• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.461-494
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• 2002

Let G = E${\ast}_{A}F$, where A is a finitely generated abelian subgroup. We prove a criterion for G to be {A}-double coset separable. Applying this result, we show that polygonal products of central subgroup separable groups, amalgamating trivial intersecting central subgroups, are double coset separable relative to certain central subgroups of their vertex groups. Finally we show that such polygonal products are conjugacy separable. It follows that polygonal products of polycyclic-by-finite groups, amalgamating trivial intersecting central subgroups, are conjugacy separable.

• Cross-Cultural Studies
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• v.38
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• pp.433-459
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• 2015

This paper aims at a better understanding of the concept of korean separable syntactic atom, of which inner parts is separable in syntax, and at examining whether or not this concept can apply to derivatives, functional complex constructions, idiomatic expressions in korean. I defined a syntactic atom as a minimum unit which is drawn directly from lexicon and then is applied to syntactic rules. And I insist that so-called 'lexical island constraint' has some problems and that the syntactic rules can be applied to inner parts of syntactic atom, if the syntactic rules is irrelevant to new syntactic atom formation. The greater part of derivatives is non-separable syntactic atoms. But the likes of '반짝거리다', '죄송스럽다', '칭얼대다' are the separable syntactic atoms. The degree of separability of them is different in the insertion of korean particles or negative adverbs and the omission of root of sytactic atom. The derivatives of 'X-적', of which roots is regular nominal roots, permit the syntactic link between roots and the syntactic combination of the root and its argument. These kinds of derivatives is separable syntactic atoms. Also the derivatives of 'bracket paradox' and 'X-답-' derivatives is separable syntactic atoms. All functional complex constructions are not separable syntactic atoms. According to the degree of grammaticalization, inner parts of some are separable, some is non-separable. Separable functional complex constructions only permit the switching of endings or Josas but not application of other syntactic rules. All idiomatic expressions which are composed of two or more syntactic atoms are separable syntactic atoms. Some of them have so strong separability to allow the insertion of syntactic atom, adverb or adnominal modification and the noun in idiomatic expression to become the head of the relative clause. And some idiomatic expressions which have weak separability only permit interrogative's substitution or form change in fraction of idiomatic expressions.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.811-827
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• 2000

We find some conditions to derive the conjugacy separability of the free product of conjugacy separable split extensions amalgamated along cyclic retracts. These conditions hold for any double coset separable groups and free-by-cyclic groups with nontrivial center. It was known that free-by-finite, polycyclic-by-finite, and fuchsian groups are double coset separable. Hence free products of those groups amalgamated along cyclic retracts are conjugacy separable.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1753-1763
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• 2013

In this paper, we show that tree products of certain subgroup separable groups amalgamating normal subgroups are cyclic subgroup separable. We then extend this result to certain graph product of certain subgroup separable groups amalgamating normal subgroups, that is we show that if the graph has exactly one cycle and the cycle is of length at least four, then the graph product is cyclic subgroup separable.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.595-602
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• 2005

Here we define Central separable semialgebras and to prove some structure theorems for central separable cancellative, semialgebras over a commutative and cancellative semiring.

• Proceedings of the Korea Information Processing Society Conference
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• 2007.11a
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• pp.1139-1142
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• 2007

Separable Gabor 필터는 기존의 2D Gabor 필터를 x축 성분과 y축 성분만을 지니는 두 개의 1D 필터로 나누어 각각 적용하는 방법으로 속도 향상을 가져왔으며, 지문인식 등에서 사용되어왔다. 하지만 정맥과 같은 경우에는 지문의 융선들 보다 더 굵기 때문에 필터의 크기 또한 매우 커진다. 따라서 Separable Gabor 필터의 경우도 지문에서만큼의 빠른 속도를 내지는 못한다. 본 논문에서는 Separable Gabor 필터 보다 더욱 고속의 연산이 가능한 Separable Symmetric Gabor 필터를 제안하였다. 이 필터는 사선 방향으로의 특징을 강조함에 있어 동시에 대칭이 되는 각도의 특성까지 강조하고, 회선 과정에서 필터의 방향 값을 고려하지 않기 때문에 인덱스 계산이 매우 단순해져 기존의 Separable Gabor 필터보다 처리 속도를 향상시킬 수 있다.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.53-58
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• 1999

In this paper, we introduce the notion of separable-like function, investigate some properties of separable-like functions, and characterize the Pettis integrability of function on a finite perfect measure space.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.69-83
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• 2015

In this paper we introduce and study the separable weak bounded approximation properties which is strictly stronger than the approximation property and but weaker than the bounded approximation property. It provides new sufficient conditions for the metric approximation property for a dual Banach space.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1233-1242
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• 2009

In 1981 S. A. Saxon and P. P. Narayanaswami ([10]) showed that every (LF)-space has an infinite dimensional separable quotient. In this note we prove that this fails for (LF)$_{tv}$-spaces. We construct a wide class of (LF)$_{tv}$-spaces, which have no infinite dimensional separable quotient.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.813-828
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• 2013

It is known that generalized free products of finitely generated nilpotent groups are conjugacy separable when the amalgamated subgroups are cyclic or central in both factor groups. However, those generalized free products may not be conjugacy separable when the amalgamated subgroup is a direct product of two infinite cycles. In this paper we show that generalized free products of finitely generated nilpotent groups are conjugacy separable when the amalgamated subgroup is ${\langle}h{\rangle}{\times}D$, where D is in the center of both factors.