using the Sullivan theorem [19], we prove that the value of a constant limit function in some stable domain for a rational function f of degree at least two lies in the closure of the set of critical orbits of f.

• 대한화학회지
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• 제54권3호
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• pp.275-282
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• 2010

분자 내 수소결합 가능성을 가지고 있는 2-fluorocyclopropanemethanol과 2-chlorocyclopropanemethanol에 대하여 MP2/6-311++G(d,p) 방법과 B3LYP/6-311++G(d,p) 방법으로 최적화 계산을 수행하였다. 두 분자 모두 가장 안정한 conformer에서 O-H의 수소가 F나 Cl을 향하고 있어 수소결합 가능성을 보이기는 하나 $H{\cdots}F$, $H{\cdots}Cl$ 거리가 van der Waals radii보다 커서 강한 수소결합이라 보기 힘들고 두 번째 안정한 conformer의 경우가 가까운 $H{\cdots}F$, $H{\cdots}Cl$ 거리를 보이며 더 강한 수소결합 가능성을 보였다. 그러나 에너지가 5 ~ 7 kJ 더 높게 나타났다. Methanol group과 F나 Cl이 서로 반대 방향을 향할 때 일반적으로 안정하나 앞의 가장 안정한 conformer보다는 에너지가 높다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권1호
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• pp.47-61
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• 2003

Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative ${\Large f}'$ given noisy data ${\Large f}_{\delta}$. Computational aspects of the problem are discussed and illustrated by examples. These examples show the practical value of the new understanding of the problem of stable differentiation.

• 대한수학회지
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• 제39권3호
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• pp.331-349
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• 2002

Let G be a reductive algebraic group and let B, F be G-modules. We denote by $VEC_{G}$ (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that $VEC_{G}$ (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor $VEC_{G}$ (B, $F^{\chi}$) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.

• 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.