• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.85-91
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• 1995

For a locally compact Hausdorff space, we denote by $C_0(X)$ the Banach space of all continuous complex valued functions defined on X which vanish at infinity, equipped with the usual sup norm. In case X is compact, we write C(X) instead of $C_0(X)$. A well-known Banach-Stone theorem states that the existence of an isometry between the function spaces $C_0(X)$ and $C_0(Y)$ implies X and Y are homemorphic. D. Amir [1] and M. Cambern [2] independently generalized this theorem by proving that if $C_0(X)$ and $C_0(Y)$ are isomorphic under an isomorphism T satisfying $\left\$\mid$ T \right\$\mid$ \left\$\mid$ T^1 \right\$\mid$ < 2$, then X and Y must also be homeomorphic.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.111-118
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• 2008

Using the Hyers-Ulam-Rassias stability method, we investigate isomorphisms in quasi-Banach algebras and derivations on quasi-Banach algebras associated with the Cauchy-Jensen functional equation $$2f(\frac{x+y}{2}+z)$$=f(x)+f(y)+2f(z), which was introduced and investigated in [2, 17]. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Furthermore, isometries and isometric isomorphisms in quasi-Banach algebras are studied.

• Journal of the Korean Arthroscopy Society
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• v.2 no.1
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• pp.4-14
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• 1998

As with anterior cruciate ligament reconstruction, posterior cruciate ligament(PCL) reconstruction requires a good understanding of the anatomy and biomechanical properties of the PCL to place the graft correctly as well as to choose the appropriate structure and material for the graft. The anatomy and function of the PCL can be somewhat confusing and continuing to evolve so far. Recent studies have focused on the insertion site anatomy and the identification of the functional components of the ligament. The issue of the ligament isometry and the role of PCL in knee kinematics are still totally resolved. This article can be provided an update on current concepts of the anatomy and biomechanics of the PCL through literature reviews. A clear understanding of these knowledges enables the clinicians to diagnose injuries to the PCL accurately and to reconstruct these structures successfully.

• Journal of Satellite, Information and Communications
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• v.10 no.3
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• pp.57-61
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• 2015

This paper describes the basic principles of 3D broadcast system and proposes new 3D broadcast technology that reduces the amount of data by applying CS(Compressed Sensing). Differences between Sampling theory and the CS technology concept was described. CS algorithm SS-CoSaMP(Single-Space Compressive Sampling Matched Pursuit) and AMP(Approximate Message Passing) was described. Image data compressed and restored by these algorithm was compared. Calculation time of the algorithm having a low complexity is determined.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.831-838
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• 2020

Let H be a complex Hilbert space and T : H → H be a bounded linear operator. Then T is said to be norm attaining if there exists a unit vector x₀ ∈ H such that ║Tx₀║ = ║T║. If for any closed subspace M of H, the restriction T|M : M → H of T to M is norm attaining, then T is called an absolutely norm attaining operator or 𝓐𝓝-operator. In this note, we discuss linear maps on B(H), which preserve the class of absolutely norm attaining operators on H.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.63-82
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• 2011

On the hyperbolic space $D^n$, codimension-one totally geodesic foliations of class $C^k$ are classified. Except for the unique parabolic homogeneous foliation, the set of all such foliations is in one-one correspondence (up to isometry) with the set of all functions z : [0, $\pi$] $\rightarrow$ $S^{n-1}$ of class $C^{k-1}$ with z(0) = $e_1$ = z($\pi$) satisfying |z'(r)| ${\leq}1$ for all r, modulo an isometric action by O(n-1) ${\times}\mathbb{R}{\times}\mathbb{Z}_2$. Since 1-dimensional metric foliations on $D^n$ are always either homogeneous or flat (that is, their orthogonal distributions are integrable), this classifies all 1-dimensional metric foliations as well. Equations of leaves for a non-trivial family of metric foliations on $D^2$ (called "fifth-line") are found.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.669-672
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• 1998

In this paper, w epropose a fast fractal coding method based on correlation coefficients of subblocks in input image. In the proposed method, domain pool is selected based on correlation analysis of input image and the isometry transform for each block is chosen based on the IFS method. To investigate the performance of the proposed method, we compared image quality and encoding time with full search PIFS method and jacquin's PIFS method. Experimental results show that proposed method yields nearly the same performance in PSNR, and its encoding time is reduced for images size of 512*512 compared with full search PIFS method and jacquin's PIFS method.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.277-287
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• 2007

We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends($1) in which every bounded energy finite p-harmonic function is asymptotically constant for almost every path, then the set $\mathcal{HBD}_p(G)$ of all bounded energy finite p-harmonic functions on G is in one to one corresponding to $\mathbf{R}^l$, where $l$ is the number of p-hyperbolic ends of G. Furthermore, we prove that if a graph G' is roughly isometric to G, then $\mathcal{HBD}_p(G')$ is also in an one to one correspondence with $\mathbf{R}^l$.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.7 no.1
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• pp.27-30
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• 1977

To insure accuracy in dental roentgenographs, it is important that the patient's head position and angulation of the x-ray tube. In 1907 Cieszynski applied the rule of isometry to dental radiography and established that in the production of an accurate image of a tooth, the central ray must be porjected perpendicularly to a plane bisecting angle formed by the longitudinal axis of the tooth and the film plane. Proper exposure of the film is a part of the production of a good dental radiograph, and correct processing also makes an essential contribution to the quality of the radiograph. The author analysed the failure of exposure and processing results, and recommended followings. 1. The patient head must be positioned that occlusal plane are parallel with the horizontal floor. 2. Central ray must be projected to the objective tooth and supporting structure and projected as perpendicularly to tooth axis and film surface as possible. 3. In processing, the temperature of the solution and the processing time must be correct.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2015.11a
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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.