• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.165-170
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• 2019

$C^1$ generically, if a diffeomorphism $f:M{\rightarrow}M$ of a closed smooth Riemannian manifold M has the asymptotic average shadowing property or the average shadowing property then f has a decomposition property.

• Korean Journal of Computational Design and Engineering
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• v.15 no.4
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• pp.297-305
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• 2010

Medical image acquisition techniques such as CT and MRI have disadvantages in that the numerous time and efforts are needed. Furthermore, a great amount of radiation exposure is an inherent proberty of the CT imaging technique, a number of side-effects are expected from such method. To improve such conventional methods, a number of novel methods that can obtain 3D medical images from a few X-ray images, such as algebraic reconstruction technique (ART), have been developed. Such methods deform a generic model of the internal body part and fit them into the X-ray images to obtain the 3D model; the initial shape, therefore, affects the entire fitting process in a great deal. From this fact, we propose a novel method that can generate a 3D vertebraic generic model based on the statistical database of CT scans in this study. Moreover, we also discuss a method to generate patient-tailored generic model using the facts obtained from the statistical analysis. To do so, the mesh topologies of CT-scanned 3D vertebra models are modified to be identical to each other, and the database is constructed based on them. Furthermore, from the results of a statistical analysis on the database, the tendency of shape distribution is characterized, and the modeling parameters are extracted. By using these modeling parameters for generating the patient-tailored generic model, the computational speed and accuracy of ART can greatly be improved. Furthermore, although this study only includes an application to the C1 (Atlas) vertebra, the entire framework of our method can be applied to other body parts generally. Therefore, it is expected that the proposed method can benefit the various medical imaging applications.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.103-108
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• 2015

In this paper we prove that $C^1$-generically, if a diffeomorphism f on a closed $C^{\infty}$ manifold M satisfies weak specification on a locally maximal set ${\Lambda}{\subset}M$ then ${\Lambda}$ is hyperbolic for f. As a corollary we obtain that $C^1$-generically, every diffeomorphism with weak specification is Anosov.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.147-159
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• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1259-1267
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• 2014

In this paper we show that any chain transitive set of a diffeomorphism on a compact $C^{\infty}$-manifold which is $C^1$-stably limit shadowable is hyperbolic. Moreover, it is proved that a locally maximal chain transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is limit shadowable.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.345-349
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• 2014

We show that $C^1$-generically, a differentiable map is positively measure expansive if and only if it is expanding.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.35-54
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• 2007

Let $M_c$ = M(2, 0, c) be the moduli space of O(l)-semistable rank 2 torsion-free sheaves with Chern classes $c_1=0\;and\;c_2=c$ on a K3 surface X, where O(1) is a generic ample line bundle on X. When $c=2n\geq4$ is even, $M_c$ is a singular projective variety equipped with a holomorphic symplectic structure on the smooth locus. In particular, $M_c$ has trivial canonical divisor. In [22], O'Grady asks if there is any symplectic desingularization of $M_{2n}$ for $n\geq3$. In this paper, we show that there is no crepant resolution of $M_{2n}$ for $n\geq3$. This obviously implies that there is no symplectic desingularization.

• YAKHAK HOEJI
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• v.49 no.4
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• pp.255-259
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• 2005

Financial standing of National Health Insurance has been experiencing a grave deterioration during the last 4-5 years, and the yearly amount paid by the insurance for drug expense rose up to 4 trillion won recently. Furthermore, the ratio of drug expenses in the total expenditure of the insurance reached about $25\%$, showing the tendency to be levelled off. As a measure to improve the financial deterioration of the insurance and to encourage generic substitution among the health professionals, we compared pharmacokinetic parameters of brand name drug (Lamisil) and generic drug (Muzonal) containing terbinafine HCl in healthy volunteers. The area under the curve (AUC) of the two drugs showed $2220.4\pm784.7\;and\;2143.1\pm861.6hr{\cdot}ng/ml$ in the corresponding order and no statistically significant difference was identified. The peak concentration $(C_{max})$ of the generic drug demonstrated $566.6\pm246.2 ng/ml$ compared to $550.8\pm204.0$ of brand name drug, which was not significantly different either. Time to reach peak concentration showed about 6 minutes difference between the drugs, which has no clinical significance to the treatment of dermatomycosis and dermatophytosis.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.259-266
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• 2024

The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to r-strongly irreducible r-ideals (endowed with Zariski topologies) of monoids, called terminal spaces. We show that terminal spaces are T₀, quasi-compact, and every nonempty irreducible closed subset has a unique generic point. We characterize rarithmetic monoids in terms of terminal spaces. Finally, we provide necessary and sufficient conditions for the subspaces of r-maximal r-ideals and r-prime r-ideals to be dense in the corresponding terminal spaces.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.569-581
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• 2020

In this paper, we introduce the new general concept of usual expansiveness which is called "positively weak measure expansiveness" and study the basic properties of positively weak measure expansive C¹-differentiable maps on a compact smooth manifold M. And we prove that the following theorems. (1) Let 𝓟𝓦𝓔 be the set of all positively weak measure expansive differentiable maps of M. Denote by int(𝓟𝓦𝓔) is a C¹-interior of 𝓟𝓦𝓔. f ∈ int(𝓟𝓦𝓔) if and only if f is expanding. (2) For C¹-generic f ∈ C¹ (M), f is positively weak measure-expansive if and only if f is expanding.