• The Transactions of the Korean Institute of Electrical Engineers B
• /
• v.48 no.3
• /
• pp.104-109
• /
• 1999

In order to design and predict the performance of the harmonic side drive motor, it is necessary to analyze the torque generated by the structure. In this paper, an analytical model is proposed for design. Conformal mapping is used to model the capacitance and torque of the motor as a function of the rotor angular position with two-dimensional approximation. Then the result of conformal mapping analysis is verified with F.E.M result.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.411-415
• /
• 2012

In 1995 it was proved by Gonz$\acute{a}$lez-Diez that the cyclic group generated by a p-gonal automorphism of a closed Riemann surface of genus at least two is unique up to conjugation in the full group of conformal automorphisms. Later, in 2008, Gromadzki provided a different and shorter proof of the same fact using the Castelnuovo-Severi theorem. In this paper we provide another proof which is shorter and is just a simple use of Sylow's theorem together with the Castelnuovo-Severi theorem. This method permits to obtain that the cyclic group generated by a conformal automorphism of order p of a handlebody with a Kleinian structure and quotient the three-ball is unique up to conjugation in the full group of conformal automorphisms.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1823-1834
• /
• 2018

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component $x^T$ of the position vector field is the most natural vector field tangent to the Euclidean submanifold M. We simply call the vector field $x^T$ the canonical vector field of the Euclidean submanifold M. In earlier articles [4,5,9,11,12], we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, torse-forming, conservative or incompressible. In this article we study Euclidean submanifolds with conformal canonical vector field. In particular, we characterize such submanifolds. Several applications are also given. In the last section we present three global results on complete Euclidean submanifolds with conformal canonical vector field.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 1999.05a
• /
• pp.43-46
• /
• 1999

Various techniques for optimizing the performance indices of sonar arrays have been discussed, Maximizing the directivity or beamforming technique with constraints have been studied, however these performances are adapted on the condition of isotropic linear array. In this paper we discuss the problems resulting from application of conformal array by using previous techniques. Finally, we could get a desired beam pattern after use of the compensated weight vector to solve the problems.

• Communications of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.177-183
• /
• 2006

The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({\alpha},\;{\beta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{\Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.725-743
• /
• 2017

We prove that there exist foliations whose leaves are the maximal integral null manifolds immersed as submanifolds of indefinite locally conformal cosymplectic manifolds. Necessary and sufficient conditions for such leaves to be screen conformal, as well as possessing integrable distributions are given. Using Newton transformations, we show that any compact ascreen null leaf with a symmetric Ricci tensor admits a totally geodesic screen distribution. Supporting examples are also obtained.

• Journal of the Optical Society of Korea
• /
• v.20 no.1
• /
• pp.174-179
• /
• 2016

In this paper, a novel full-aperture reflective null measuring method is proposed to detect the transmission wavefront of a conformal dome surface. An aspheric compensator is designed and placed behind the dome to reflect the aspheric testing wave back to the same path. To ensure the feasibility of this method, tolerance analysis is conducted, and guidance to assembly is given accordingly. The accuracy of this method is verified to be λ/30 (λ =3.39 μm) by Monte Carlo algorithm. In addition, the influence of different error factors, including the thickness error and decenter error of the dome, on the testing wavefront is analyzed. Simulation and experiment indicate that this method is practical and simple, and can measure the conformal domes precisely and comprehensively.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.795-806
• /
• 2007

We investigate F-traceless component of the conformal curvature tensor defined by (3.6) in $K\ddot{a}hler$ manifolds of dimension ${\geq}4$, and show that the F-traceless component is invariant under concircular change. In particular, we determine $K\ddot{a}hler$ manifolds with parallel F-traceless component and improve some theorems, provided in the previous paper([2]), which are concerned with the traceless component of the conformal curvature tensor and the spectrum of the Laplacian acting on $p(0{\leq}p{\leq}2)$-forms on the manifold by using the F-traceless component.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.41 no.12
• /
• pp.1748-1751
• /
• 2016

In this correspondence, we studied 3D uniform rectangular array as an extension of interpolation technique to compensate the beam pattern of 3D conformal array. The simulation result shows outstanding performance comparing to 2D interpolations.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.4
• /
• pp.351-365
• /
• 2019

This article presents a new approach for conformal flattening with optimal cone singularity. The algorithm here takes an optimal control for selecting optimal cones and uses the Ricci flow to force the flattening. This work is considered as a modification to the work of Soliman et al. [1] in the sense that they make use of the Yamabe equation for the flattening, which is an approximation of the Ricci flow. We present a numerical algorithm based on the optimal control with the mathematical background. Several numerical results validate that our method is optimal in total cone angle and usage of the Ricci flow ensures the conformal flattening while selecting optimal cones.