• 대한수학회논문집
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• 제11권4호
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• pp.1061-1066
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• 1996

We will give an example which is a normal Hausdorff countable dense homogeneous space but not a densely homogeneous space. Next, we will give a proof for the fact that every nondegenerate component of densely homogenous spaces is open and densely homogeneous.

• Journal of Information Processing Systems
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• 제12권4호
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• pp.591-611
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• 2016

High dimensional space is the biggest problem when classification process is carried out, because it takes longer time for computation, so that the costs involved are also expensive. In this research, the facial space generated from homogeneous and non-homogeneous polynomial was proposed to extract the facial image features. The homogeneous and non-homogeneous polynomial-based eigenspaces are the second opinion of the feature extraction of an appearance method to solve non-linear features. The kernel trick has been used to complete the matrix computation on the homogeneous and non-homogeneous polynomial. The weight and projection of the new feature space of the proposed method have been evaluated by using the three face image databases, i.e., the YALE, the ORL, and the UoB. The experimental results have produced the highest recognition rate 94.44%, 97.5%, and 94% for the YALE, ORL, and UoB, respectively. The results explain that the proposed method has produced the higher recognition than the other methods, such as the Eigenface, Fisherface, Laplacianfaces, and O-Laplacianfaces.

• 대한수학회지
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• 제42권3호
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• pp.485-498
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• 2005

In this article we show that every quasi-homogeneous convex affine domain whose boundary is everywhere differentiable except possibly at a finite number of points is either homogeneous or covers a compact affine manifold. Actually we show that such a domain must be a non-elliptic strictly convex cone if it is not homogeneous.

• 대한수학회보
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• 제60권6호
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• pp.1607-1620
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• 2023

In this paper, we mainly study the problem of the existence of homogeneous geodesics in sub-Finsler manifolds. Firstly, we obtain a characterization of a homogeneous curve to be a geodesic. Then we show that every compact connected homogeneous sub-Finsler manifold and Carnot group admits at least one homogeneous geodesic through each point. Finally, we study a special class of ℓ^p-type bi-invariant metrics on compact semi-simple Lie groups. We show that every homogeneous curve in such a metric space is a geodesic. Moreover, we prove that the Alexandrov curvature of the metric space is neither non-positive nor non-negative.

• 응용통계연구
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• 제18권1호
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• pp.183-196
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• 2005

본 논문에서는 다변량 정규분포하에서 비동차(non-homogeneous) 이차형식의 분포 함수에 대한 안장점근사법을 다루었다. 이는 Kuonen (1999)의 동차(homogeneous) 이차형식에 대한 안장점근사를 비동차의 경우로 확장한 것이다. 안장점근사의 적용을 위해 비동차 이차형식의 누율생성함수 및 관련 성질들을 유도하였다. 모의실험을 통해 안장점근사의 정도가 매우 뛰어남을 확인하였다.

• 대한수학회보
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• 제53권4호
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• pp.971-983
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• 2016

A partially ordered set P is ideal-homogeneous provided that for any ideals I and J, if $$I{\sim_=}_{\sigma}J$$, then there exists an automorphism ${\sigma}^*$ such that ${\sigma}^*{\mid}_I={\sigma}$. Behrendt [1] characterizes the ideal-homogeneous partially ordered sets of height 1. In this paper, we characterize the ideal-homogeneous partially ordered sets of height 2 and nd some families of ideal-homogeneous partially ordered sets.

• 대한수학회지
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• 제43권6호
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• pp.1301-1324
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• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• 대한수학회지
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• 제53권2호
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• pp.433-446
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• 2016

We construct projective embeddings of horospherical varieties of Picard number one by means of Fano varieties of cones over rational homogeneous varieties. Then we use them to give embeddings of smooth horospherical varieties of Picard number one as linear sections of rational homogeneous varieties.

• 충청수학회지
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• 제24권4호
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• pp.825-832
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• 2011

In this paper, we make a minute and detailed proof of a part which is omitted in the process of obtaining the value of the curvature tensor for an invariant affine connection at the point {H} of a reductive homogeneous space G/H in the paper 'Invariant affine connections on homogeneous spaces' by K. Nomizu.

• 대한의용생체공학회:의공학회지
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• 제43권6호
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• pp.369-374
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• 2022

Purpose: Focused ultrasound is an emerging technology for treating the brain locally in a noninvasive manner. In this study, we have investigated the influence of skull properties on simulating transcranial pressure field. Methods: A 3D computational model of transcranial focused ultrasound was constructed using female and male CT data to solve for intracranial pressure. For heterogeneous model, the acoustic properties were calculated from CT Hounsfield units based on a porosity. The homogeneous model assigned constant acoustic properties for the single-layered skull. Results: A computational model was validated against empirical data. The homogeneous models were then compared with the heterogeneous model, resulted in 10.87% and 7.19% differences in peak pressure for female and male models respectively. For the focal volume, homogeneous model demonstrated more than 94% overlap compared with the heterogeneous model. Conclusion: Homogeneous model can be constructed using MR images that are commonly used for the segmentation of the skull. We propose the possibility of the homogeneous model for the simulating transcranial pressure field owing to comparable focal volume between homogeneous model and heterogeneous model.