• Honam Mathematical Journal
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• v.44 no.1
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• pp.121-134
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• 2022

In this study, we obtain the spherical images of minimal curves in the complex space in ℂ⁴ which are obtained by translating Cartan frame vector fields to the centre of hypersphere, and present their properties such as becoming isotropic cubic, pseudo helix, and spherical involutes. Also, we examine minimal curves which are characterized by a system of differential equations.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.391-401
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• 2022

In this study, we investigate the explicit characterization of spherical curves using the Flc (Frenet like curve) frame in Euclidean 3-space. Firstly, the axis of curvature and the osculating sphere of a polynomial space curve are calculated using Flc frame invariants. It is then shown that the axis of curvature is on a straight line. The position vector of a spherical curve is expressed with curvatures connected to the Flc frame. Finally, a differential equation is obtained from the third order, which characterizes a spherical curve.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.653-659
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• 2017

Let $p{\geq}1$ be a real number. A tuple $T=(T_1,{\ldots},T_n)$ of commuting bounded linear operators on a Banach space X is called an ${\ell}^p$-spherical isometry if ${\sum_{i=1}^{n}}{\parallel}T_ix{\parallel}^p={\parallel}x{\parallel}^p$ for all $x{\in}X$. The tuple T is called a toral isometry if each Ti is an isometry. By a result of Ansari, Hedayatian, Khani-Robati and Moradi, for every $n{\geq}1$, there is a supercyclic ${\ell}^2$-spherical isometric n-tuple on ${\mathbb{C}}^n$ but there is no supercyclic ${\ell}^2$-spherical isometry on an infinite-dimensional Hilbert space. In this article, we investigate the supercyclicity of ${\ell}^p$-spherical isometries and toral isometries on Banach spaces. Also, we introduce the notion of semicommutative tuples and we show that the Banach spaces ${\ell}^p$ ($1{\leq}p$ < ${\infty}$) support supercyclic ${\ell}^p$-spherical isometric semi-commutative tuples. As a result, all separable infinite-dimensional complex Hilbert spaces support supercyclic spherical isometric semi-commutative tuples.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.690-695
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• 2000

This article deals with the analytic results on the development and application of the Spherical CVT. The Spherical CVT is marked by its simple configuration, the infinite torque multiplication characteristic, and the smooth transitions between forward/neutral/reverse states of output speed. In this study, we describe the conceptual principles behind the Spherical CVT and some applications of it, which we developed recently. And, we propose the shifting algorithm based on the analytic consideration of CVT powertrain system. Contrary to conventional shifting algorithms using the OOL(optimal operating line) of the power source, the proposed shifting algorithm is represented as a $2^{nd}$ order equation in an explicit form, and it reveals the possibility of theoretic design of all optimal controller. As an example, we present numerical results that demonstrate the energy saving possible and the proposed shifting algorithm from the use of the Spherical CVT over standard reduction gear unit, using an ideal dc motor model.

• Journal of Korea Game Society
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• v.17 no.6
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• pp.139-152
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• 2017

In this paper, we propose a ground area detection technique based on region segmentation in the spherical image. We modified the Watershed planar image segmentation method to segment spherical images. After regions are segmented, the ground area is detected by comparing colors and textures of pixels of the assumed ground region with the pixels of other regions. The ground detection technique for planar images cannot be used for spherical images due to the spherical distortion. Considering the spherical distortion, we designed the ground shape detection algorithm to detect the ground area in the spherical images. Our experimental results show that the proposed technique properly detects ground areas both for the flat ground and the obstacle-filled ground environments.

• Journal of Korea Game Society
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• v.17 no.6
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• pp.153-164
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• 2017

In spherical panoramic images, SURF, a feature description method for planar patterns, does not work correctly due to heavy spherical distortion. Since a plane pattern is distorted in a spherical image, the pattern search and replacement in a spherical panoramic image should be treated differently from the case of the planar image. This paper proposes a planar texture replacement method, which transforms a spherical panoramic image into a cubemap panoramic image, searches a pattern using SURF, replaces a plane pattern, and then converts it into a spherical panoramic image.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.555-581
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• 2015

Triangular pyramid and Quadrangular pyramid elements for partial double-layer spherical reticulated shells of pyramidal system are investigated in the present study. Macro programs for six typical partial double-layer spherical reticulated shells of pyramidal system are compiled by using the ANSYS Parametric Design Language (APDL). Internal force analysis of six spherical reticulated shells is carried out. Distribution regularity of the stress and displacement are studied. A shape optimization program is proposed by adopting the sequence two-stage algorithm (RDQA) in FORTRAN environment based on the characteristics of partial double-layer spherical reticulated shells of pyramidal system and the ideas of discrete variable optimization design. Shape optimization is achieved by considering the objective function of the minimum total steel consumption, global and locality constraints. The shape optimization of six spherical reticulated shells is calculated with the span of 30m~120m and rise to span ratio of 1/7~1/3. The variations of the total steel consumption along with the span and rise to span ratio are discussed with contrast to the results of shape optimization. The optimal combination of main design parameters for six spherical reticulated shells is investigated, i.e., the number of the optimal grids. The results show that: (1) The Kiewitt and Geodesic partial double-layer spherical reticulated shells of triangular pyramidal system should be preferentially adopted in large and medium-span structures. The range of rise to span ratio is from 1/6 to 1/5. (2) The Ribbed and Schwedler partial double-layer spherical reticulated shells of quadrangular pyramidal system should be preferentially adopted in small-span structures. The rise to span ratio should be 1/4. (3) Grids of the six spherical reticulated shells can be optimized after shape optimization and the total steel consumption is optimized to be the least.

• Structural Engineering and Mechanics
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• v.56 no.5
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• pp.813-833
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• 2015

Spherical reticulated shells are widely applied in structural engineering due to their good bearing capability and attractive appearance. Parametric modeling of spherical reticulated shells is the basis of internal analysis and optimization design. In the present study, generation methods of nodes and the corresponding connection methods of rod elements are proposed. Modeling programs are compiled by adopting the ANSYS Parametric Design Language (APDL). A shape optimization method based on the two-stage algorithm is presented, and the corresponding optimization program is compiled in FORTRAN environment. Shape optimization is carried out based on the objective function of the minimum total steel consumption and the restriction condition of strength, stiffness, slenderness ratio, stability. The shape optimization of four typical Schwedler spherical reticulated shells is calculated with the span of 30 m~80 m and rise to span ratio of 1/7~1/2. Compared with the shape optimization results, the variation rules of total steel consumption along with the span and rise to span ratio are discussed. The results show that: (1) The left and right rod-Schwedler spherical reticulated shell is the most optimized and should be preferentially adopted in structural engineering. (2) The left diagonal rod-Schwedler spherical reticulated shell is second only to left and right rod regarding the mechanical behavior and optimized results. It can be applied to medium and small-span structures. (3) Double slash rod-Schwedler spherical reticulated shell is advantageous in mechanical behavior but with the largest total weight. Thus, this type can be used in large-span structures as far as possible. (4) The mechanical performance of no latitudinal rod-Schwedler spherical reticulated shell is the worst and with the second largest weight. Thus, this spherical reticulated shell should not be adopted generally in engineering.

• Journal of Digital Convergence
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• v.11 no.1
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• pp.315-320
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• 2013

We have investigated the variation of spherical aberration of the anterior and posterior surface in a Korean sample population with various age between 20 to 71 years old. We used Pentacam (Oculus Inc., Germany) to measure the corneal radius, asphericity, and spherical aberration of 290 patients with normal cornea. There were negative correlation between corneal anterior radius and spherical aberration(r = -0.22, p<0.0001), and, there were negative correlation between corneal posterior radius and spherical aberration(r=-0.27, p < 0.0001). There were positive correlation between anterior asphericity and spherical aberration(r = 0.24, p < 0.0001), however there were negative correlation between posterior asphericity and spherical aberration(r = -0.17, p=0.00288).The average of anterior spherical aberration and posterior spherical aberration was $0.482{\pm}0.099{\mu}m$ and $-0.098{\pm}0.029{\mu}m$. The average of spherical aberration was $0.385{\pm}0.097{\mu}m$. There were significant positive correlations between anterior spherical aberration and age(r = 0.227, p<0.0001), and there were positive correlations between posterior aberration and age(r = 0.349, p<0.0001). It is considered that this data can be used as basic information for furture studies for improving the quality of vision of modern human and, through the analysis of the spherical aberration of cornea was to provide a better understanding of the optical part of the Korean's eye.

• Journal of Magnetics
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• v.15 no.2
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• pp.78-84
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• 2010

A 3-D.O.F. spherical PM motor has 3 degrees of freedom in its motion by tilting and rotating of a shaft, which can be applied in a range of fields. The back-EMF is proportional to the field flux and angular velocity. The back-EMF constant in conventional rotating machine has a uniform value. However, in a spherical PM motor, the back-EMF constant of the coils varies according to the tilting conditions regardless of whether the angular speed is constant. Consideration of the back-EMF constant is useful for designing 3-D.O.F. spherical PM motors. In this study, the back-EMF constant of the spherical PM motor was considered carefully.