• East Asian mathematical journal
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• 제26권1호
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• pp.75-79
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• 2010

Let G be a compact connected semisimple Lie group, g the Lie algebra of G, g the canonical metric (the biinvariant Riemannian metric which is induced from the Killing form of g), and $\nabla$ be the Levi-Civita connection for the metric g. Then, we get the fact that the Levi-Civita connection $\nabla$ in the tangent bundle TG over (G, g) is a Yang-Mills connection.

• 대한수학회보
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• 제56권6호
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• pp.1525-1537
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• 2019

Let ${\tilde{M}}$ be a Riemannian manifold equipped with a concircular vector field ${\tilde{X}}$ and M a submanifold (with its induced metric) of ${\tilde{M}}$. Denote by X the restriction of ${\tilde{X}}$ on M and by $X^T$ the tangential component of X, called the canonical field of M. In this article we study submanifolds of ${\tilde{M}}$ whose canonical field $X^T$ is also concircular. Several characterizations and classification results in this respect are obtained.

• 충청수학회지
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• 제23권4호
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• pp.813-821
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• 2010

Let G and H be compact connected Lie groups with biinvariant Riemannian metrics g and h respectively, ${\phi}$ a group isomorphism of G onto H, and $E:={\phi}^{-1}TH$ the induced bundle by $\phi$ over the base manifold G of the tangent bundle TH of H. Let ${\nabla}$ and $^H{\nabla}$ be the Levi-Civita connections for the metrics g and h respectively, $\tilde{\nabla}$ the induced connection by the map ${\phi}$ and $^H{\nabla}$. Then, a necessary and sufficient condition for $\tilde{\nabla}$ in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) to be a Yang- Mills connection is the fact that the Levi-Civita connection ${\nabla}$ in the tangent bundle over (G, g) is a Yang- Mills connection. As an application, we get the following: Let ${\psi}$ be an automorphism of a compact connected semisimple Lie group G with the canonical metric g (the metric which is induced by the Killing form of the Lie algebra of G), ${\nabla}$ the Levi-Civita connection for g. Then, the induced connection $\tilde{\nabla}$, by ${\psi}$ and ${\nabla}$, is a Yang-Mills connection in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) over the base manifold (G, g).

• 대한수학회논문집
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• 제35권4호
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• pp.1269-1281
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• 2020

In this article, we show that a pseudo-Hermitian magnetic curve in a normal almost contact metric 3-manifold equipped with the canonical affine connection ${\hat{\nabla}}^t$ is a slant helix with pseudo-Hermitian curvature ${\hat{\kappa}}={\mid}q{\mid}\;sin\;{\theta}$ and pseudo-Hermitian torsion ${\hat{\tau}}=q\;cos\;{\theta}$. Moreover, we prove that every pseudo-Hermitian magnetic curve in normal almost contact metric 3-manifolds except quasi-Sasakian 3-manifolds is a slant helix as a Riemannian geometric sense. On the other hand we will show that a pseudo-Hermitian magnetic curve γ in a quasi-Sasakian 3-manifold M is a slant curve with curvature κ = |(t - α) cos θ + q| sin θ and torsion τ = α + {(t - α) cos θ + q} cos θ. These curves are not helices, in general. Note that if the ambient space M is an α-Sasakian 3-manifold, then γ is a slant helix.

• 대한수학회논문집
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• 제9권2호
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• pp.393-400
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• 1994

Let M(f,η,ξ,g) be a (2m ＋ 1)-dimensional Sasakian manifold with soldering form dp ∈ ΓHom(Λ/sup q/TM, TM) (dp: canonical vector-valued 1-form) where f,η,ξ and g are the (1,1)-tensor field, the structure 1-form, the structure vector field and the metric tensor of M, respectively.(omitted)

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제7권4호
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• pp.819-833
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• 2013

Computing global features based on local features using a bio-inspired framework has shown promising performance. However, for some tough applications with large intra-class variances, a single local feature is inadequate to represent all the attributes of the images. To integrate the complementary abilities of multiple local features, in this paper we have extended the efficacy of the bio-inspired framework, HMAX, to adapt heterogeneous features for global feature extraction. Given multiple global features, we propose an approach, designated as parameterized metric learning, for high dimensional feature fusion. The fusion parameters are solved by maximizing the canonical correlation with respect to the parameters. Experimental results show that our method achieves significant improvements over the benchmark bio-inspired framework, HMAX, and other related methods on the Caltech dataset, under varying numbers of training samples and feature elements.

• 대한수학회지
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• 제41권2호
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• pp.369-378
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• 2004

A canonical Finsler connection Nr is defined by a generalized Finsler structure called a (G, N)-structure, where G is a generalized Finsler metric and N is a nonlinear connection given in a differentiable manifold, respectively. If NT is linear, then the(G, N)-structure has a linearity in a sense and is called Berwaldian. In the present paper, we discuss what it means that NT is with a vanishing hv-torsion: ${P^{i}}\;_{jk}\;=\;0$ and introduce the notion of a stronger type for linearity of a (G, N)-structure. For important examples, we finally investigate the cases of a Finsler manifold and a Rizza manifold.

• 대한수학회지
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• 제41권1호
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• pp.107-130
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• 2004

A $JB^{*}-triple$ is a Banach space A on which the group Aut(B) of biholomorphic automorphisms acts transitively on the open unit ball B of A. In this case, a triple product {$\cdots$} from $A\;\times\;A\;\times\;A\;to\;A$ can be defined in a canonical way. If A is also the dual of some Banach space $A_{*}$, then A is said to be a JBW triple. A projection R on A is said to be structural if the identity {Ra, b, Rc} = R{a, Rb, c, }holds. On $JBW^{*}-triples$, structural projections being algebraic objects by definition have also some interesting metric properties, and it is possible to give a full characterization of structural projections in terms of the norm of the predual $A_{*}$ of A. It is shown, that the class of structural projections on A coincides with the class of the adjoints of neutral GL-projections on $A_{*}$. Furthermore, the class of GL-projections on $A_{*}$ is naturally ordered and is completely ortho-additive with respect to L-orthogonality.

• 한국어류학회지
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• 제34권2호
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• pp.102-112
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• 2022

본 연구는 위내용물 분석과 안정동위원소(δ¹³C and δ¹⁵N) 분석을 통하여 우리나라 동해 북부 연안에 출현하는 명태(Gadus chalcogrammus)와 대구(G. macrocephalus)의 종내 및 종간 먹이자원 분할을 조사하였다. 두 종은 중층성 육식성 어종으로 명태는 저서성 및 중층성 갑각류를 주로 섭식하였고, 대구는 어류를 주로 섭식하였다. 위내용물 분석 결과에 대한 Non-metric multidimensional scaling (nMDS) ordination과 permutational multivariate analysis of variance (PERMANOVA)은 두 종의 종내 및 종간 먹이조성의 차이와 먹이자원 분할을 보여줬다. 안정동위원소 분석 결과 δ¹⁵N 값은 종간 유사하였지만, δ¹³C 값은 대구가 높은 값을 나타내어 두 종간 생태지위 차이를 보여줬다. 명태는 체장 증가에 따라 큰 체장군에서 새우류와 두족류를 더 많이 섭식하는 먹이 전환을 나타냈지만, 대구는 체장군 간 먹이조성이 유사하였다. 안정동위원소 분석에서도 체장군 간 차이를 보였는데, 두 종의 큰 체장군은 작은 체장군에 비해 더 높은 δ¹⁵N 값을 나타낸다. 결론적으로 본 연구는 명태와 대구의 위내용물 분석과 안정동위원소 분석을 통하여 종내 및 종간 먹이 차이와 생태지위 분할의 증거를 보여줬다.

• 한국환경복원기술학회지
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• 제20권2호
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• pp.37-59
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• 2017

The Korean peninsula belongs to the temperate forest biome dominated by many deciduous oaks. We quantitatively and qualitatively studied vertical and horizontal distributions and habitat characteristics on the major oak species such as Quercus mongolica, Q. serrata, Q. variabilis, Q. dentata, Q. aliena and Q. acutissima. A total of 5,278 samples were analyzed with a species coverage and 6 principal environmental variables extracted from public database of nationwide natural environment survey. Correlation analysis was accomplished by the CANOCO using Canonical Correspondence Analysis and the Pearson correlation coefficient using PASW Statistics. The hierarchical distribution tendency of six oaks was finalized using the Goodman-Kruskal lambda coefficient of non-metric multidimensional scaling by SYN-TAX 2000. The utmost factor on the distributional segregation of oak species was the elevation, i.e. temperature. Q. serrata and Q. mongolica show clearly a diametrical distribution patterns with zonal distribution. Q. variabilis was determined as a thermophilic and xerophilous species that is a component of not only natural pseudo-climax forest but also secondary forest. The highest frequency of the dominant forest was found Q. mongolica. Whereas, Q. serrata showed the highest frequency of individual tree but the relatively lower frequency of dominant forest, which is resulted from the original habitat loss. By the benefit of the traditional Soopjeong-E, Q. acutissima dominant forests were remained rather largely. Individuals of Q. dentata occurred horizontally nationwide, but its dominant forest was the poorest. Dominant forest of Q. aliena, which is a natural vegetation, was the most rare due to a limited potential habitat.