• 대한수학회보
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• 제59권3호
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• pp.709-723
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• 2022

In this note, we revise some vanishing and finiteness results on hypersurfaces with finite index in ℝⁿ⁺¹. When the hypersurface is stable minimal, we show that there is no nontrivial L^2p harmonic 1-form for some p. The our range of p is better than those in [7]. With the same range of p, we also give finiteness results on minimal hypersurfaces with finite index.

• 대한수학회보
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• 제30권2호
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• pp.285-293
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• 1993

In [4], Baumslag and Tretkoff proved a residual finiteness criterion for HNN extensions (Theorem 1.2, below). This result has been used extensively in the study of the residual finiteness of HNN extensions. Note that every one-relator group can be embedded in a one-relator group whose relator has zero exponent sum on a generator, and the latter group can be considered as an HNN extension. Hence the properties of an HNN extension play an important role in the study of one-relator groups [3], [2]. In this paper we prove a criterion for HNN extensions to be .pi.$_{c}$(Theorem 2.2). Moreover, we can prove that certain one-relator groups, known to be residually finite, are actually .pi.$_{c}$. It was known by Mostowski [10] that the word problem is solvable for finitely presented, residually finite groups. In the same way, the power problem is solvable for finitely presented .pi.$_{c}$ groups. Another application of subgroup separability with respect to special subgroups was mentioned by Thurston [12, Problem 15].m 15].

• 대한수학회지
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• 제49권6호
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• pp.1215-1227
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• 2012

The membership of the generalized local cohomology modules $H_a^i$(M,N) of two R-modules M and N with respect to an ideal a in certain Serre subcategories of the category of modules is studied from below ($i<t$). Furthermore, the behaviour of the $n$th graded component $H_a^i(M,N)_n$ of the generalized local cohomology modules with respect to an ideal containing the irrelevant ideal as $n{\rightarrow}-{\infty}$ is investigated by using the above result, in certain graded situations.

• 대한수학회지
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• 제52권5호
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• pp.955-964
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• 2015

Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let ${\alpha}_0{\in}{\mathbb{A}}^1(K){\subset}{\mathbb{P}}^1(K)$ and let ${\Gamma}_0$ be the set of the images of ${\alpha}_0$ under especially all Chebyshev morphisms. Then for any ${\alpha}{\in}{\mathbb{A}}^1(K)$, we show that there are only a finite number of elements in ${\Gamma}_0$ which are S-integral on ${\mathbb{P}}^1$ relative to (${\alpha}$). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on ${\mathbb{P}}^1$, which generalizes the above finiteness result for Chebyshev morphisms.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.531-539
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• 2009

In this paper we first present a structure theorem for an infinite locally finite 3-connected VAP-free planar graph, and in connection with this result we study a possible classification of infinite locally finite planar graphs by reducing modulo finiteness.

• 대한수학회보
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• 제38권1호
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• pp.143-148
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• 2001

First, we show the finiteness property of the homotopy fixed point set of p-discrete toral group. Let $G_\infty$ be a p-discrete toral group and X be a finite complex with an action of $G_\infty such that X^K$ is nilpotent for each finit p-subgroup K of $G_\infty$. Assume X is $F_\rho-complete$. Then X(sup)hG$\infty$ is F(sub)p-finite. Using this result, we give the condition so that X$^{hG}$ is $F_\rho-finite for \rho-compact$ toral group G.

• 한국항해항만학회지
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• 제26권4호
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• pp.419-426
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• 2002

기존 RTK-GPS(Real Time Kinematic-Global Positioning System)는 고가의 장비인 RF(Radio Frequency) 방식의 무선 모뎀을 사용하므로 사용자의 무선국 허가, 전파의 지리적 장애물에 의한 영향, 전송거리의 제한, 주파수 혼신, 주파수 자원의 유한성 등의 문제점이 있다. 본 논문에서는 이런 문제점을 해결하기 위해서 RTK-GPS 수신기의 무선 모뎀을 대체할 수 있는 방법으로 휴대전화를 이용한 DGPS 수신기와의 보정신호 전송기법을 설계하고, RTK-GPS 수신기와 휴대전화간의 연동을 위한 인터페이스 모듈의 설계 및 PIC(Programmable Integrated Circuit)를 이용한 하드웨어 모듈을 구현하였다. 그 결과 인터페이스 모듈은 GPS 수신기와 휴대전화간의 인터페이스 모듈로서 RS-232C와 통신 제어를 통한 보정신호의 전송을 가능함과 이동국에서는 송신 및 수신 된 보정신호 데이터를 이용하여 상대 측위를 통한 정밀한 측위가 이루어짐을 얻었다. 기준국과 이동국의 휴대전화를 연동한 인터페이스 모듈 시스템은 기존의 RF 방식의 무선 모뎀 시스템과 비교하여 거의 동일한 정밀도를 얻을 수 있었다.