• 충청수학회지
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• 제36권2호
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• pp.125-133
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• 2023

We establish a characterization theorem of elliptic paraboloids in the (n+1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with extrinsic properties such as the (n+1)-dimensional volumes of regions enclosed by the hyperplanes and hypersurfaces, and the n-dimensional areas of projections of the sections of hypersurfaces cut off by hyperplanes.

• 대한수학회보
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• 제33권4호
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• pp.613-618
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• 1996

In this paper, M will always denote an n- dimensional complete Riemannian manifold and $\omega_n$ is the volume of $S^n$.

• 대한수학교육학회지:학교수학
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• 제8권1호
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• pp.27-43
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• 2006

이 연구의 목적은 예비중등교사들의 실제적인 수학화 능력을 신장할 수 있도록 n-단체의 n-부피를 탐구하는 교수단원 를 설계하는 것이다. 이 교수단원에서는 2차원 도형인 삼각형의 넓이와 3차원 도형인 사면체의 부피를 n-단체의 n-부피로 일반화하는 것에 초점을 맞추고 있다. 이 일반화 과정에는 형식불역의 원리와 카발리에리의 원리가 적용된다. n-단체의 n-부피를 구하기 위해 n-직교삼각기둥을 정의하고, 그것의 n-부피를 공리적으로 탐색한다. 그리고 n-단체의 n-부피를 벡터와 행렬식을 이용하여 구한다. 이 교수단원을 통해 예비 중등교사들은 삼각형과 사면체의 일반화된 도형인 n-단체, 그리고 삼각형의 넓이와 사면체의 부피의 일반화된 n-단체의 부피를 이해하고 탐구할 수 있고, 학교수학과 학문수학의 자연스런 연결을 도모할 수 있다.

• 대한수학회지
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• 제55권6호
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• 한국CDE학회논문집
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• 제4권2호
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• pp.162-171
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• 1999

Plane sweep plays an important role in computational geometry. This paper shows that an extension of topological plane sweep to three-dimensional space can calculate the volume swept by rotating a solid polyhedral object about a fixed axis. Analyzing the characteristics of rotational swept volumes, we present an incremental algorithm based on the three-dimensional topological sweep technique. Our solution shows the time bound of O(n²·2?+T?), where n is the number of vertices in the original object and T? is time for handling face cycles. Here, α(n) is the inverse of Ackermann's function.

• Korean Journal of Radiology
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• 제22권3호
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• pp.435-441
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• 2021

Objective: To evaluate the usefulness of the ventricular volume percentage quantified using three-dimensional (3D) brain computed tomography (CT) data for interpreting serial changes in hydrocephalus. Materials and Methods: Intracranial and ventricular volumes were quantified using the semiautomatic 3D threshold-based segmentation approach for 113 brain CT examinations (age at brain CT examination ≤ 18 years) in 38 patients with hydrocephalus. Changes in ventricular volume percentage were calculated using 75 serial brain CT pairs (time interval 173.6 ± 234.9 days) and compared with the conventional assessment of changes in hydrocephalus (increased, unchanged, or decreased). A cut-off value for the diagnosis of no change in hydrocephalus was calculated using receiver operating characteristic curve analysis. The reproducibility of the volumetric measurements was assessed using the intraclass correlation coefficient on a subset of 20 brain CT examinations. Results: Mean intracranial volume, ventricular volume, and ventricular volume percentage were 1284.6 ± 297.1 cm³, 249.0 ± 150.8 cm³, and 19.9 ± 12.8%, respectively. The volumetric measurements were highly reproducible (intraclass correlation coefficient = 1.0). Serial changes (0.8 ± 0.6%) in ventricular volume percentage in the unchanged group (n = 28) were significantly smaller than those in the increased and decreased groups (6.8 ± 4.3% and 5.6 ± 4.2%, respectively; p = 0.001 and p < 0.001, respectively; n = 11 and n = 36, respectively). The ventricular volume percentage was an excellent parameter for evaluating the degree of hydrocephalus (area under the receiver operating characteristic curve = 0.975; 95% confidence interval, 0.948-1.000; p < 0.001). With a cut-off value of 2.4%, the diagnosis of unchanged hydrocephalus could be made with 83.0% sensitivity and 100.0% specificity. Conclusion: The ventricular volume percentage quantified using 3D brain CT data is useful for interpreting serial changes in hydrocephalus.

• 대한의용생체공학회:학술대회논문집
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• 대한의용생체공학회 1997년도 추계학술대회
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• pp.533-536
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• 1997

In this paper, we visualized 3-dimensional volume of heart using volume method by thresholding in EBT slices data. Volume rendering is the method that acquire the color by casting a pixel ray to volume data. The gray level of heart region is so high that we decide heart region by thresholding method. When a pixel ray is cast to volume data, the region that is higher than threshold value becomes heart region. We effectively rendered the heart volume and showed the 3-dimensional heart volume.

• 호남수학학술지
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• 제35권1호
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• pp.37-49
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• 2013

Consider a non-degenerate open convex cone C with vertex the origin in the $n$2-dimensional Euclidean space $E^n$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $p$ is independent of the point $p{\in}M$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.

• 대한수학회보
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• 제60권4호
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• pp.905-913
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• 2023

Suppose that M is a strictly convex hypersurface in the (n + 1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with the origin o in its convex side and with the outward unit normal N. For a fixed point p ∈ M and a positive constant t, we put 𝚽_t the hyperplane parallel to the tangent hyperplane 𝚽 at p and passing through the point q = p - tN(p). We consider the region cut from M by the parallel hyperplane 𝚽_t, and denote by I_p(t) the (n + 1)-dimensional volume of the convex hull of the region and the origin o. Then Schneider's characterization theorem for ellipsoids states that among centrally symmetric, strictly convex and closed surfaces in the 3-dimensional Euclidean space 𝔼³, the ellipsoids are the only ones satisfying I_p(t) = 𝜙(p)t, where 𝜙 is a function defined on M. Recently, the characterization theorem was extended to centrally symmetric, strictly convex and closed hypersurfaces in 𝔼ⁿ⁺¹ satisfying for a constant 𝛽, I_p(t) = 𝜙(p)t^𝛽. In this paper, we study the volume I_p(t) of a strictly convex and complete hypersurface in 𝔼ⁿ⁺¹ with the origin o in its convex side. As a result, first of all we extend the characterization theorem to strictly convex and closed (not necessarily centrally symmetric) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽. After that we generalize the characterization theorem to strictly convex and complete (not necessarily closed) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽.

• International Journal of Naval Architecture and Ocean Engineering
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• 제1권1호
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• pp.20-28
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• 2009

In thus paper we validate a numerical model for wave-structure interaction by comparing numerical results with laboratory data. The numerical model is based on the Navier-Stokes (N-S) equations for an incompressible fluid. The N-S equations are solved by a two-step projection finite volume scheme and the free surface displacements are tracked by the volume of fluid (VOF) method The numerical model is used to simulate solitary waves and their interaction with a group of slender vertical piles. Numerical results are compared with the laboratory data and very good agreement is observed for the time history of free surface displacement, fluid particle velocity and wave force. The agreement for dynamic pressure on the cylinder is less satisfactory, which is primarily caused by instrument errors.