• 대한수학회보
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• 제40권1호
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• pp.9-15
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• 2003

In this paper, we will deal with the Aleksandrov-Rassias problem. More precisely, we prove some theorems concerning the mappings preserving one or two distances.

• 대한기계학회논문집A
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• 제30권4호
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• pp.457-464
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• 2006

The anterior cruciate ligament (ACL) is liable to a major injury that often results in a functional impairment requiring surgical reconstruction. The success of reconstruction depends on such factors as attachment positions, initial tension of ligament and surgical methods of fixation. The purpose of this study is to find isometric positions of the substitute during flexion/extension. The distance between selected attachments on the femur and tibia was computed from a set of measurements using a 6 degree-of-freedom magnetic sensor system. A three-dimensional knee model was constructed from CT images and was used to simulate length change during knee flexion/extension. This model was scaled for each subject. Twenty seven points on the tibia model and forty two points on the femur model were selected to calculate length change. This study determined the maximum and minimum distances to the tibial attachment during flexion/extension. The results showed that minimum length changes were $1.9{\sim}5.8mm$ (average $3.6{\pm}1.4mm$). The most isometric region was both the posterosuperior and anterior-diagonal areas from the over-the-top. The proposed method can be utilized and applied to an optimal reconstruction of ACL deficient knees.

• 대한수학회논문집
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• 제10권3호
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• pp.653-659
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• 1995

We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.

• 대한수학회지
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• 제54권5호
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• pp.1441-1456
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• 2017

We consider a 3-dimensional Riemannian manifold M with a circulant metric g and a circulant structure q satisfying $q^3=id$. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We introduce three classes of such manifolds. Two of them are determined by special properties of the curvature tensor. The third class is composed by manifolds whose structure q is parallel with respect to the Levi-Civita connection of g. We obtain some curvature properties of these manifolds (M, g, q) and give some explicit examples of such manifolds.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2015년도 추계학술대회
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• pp.51-53
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• 2015

In this paper, we propose an efficient sparse signal recovery algorithm referred to as the matching pursuit with a tree pruning (TMP). Two key ingredients of TMP are the pre-selection to put a restriction on columns of the sensing matrix to be investigated and the tree pruning to eliminate unpromising paths from the search tree. In our analysis, we show that the sparse signal is accurately reconstructed when the sensing matrix satisfies the restricted isometry property. In our simulations, we confirm that TMP is effective in recovering sparse signals and outperforms conventional sparse recovery algorithms.

• 대한전자공학회논문지SP
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• 제46권5호
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• pp.15-24
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• 2009

Compressed sensing은 소수의 선형 관측으로부터 sparse 신호를 복원하는 문제를 언급하고 있다. 최근 벡터 경우에서의 성공적인 연구 결과가 행렬의 경우로 확장되었다. Low-rank 행렬의 compressed sensing은 ill-posed inverse problem을 low-rank 정보를 이용하여 해결한다. 본 문제는 rank 최소화 혹은 low-rank 근사의 형태로 나타내질 수 있다. 본 논문에서는 최근 제안된 여러 가지 효율적인 알고리즘에 대한 survey를 제공한다.

• 한국위성정보통신학회논문지
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• 제9권3호
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• pp.59-63
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• 2014

본 논문에서는 3D 방송의 기본적인 원리를 설명하고 압축 센싱(Compressed Sensing) 기술을 적용하여 3D 방송의 데이터 용량을 줄이는 방식을 제안한다. 샘플링 이론과 압축 센싱 기술의 차이점을 설명하고 개념과 동작원리를 설명한다. 최근 제안된 압축 센싱의 복원 알고리즘인 SS-CoSaMP(Single-Space Compressive Sampling Matched Pursuit) 와 CoSaMP(Compressive Sampling Matched Pursuit)를 소개하고 이를 이용하여 데이터를 압축 복원하여 정확도를 비교한다. 두 알고리즘의 다양한 이미지 복원을 수행하고 계산시간을 비교한다. 결론적으로 낮은 복잡도를 갖는 3D 방송에 적합한 알고리즘을 판단한다.

• 대한수학회보
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• 제20권2호
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• pp.71-74
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• 1983

The problems of the continuity of homomorphisms between Banach algebras have been studied widely for the last two decades to obtain various fruitful results, yet it is far from characterizing the calss of Banach algebras for which each homomorphism from a member of the class into a Banach algebra is conitnuous. For commutative Banach algebras A and B a simple proof shows that every homomorphism .theta. from A into B is continuous provided that B is semi-simple, however, with a non semi-simple Banach algebra B examples of discontinuous homomorphisms from C(K) into B have been constructed by Dales [6] and Esterle [7]. For non commutative Banach algebras the problems of automatic continuity of homomorphisms seem to be much more difficult. Many positive results and open questions related to this subject may be found in [1], [3], [5] and [8], in particular most recent development can be found in the Lecture Note which contains [1]. It is well-known that a$^{*}$-isomorphism from a $C^{*}$-algebra into another $C^{*}$-algebra is an isometry, and an isomorphism of a Banach algebra into a $C^{*}$-algebra with self-adjoint range is continuous. But a$^{*}$-isomorphism from a $C^{*}$-algebra into an involutive Banach algebra is norm increasing [9], and one can not expect each of such isomorphisms to be continuous. In this note we discuss an isomorphism from a commutative $C^{*}$-algebra into a commutative Banach algebra with dense range via separating space. It is shown that such an isomorphism .theta. : A.rarw.B is conitnuous and maps A onto B is B is semi-simple, discontinuous if B is not semi-simple.

• 대한수학회보
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• 제26권1호
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• pp.47-52
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• 1989

Methods of Riemannian geometry has played an important role in the study of compact transformation groups. Every effective action of a compact Lie group on a differential manifold leaves a Riemannian metric invariant and the study of such actions reduces to the one involving the group of isometries of a Riemannian metric on the manifold which is, a priori, a Lie group under the compact open topology. Once an action of a compact Lie group is given an invariant metric is easily constructed by the averaging method and the Lie group is naturally imbedded in the group of isometries as a Lie subgroup. But usually this invariant metric has more symmetries than those given by the original action. Therefore the first question one may ask is when one can find a Riemannian metric so that the given action coincides with the action of the full group of isometries. This seems to be a difficult question to answer which depends very much on the orbit structure and the group itself. In this paper we give a sufficient condition that a subgroup action of a compact Lie group has an invariant metric which is not invariant under the full action of the group and figure out some aspects of the action and the orbit structure regarding the invariant Riemannian metric. In fact, according to our results, this is possible if there is a larger transformation group, containing the oringnal action and either having larger orbit somewhere or having exactly the same orbit structure but with an orbit on which a Riemannian metric is ivariant under the orginal action of the group and not under that of the larger one. Recently R. Saerens and W. Zame showed that every compact Lie group can be realized as the full group of isometries of Riemannian metric. [SZ] This answers a question closely related to ours but the situation turns out to be quite different in the two problems.