• 대한수학회보
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• 제48권6호
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• pp.1329-1339
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• 2011

For a manifold with a linear connection, we find an obstruction class to have a volume form parallel with respect to its connection which corresponds to the Chern-Simons secondary invariant in the frame bundle of the manifold.

• 대한수학회보
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• 제52권2호
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• pp.351-361
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• 2015

We give examples of Lie ideals in a tridiagonal algebra $Alg\mathcal{L}_{\infty}$ and study some properties of Lie ideals in $Alg\mathcal{L}_{\infty}$. We also investigate relationships between Lie ideals in $Alg\mathcal{L}_{\infty}$. Let k be a fixed natural number. Let $\mathcal{A}$ be a linear manifold in $Alg\mathcal{L}_{\infty}$ such that $T_{(2k-1,2k)}=0$ for all $T{\in}\mathcal{A}$. Then $\mathcal{A}$ is a Lie ideal if and only if $T_{(2k-1,2k-1)}=T_{(2k,2k)}$ for all $T{\in}\mathcal{A}$.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.237-244
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• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• 호남수학학술지
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• 제39권1호
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• pp.93-100
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• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• 대한수학회지
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• 제36권5호
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• pp.959-1008
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• 1999

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand the torsion of a connection. The latter parts of the paper deal with the Levi-Civita connection of a Riemannian manifold. The idea is to get at the connection by first finding its.spary. This is a second order vector field that encodes the second order differential equation for geodesics. The paper also develops some machinery involving lifts of vector fields form a manifold to its tangent bundle and uses a variational approach to produce the Riemannian spray.

• 대한수학회논문집
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• 제39권2호
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• pp.421-436
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• 2024

In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.

• 대한수학회보
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• 제59권3호
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• pp.789-799
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• 2022

We establish a sharp integral inequality related to compact (without boundary) linear Weingarten hypersurfaces (immersed) in a locally symmetric Einstein manifold and we apply it to characterize totally umbilical hypersurfaces and isoparametric hypersurfaces with two distinct principal curvatures, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Alías and Meléndez in [4] for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.

• 대한원격탐사학회지
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• 제29권5호
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• pp.509-516
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• 2013

초분광 영상에 내재된 비선형 현상을 다루기 위해서는 과거에 주로 사용되었던 선형 피처 추출 방법은 적합하지 않았다. 따라서 최근 Manifold learning이라 불리우는 비선형 피처 추출 방법이 초분광 원격탐사 분야를 비롯 여러 분야에서 관심이 증가되고 있다. Manifold learning 방법 중 널리 이용되는 Isomap은 분류와 분광 혼합 분석 등의 분야에서 좋은 결과를 보여주지만, 지나치게 복잡하고 높은 계산량은, 특히 원격탐사 자료와 같이 자료의 크기가 큰 경우 문제가 된다. 따라서 자료의 일부분을 이용하는 랜드마크 기법이 해결책으로 제안 되었다. 본 연구에서는 좀 더 통제가 가능한 랜드마크 추출을 위해 자료를 구성하는 최대 부피를 지닌 Simplex를 이용하여 랜드마크를 선택하는 방법을 제안한다. 초분광 영상을 이용하여 랜드마크의 개수, 선택 방법에 따른 분류 정확도와 편차, 그리고 처리 시간을 비교하였고, 그 결과 제안된 랜드마크 선택 기법은 분류 정확도, 처리시간 모두에서 효율적인 결과를 보여주었다.

• 호남수학학술지
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• 제34권4호
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• pp.513-517
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• 2012

Let L(M) be the bundle of all linear frames over a smooth manifold M, $u$ an arbitrarily given point of L(M), and ${\nabla}:\mathfrak{X}(M){\times}\mathfrak{X}(M){\rightarrow}\mathfrak{X}(M)$ a linear connection on M. Then the following result is well known: the horizontal subspace at the point $u$ may be written in terms of local coordinates of $u{\in}L(M)$ and Christoel's symbols defined by ${\nabla}$. This result is very fundamental on the study of the theory of connections. In this paper we show that the local expression of the horizontal subspace at the point u does not depend on the choice of a local coordinate system around the point $u{\in}L(M)$, which is rarely seen.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1989년도 추계학술대회 논문집 학회본부
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• pp.430-433
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• 1989

This paper describes dynamic engine model that is appricable to idle speed control system development. A basic linear engine model responds to throttle and load torque Inputs to provide manifold pressure and speed outputs. Transfer functions are then derived for the modified linear engine model and significant dynamic characteristics are discussed. Lastly, the strategy for controlling idle speed uses the linear optimal control theory. The linear optimal regulator was designed using a state variable and the performance Index was minimized.