• 대한수학회보
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• 제51권5호
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• pp.1259-1267
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• 2014

In this paper we show that any chain transitive set of a diffeomorphism on a compact $C^{\infty}$-manifold which is $C^1$-stably limit shadowable is hyperbolic. Moreover, it is proved that a locally maximal chain transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is limit shadowable.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.333-340
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• 2013

In this paper, we prove that on a K$\ddot{a}$hler spin foliatoin of codimension $q=2n$, any eigenvalue ${\lambda}$ of type $r(r{\in}\{1,{\cdots},[\frac{n+1}{2}]\})$ of the basic Dirac operator $D_b$ satisfies the inequality ${\lambda}^2{\geq}\frac{r}{4r-2}\;{\inf}_M{\sigma}^{\nabla}$, where ${\sigma}^{\nabla}$ is the transversal scalar curvature of $\mathcal{F}$.

• 대한수학회지
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• 제46권5호
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• pp.1087-1103
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• 2009

Given a system of s independent 1-forms on a smooth manifold M of dimension m, we study the existence of integral manifolds by means of various generalized versions of the Frobenius theorem. In particular, we present necessary and sufficient conditions for there to exist s'-parameter (s' < s) family of integral manifolds of dimension p := m-s, and a necessary and sufficient condition for there to exist integral manifolds of dimension p', p' $\leq$ p. We also present examples and applications to complex analysis in several variables.

• 대한수학회보
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• 제56권1호
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• pp.229-243
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• 2019

We use the so-called pseudoinversion of degenerate metrics technique on foliated compact null hypersurface, $M^{n+1}$, in Lorentzian manifold ${\overline{M}}^{n+2}$, to derive an integral formula involving the r-th order mean curvatures of its foliations, ${\mathcal{F}}^n$. We apply our formula to minimal foliations, showing that, under certain geometric conditions, they are isomorphic to n-dimensional spheres. We also use the formula to deduce expressions for total mean curvatures of such foliations.

• 호남수학학술지
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• 제46권2호
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• pp.224-236
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• 2024

This study inspects the structure of CR-product of a holomorphic statistical manifold. Findings concerning geodesic submanifolds and totally geodesic foliations in the context of dual connections have been demonstrated. The integrability of distributions in CR-statistical submanifolds has been characterized. The statistical version of CR-product in the holomorphic statistical manifold has been researched. Additionally, some assertions for curvature tensor field of the holomorphic statistical manifold have been substantiated.

• 한국지반환경공학회 논문집
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• 제13권11호
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• pp.27-35
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• 2012

암반의 불연속면은 암반의 역학적 거동에 영향을 미치는 중요한 요소 중 하나이다. 편마암으로 이루어진 비탈면은 광범위한 범위에서 변성작용을 받아 형성되는 편마암생성과정과 엽리가 존재하는 이방성 구조 때문에 지질구조가 복잡하다. 본 연구대상 지역의 경우 절취공사 이전에 실시된 시추조사에서는 양호한 암반으로 조사되었으나, 약 20m 이상의 대절취공사를 수행하는 중인장균열이 약 170m 구간에 걸쳐 발생하였다. 인장균열 원인분석을 위하여 지표지질조사, 시추조사, 전기비저항탐사, 시추공영상촬영 등을 실시하였다. 전기비저항탐사와 지표지질조사를 통하여 광역에 걸친 단층대의 규모를 추정할 수 있었고, 종합분석한 결과 대규모의 단층활면 및 단층점토가 발견되었다.

• 한국약용작물학회지
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• 제17권4호
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• pp.251-256
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• 2009

The parts of leaves, flowers and stems in ginseng were obtained for analyzing the component of saponin on 15th April, 25th April, 5th May, 25th May, which were considered as ginseng foliation stage. The total saponin content of the leaves were 97.29, 66.42, 67.61, 36.24 mg/g, respectively, in which the content of Re, $Rb_1$ and Rd were more than 2/3 amount of total saponin. Especially, the saponin content of leaves decreased according to the sequential collection days, in which the similar results were observed from the flowers and stems of ginseng. The total saponin content of the flowers and stems were 141.09,143.84,139.25,133.47 and 13.32, 9.85, 8.00, 4.65 mg/g, respectively. Among them, the content of Re, Rd and $Rb_2$ in flowers were more than 2/3 while the content of Re, $Rg_1$ and Rd in stems showed more than 9/10 amount of total saponin. The total saponin content of individual leaf were 19.46, 28.56, 58.82 and 169.24 mg/plant, 2.53, 2.76, 5.20 and 12.32 mg/plant in stems, and 14.11, 30.21, 37.60 and 73.41 mg/plant in flowers. Therefore, the total saponin content of aboveground parts in ginseng were leaves > flowers > stems.

• 자원환경지질
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• 제30권5호
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• pp.459-467
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• 1997

In order to examine the primary trends and characteristics of geological lineaments along the southwestern boundary of Okcheon zone, we carried out the analysis of geological lineament trends over six selected sub-areas using Landsat-5 TM images and digital elevation model. The trends of lineaments is determined by a minimum variance method, and the resulting geological lineament map can be obtained through generalized Hough transform. We have corrected look direction biases reduces the interpretability of remotely sensed image. An approach of histogram modification is also adopted to extract drainage pattern specifically in alluvial plains. The lineament extracting method adopted in this study is very effective to analyze geological lineaments, and that helps estimate geological trends associated various with the tectonic events. In six sub-areas, the general trends of lineaments are characterized NW, NNW, NS-NNE, and NE directions. NW trends in Cretaceous volcanic rocks and Jurassic granite areas may represent tension joints that developed by rejuvenated end of the Early Cretaceous left-lateral strike-slip motion along the Honam Shear Zone, while NE and NS-NNE trends correspond to fault directions which are parallel to the above Shear Zone. NE and NW trends in Granitic Gneiss are parallel to the direction of schitosity, and NS-NNE and NE trends are interpreted the lineation by compressive force which acted by right-lateral strike-slip fault from late Triassic to Jurassic. And in foliated Granite, NE and NNE trends are coincided with directions of ductile foliation and Honam Shear Zone, and NW-NNW trends may be interpreted direction of another compressional foliation (Triassic to Early Jurassic) or end of the Early Cretaceous tensional joints. We interpreted NS-NNE direction lineation is related with the rejuvenated Chugaryung Fault System.

• 터널과지하공간
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• 제18권3호
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• pp.185-193
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• 2008

이 연구에서는 시추공 분석 작업을 통해 획득된 암반절리 방향성이 심도에 따라 변화하는 양상의 확인을 위해 피어슨 카이제곱 통계검정이 실시되었다. 대상 암반은 모암이 화강암질 편마암인 두 지역으로서, 이와같은 엽리가 발달하지 않은 괴상의 암상 선정은, 엽리가 존재하는 암석의 경우 절리 방향성이 엽리에 의해 영향을 받고 엽리의 방향은 습속 등의 지질작용에 의해 심도에 따라 다를 수가 있기 때문이다. 암반 절리들의 방향 파악을 위해 시추공 영상이 이용되었다. 획득된 방향자료를 천부구간과 심부구간의 자료로 분류한 후 21 영역으로 구성된 분할망에 각각 투영 후, 분류표를 작성하여 통계검정을 실시하였으며, 분석결과 두 지역 중 한 지역의 자료는 비동질로 나타났다. 이러한 결과는 터널과 같은 지하구조물의 설계를 위한 암반공학적으로 중요한 절리면의 방향성에 대한 조사시 원위치 조사가 바람직함을 시사한다.

• 자원환경지질
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• 제17권3호
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• pp.197-214
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• 1984

This studg is to clarify intrusion sequence and petrogenetic processes of the so-called schistose granites in the northeastheastern part of the Kwangju, Chonnam Province. The study area is composed of the Pre-cambrian and Unknown age metasediments, the Unknown age schistose granites and basic plutons, the Cretaceous sedimentary and volcanic rocks, and the Cretaceous Ogang-ri granite and dykes. The schistose granites of the study area is divided into three rock units based on relative intrusion age, mineralogical constituent and texture;SoonChang schistose granite, two mica granite and Sam-o-ri schistose granite. The schistose granites intruded into metasediments, are intruded by Ogang-ri granite and dikes, and overlain by the Cretaceous sedimentary and volcanic rocks. The schistose granites vary widely in composition (granite-granodiorite-tonalite) and content of porphyroblastic feldspar Caugen and rectangular shaped). The foliation of schistose granites shows similar trend to the Shinian direction. In especially, strong foliation reflects dynamic metamorphism by mortar texture and much content of well oriented biotite. These schistose granites are characterized by its gray feldspar porphyroblasts. This feldspar is considered to be formed by potassic metasomatism and assimilation of pelitic metasediments of unexposed highly metamorphosed rocks deeply buried under the level of the schistose granites emplacement. Variation of silica versus oxides of major elements shows that the schistose granites are similar to the trend of Daly's average basalt-andesite-dacite-rhyolite which shows the trend of the fractional crystallization of magma. AMF diagram shows that the schistose granite is corresponded to contaminated differentiation products such as Lower California batholith and Cascade lava. These evidence suggest that the schistose granite is a series of differentiation products formed by fractional crystallization that associated with srtongly contamination and potassic metasomatism.