• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제6권2호
• /
• pp.25-30
• /
• 2002

Let $E/{\mathbb{Q}$ be an elliptic curve defined over rationals, P is a non-torsion rational point of E and $$S=\{[n]P{\mid}n{\in}{\mathbb{Z}}\}$$. then S is dense in the component of $E({\mathbb{R}})$ which contains the infinity in the usual Euclidean topology or in the topology defined by the invariant Haar measure and it is uniformly distributed.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제10권2호
• /
• pp.71-102
• /
• 2003

The purpose of this paper is to study the geometry of null curves in a 6-dimensional semi-Riemannian manifold $M_q$ of index q, since the general n-dimensional cases are too complicated. We show that it is possible to construct three types of Frenet equations of null curves in $M_q$, supported by one example. We find each types of Frenet equations invariant under any causal change. And we discuss some properties of null curves in $M_q$.

• 한국정밀공학회지
• /
• 제22권3호
• /
• pp.52-60
• /
• 2005

This paper deals with the position control fur a feed drive system in CNC milling machine, which utilizes a modified error signal for the elimination of steady-state error. A linear time-invariant (LTI) system has consistent properties in response to standard test signal inputs. Those also appear in an error curve acquired from the response. From such properties, constructed is an error model for the position control of the feed drive. And then added is the output of the error model to the current error signal. Consequently the resulting proportional control system brings performance improvement in view of the steady-state error. The effectiveness of the proposed scheme is confirmed through simulations and experiments.

• 대한수학회보
• /
• 제44권2호
• /
• pp.379-383
• /
• 2007

We show that the modular equation ${\phi}^{T_n}_m$ (X, Y) for the Thompson series $T_n$ corresponding to ${\Gamma}_0$(n) gives an affine model of the modular curve $X_0$(mn) which has better properties than the one derived from the modular j invariant. Here, m and n are relative prime. As an application, we construct a ring class field over an imaginary quadratic field K by singular values of $T_n(z)\;and\;T_n$(mz).

• 대한전기학회논문지:시스템및제어부문D
• /
• 제54권10호
• /
• pp.604-614
• /
• 2005

Color segmentation takes great attentions since a color is an effective and robust visual cue for characterizing one object from other objects. Color segmentation is, however, suffered from color variation induced from irregular illumination changes. This paper proposes a reliable color modeling approach in HSI (Hue-Saturation-Intensity) rotor space considering intensity information by adopting B-spline curve fitting to make a mathematical model for statistical characteristics of a color with respect to brightness. It is based on the fact that color distribution of a single-colored object is not invariant with respect to brightness variations even in HS (Hue-Saturation) plane. The proposed approach is applied for the segmentation of human skin areas successfully under various illumination conditions.

• 대한수학회지
• /
• 제58권1호
• /
• pp.123-132
• /
• 2021

Let K be a number field and L a finite abelian extension of K. Let E be an elliptic curve defined over K. The restriction of scalars ResKLE decomposes (up to isogeny) into abelian varieties over K $$Res^L_KE{\sim}{\bigoplus_{F{\in}S}}A_F,$$ where S is the set of cyclic extensions of K in L. It is known that if L is a quadratic extension, then AL is the quadratic twist of E. In this paper, we consider the case that K is a number field containing a primitive third root of unity, $L=K({\sqrt[3]{D}})$ is the cyclic cubic extension of K for some D ∈ K×/(K×)3, E = Ea : y2 = x3 + a is an elliptic curve with j-invariant 0 defined over K, and EaD : y2 = x3 + aD2 is the cubic twist of Ea. In this case, we prove AL is isogenous over K to $E_a^D{\times}E_a^{D^2}$ and a property of the Selmer rank of AL, which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제2권6호
• /
• pp.280-298
• /
• 2008

For efficient content-based image retrieval, diverse visual features such as color, texture, and shape have been widely used. In the case of leaf images, further improvement can be achieved based on the following observations. Most plants have unique shape of leaves that consist of one or more blades. Hence, blade-based matching can be more efficient than whole shape-based matching since the number and shape of blades are very effective to filtering out dissimilar leaves. Guaranteeing rotational invariance is critical for matching accuracy. In this paper, we propose a new shape representation, indexing and matching scheme for leaf image retrieval. For leaf shape representation, we generated a distance curve that is a sequence of distances between the leaf’s center and all the contour points. For matching, we developed a blade-based matching algorithm called rotation invariant - partial dynamic time warping (RI-PDTW). To speed up the matching, we suggest two additional techniques: i) priority queue-based pruning of unnecessary blade sequences for rotational invariance, and ii) lower bound-based pruning of unnecessary partial dynamic time warping (PDTW) calculations. We implemented a prototype system on the GEMINI framework [1][2]. Using experimental results, we showed that our scheme achieves excellent performance compared to competitive schemes.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
• /
• pp.16-19
• /
• 1996

In this paper, a sliding mode control scheme that guarantees the smoothness of the control signal and the exponential error convergence is proposed for robot manipulators. The proposed method inserts a low pass filter (LPF) in front of the plant, and the virtual controller is designed for the virtual plant - the combination of the LPF and the robot manipulator. The virtual control signal contains high frequency components because of a switching function. The real control signal, however, always shows a smooth curve since it is an output of the LPF. In addition to the smoothness of the control signal is always assured, the overall system is in the sliding mode at all times, that is, its performance is always invariant under the existence of parameter uncertainties and external disturbances. The closed-loop system is shown to be globally exponentially stable.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2003년도 하계종합학술대회 논문집 V
• /
• pp.2589-2592
• /
• 2003

In this paper, a robust mixed H$_2$/H$\_$$\infty$/ output feedback control method is applied to the design of loop filter for PLL carrier phase tracking. The proposed method successfully copes with large S-curve slope uncertainty and a significant decision delay in the closed-loop that may exist In modern receivers due to a convolutional decoder or an equalizer. The objective is to design an output feedback controller which minimizes the H$_2$performance while satisfying the H$\_$$\infty$/ performance to guarantee the gain margin and phase margin for linear time invariant(LTI) polytopic uncertain systems. LMIs based approach is given to solve this problem. We can verify the H$\_$$\infty$/ performance satisfaction and minimize the phase detector error through the simulation result.

• 대한전기학회논문지
• /
• 제41권9호
• /
• pp.953-959
• /
• 1992

As the TC(time-current) curve corresponding to symmetrical time invariant RMS value has been traditionally chosen and used for setting the relay, it has caused the misoperation errors on relay coordination because of CT secondary current being actually an asymmetrical time varying RMS value. In this paper, an algorithm for calculating the relay operating time is developed to study the asymmetrical effect using the step-by-step method. We represent the relay operating time errors between with and without DC offset versus PSM(plug setting multiplier), TMS(time multiplier setting) and X/R ratio. And also we present the correction factor. Finally we confirm the validity of this technique through the case study.