• Journal of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1321-1336
• /
• 2018

In this paper, we obtain some necessary and sufficient conditions for the Reeb vector field of a trans-Sasakian 3-manifold to be minimal or harmonic. We construct some examples to illustrate main results. As applications of the above results, we obtain some new characteristic conditions under which a compact trans-Sasakian 3-manifold is homothetic to either a Sasakian or cosymplectic 3-manifold.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.713-720
• /
• 2009

We find all left-invariant minimal unit vector fields and strongly normal unit vector fields on a Lie group which is isometric to the hyperbolic space.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1339-1350
• /
• 2018

We will find a necessary and sufficient condition for unit Killing vector fields to be minimal and provide an application of the obtained result.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.951-960
• /
• 2010

We provide the set of left-invariant minimal unit vector fields on the semi-direct product $\mathbb{R}^n\;{\rtimes}_p\mathbb{R}$, where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form $\mathbb{R}^3\;{\rtimes}_p\mathbb{R}$ which are unimodular and of type (R).

• Communications of the Korean Mathematical Society
• /
• v.30 no.4
• /
• pp.457-469
• /
• 2015

From the point of view of pseudohermitian geometry, we classify Legendre surfaces of Sasakian space forms with non-minimal ${\hat{C}}$-parallel mean curvature vector field for the Tanaka-Webster connection.

• Bulletin of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.193-200
• /
• 1994

Let x : $M^{n}$ .rarw. $E^{m}$ be an isometric immersion of a manifold $M^{n}$ into the Euclidean space $E^{m}$ and .DELTA. the Laplacian of $M^{n}$ defined by -div.omicron.grad. The family of such immersions satisfying the condition .DELTA.x = .lambda.x, .lambda..mem.R, is characterized by a well known result ot Takahashi (8]): they are either minimal in $E^{m}$ or minimal in some Euclidean hypersphere. As a generalization of Takahashi's result, many authors ([3,6,7]) studied the hypersurfaces $M^{n}$ in $E^{n+1}$ satisfying .DELTA.x = Ax + b, where A is a square matrix and b is a vector in $E^{n+1}$, and they proved independently that such hypersurfaces are either minimal in $E^{n+1}$ or hyperspheres or spherical cylinders. Since .DELTA.x = -nH, the submanifolds mentioned above satisfy .DELTA.H = .lambda.H or .DELTA.H = AH, where H is the mean curvature vector field of M. And the family of hypersurfaces satisfying .DELTA.H = .lambda.H was explored for some cases in [4]. In this paper, we classify space curves x : R .rarw. $E^{3}$ satisfying .DELTA.x = Ax + b or .DELTA.H = AH, and find conditions for such curves to be equivalent.alent.alent.

• Journal of IKEEE
• /
• v.23 no.4
• /
• pp.1400-1407
• /
• 2019

In this paper, we propose a support vector machine (SVM) based gas classifier that can support real-time self-learning. The modified sequential minimal optimization (MSMO) algorithm is employed to train the proposed SVM. By using a shared structure for learning and classification, the proposed SVM reduced the hardware area by 35% compared to the existing architecture. Our system was implemented with 3,337 CLB (configurable logic block) LUTs (look-up table) with Xilinx Zynq UltraScale+ FPGA (field programmable gate array) and verified that it can operate at the clock frequency of 108MHz.

• The Transactions of the Korean Institute of Power Electronics
• /
• v.6 no.2
• /
• pp.115-124
• /
• 2001

In this paper, authors propose a new nonlinear rotor flux observer for rotor field oriented control of an induction motor which is designed based on the extended Luenberger Observer theory. Extended Luenberger Observer requires minimal solution of nonlinear partial differential equation on its coordinate transformation and linearization needed on a nonlinear observer design in general. The proposed rotor flux observer is derived from the 2 phase model of induction motor on the orthogonal coordination and it has the reduce gain matrix. Simulation and experimentation were performed under the conventional indirect vector control and direct vector control with the proposed observer at different rotor resistance. Simulation results show that the convergence of the proposed observer is influenced by the chosen eigenvalues. Experimentation results on load operation show the direct vector control with the proposed observer is better than the indirect vector control to maintain the characteristics of the vector control.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.40 no.6
• /
• pp.567-573
• /
• 1991

Full direct digital control of induction motor driver is implemented with a minimal hardware structure. This paper deals with the presentation of a low-cost single-chip microprocessor-based control system for three-phase PWM generation and vector control that control speed of the induction motor using the field-oriented control method. Rotor flux is estimated using the indirect sensing method based on the rotor circuit equation in the synchronously rotation reference frame, and slip angle and rotor position are calculated from rotor angular velocity and stator current. Through simulation and experiment, it is shown that the proposed scheme gives good static and dynamic performance to the induction motor drive.

• Journal of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.685-697
• /
• 2015

For a field K, a square-free monomial ideal I of K[$x_1$, . . ., $x_n$] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an $(n, d)^{th}$ f-ideal. In this paper, we prove the existence of $(n, d)^{th}$ f-ideal for $d{\geq}2$ and $n{\geq}d+2$, and we also give some algorithms to construct $(n, d)^{th}$ f-ideals.