• Bulletin of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.1-20
• /
• 2021

We examine the theory of surfaces in the isotropic three-space, with emphases on the surfaces related to the zero mean curvature.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.953-965
• /
• 2017

In this paper, we classify translation surfaces of Type 2 in the three dimensional simply isotropic space ${\mathbb{I}}_3^1$ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental form of the surface. We also give explicit forms of these surfaces.

• Tunnel and Underground Space
• /
• v.5 no.4
• /
• pp.318-322
• /
• 1995

For transversely isotropic rocks such as schist, shale, etc, a method to determine the anisotropic elastic constants was proposed. Theoretically, equations of elastic constants E1, E2, and G2 can be derived from the measured strains in arbitrary three directions. If we attach three strain gages in accordance with the directons of anisotropy on the rock specimen under uni-axial compression, anisotropic elastic constants can be determined by these equations. With this method, the degree of anisotropy of transversely isotropic rocks will be easily evaluated by simple laboratory test.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.519-530
• /
• 2016

In this paper, we study surfaces of revolution in the three dimensional pseudo-Galilean space. We classify surfaces of revolution generated by a non-isotropic curve in terms of the Gauss map and the Laplacian of the surface. Furthermore, we give the classification of surfaces of revolution generated by an isotropic curve satisfying pointwise 1-type Gauss map equation.

• Investigative Magnetic Resonance Imaging
• /
• v.22 no.4
• /
• pp.229-239
• /
• 2018

Purpose: To assess the diagnostic performance in detecting rotator cuff tears at 3T of non-arthrographic shoulder magnetic resonance imaging (MRI) using 3D isotropic turbo spin-echo (TSE-SPACE) sequence as compared with 2D sequences. Materials and Methods: Seventy-four patients who were arthroscopically confirmed to have underwent non-arthrographic shoulder MRI with 2D sequences and TSE-SPACE were included. Three independent readers retrospectively scored supraspinatus and infraspinatus tendon (SST-IST) and subscapularis tendon (SCT) tears on 2D sequences and TSE-SPACE. Results: The mean sensitivity, specificity, and accuracy of the three readers were 95%, 100%, and 95% on TSE-SPACE and 99%, 93%, and 98% on 2D sequences for detecting SST-IST tears, respectively, whereas those were 87%, 49%, and 68% on TSESPACE and 88%, 66%, and 77% on 2D sequences for detecting SCT tears, respectively. There was no statistical difference between the two sequences, except for in the specificity of one reader for detecting SCT tears. The mean AUCs of the three readers on TSE-SPACE and 2D sequences were 0.96 and 0.98 for detecting SST-IST tears, respectively, which were not significantly different, while those were 0.71 and 0.82 for detecting SCT tears, respectively, which were significantly different (P < 0.05). Conclusion: TSE-SPACE may have accuracy and reliability comparable to conventional 2D sequences for SST-IST tears at non-arthrographic 3T shoulder MRI, whereas TSE-SPACE was less reliable than conventional 2D sequences for detecting SCT tears.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.6
• /
• pp.1581-1590
• /
• 2020

In [1], there are some mistakes in calculations and solutions of differential equations and theorems that appeared in the paper. We here provide correct solutions and theorems.

• Structural Engineering and Mechanics
• /
• v.23 no.2
• /
• pp.115-127
• /
• 2006

The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.32 no.8
• /
• pp.82-90
• /
• 2004

The mechanical characteristics of three types of core with two-dimensional isotropic patterns-triangular, hexagonal and starcell-were studied in applications to sandwich structures. The Young's modulus and shear modulus were calculated for the three core types in the direction normal to the faces. The compressive buckling strength and shear buckling strength were calculated by modeling each cell wall of the core as a plate under compressive or shear load. To verify this model, tests were conducted on scaled specimens to measure the compressive buckling strength of each core. The bending flexibilites of the three cores were also studied. Compliances for the three cores were measured using biaxial flexural tests. The three isotropic core patterns exhibited distinct characteristics. In the direction normal to the faces, all three cores had the same stiffness. However, the starcell core exhibited high flexibility compared to the other cores, indicating potential for application to curved sandwich structures.

• International Journal of Aeronautical and Space Sciences
• /
• v.14 no.4
• /
• pp.350-355
• /
• 2013

Electrical resistance change measurements were performed, to detect fatigue damage of a quasi-isotropic CFRP and cross-ply CFRP laminates. A four-probe method was used to measure the exact electrical resistance change. A three-probe method was used to measure the electrical contact resistance change, during long cyclic loading. The specimen side surface was observed using a video-microscope to detect damage. The measured electrical resistance changes were compared with the observed damage. The results of this study show that the electrical resistance increase of the quasi-isotropic laminate was caused by a delamination crack between ${\pm}45^{\circ}$ plies. Matrix cracking caused a small electrical resistance increase of the cross-ply laminate, but the decreased electrical resistance caused by the shear-plastic deformation impedes matrix-cracking detection.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2004.10a
• /
• pp.525-529
• /
• 2004

A novel translational 3-dof parallel mechanism is proposed and analyzed. The mechanism consists of three RRPS serial subchains and an additional passive 3-dof type serial subchain. Three RRPS serial subchains alone may form a structure of the 6-DOF Stewart Platform mechanism. However, in the proposed mechanism, an additional passive serial subchain acts as constraints to restrict the output motion of the mechanism in 3-DOF translational space. The closed form position solutions of the proposed mechanism and its first-order kinematic model are derived. Then its workspace size and kinematic characteristics are examined via kinematic isotropic index.