• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.4 s.247
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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.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.25-36
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• 2009

We compute spectrums of left regular isometries and weighted left regular isometries of a strongly perforated semigroup $P=\{0,2,3,4,{\cdots}\}$.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.967-974
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• 1996

We discuss contraction operators T in the class A, where A is the class of absolutely continuus contractions for which the Sz.-Nagy-Foias functional calculus is isometry. We obtain relationship between the class $A_{n, \aleph_0}$ and hereditary property $(\tilde{P}_n)$.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.895-904
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• 1997

Let B(z) be a power series with operator coefficients where multiplication by B(z), T, is a contractive and everywhere defined transforamtion in the square summable power series. Then there is a Julia operator U for T such that $$ U = (T D)(\tilde{D}^* L) \in B(H \oplus D, K \oplus \tilde{D}), $$ where D is the state space of a conjugate canonical linear system with transfer function B(z).

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.467-476
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• 1999

In the present paper, we describe the action of isometry groups of 30dimensional weakly symmetric spaces and classify 3-dimensional connected weaky symmetric spaces. Further, we determine 3-dimensional weakly symmetric spaces in terms of the eigen- values of the Ricci transformation.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.513-521
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• 2009

We first introduce a complex hyperbolic space and a complex hyperbolic manifold. After defining the canonical horoball and the canonical cusp on the complex hyperbolic manifold, we estimate the volumes of canonical cusps of complex hyperbolic manifolds. Finally, we deal with cusped, complex hyperbolic 2-manifolds, and in particular, the ones with only one cusp.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.771-776
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• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).

• Journal for History of Mathematics
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• v.20 no.4
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• pp.49-60
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• 2007

In this article, the concept of rigidity of smooth surfaces in the three dimensional Euclidean space which naturally arises in elementary geometry is introduced, and the natural process of the development of rigidity theory for compact surfaces and its generalizations are investigated.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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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.