• 대한수학회보
• /
• 제55권3호
• /
• pp.819-835
• /
• 2018

Let $f=h+{\bar{g}}$ be a normalized harmonic mapping in the unit disk $\mathbb{D}$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D^{\epsilon}{_f}=zf_z-{\epsilon}{\bar{z}}f_{\bar{z}}({\mid}{\epsilon}{\mid}=1)$ and $F_{\lambda}(z)=(1-{\lambda)f+{\lambda}D^{\epsilon}{_f}(0{\leq}{\lambda}{\leq}1)$ when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function $f=h+{\bar{g}}$. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].

• Journal of Information Processing Systems
• /
• 제10권1호
• /
• pp.23-35
• /
• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.

• 대한수학회보
• /
• 제52권6호
• /
• pp.1925-1935
• /
• 2015

In this paper, we study right half-plane harmonic mappings $f_0$ and f, where $f_0$ is fIxed and f is such that its dilatation of a conformal automorphism of the unit disk. We obtain a sufficient condition for the convolution of such mappings to be convex in the direction of the real axis. The result of the paper is a generalization of the result of by Li and Ponnusamy [11], which itself originates from a problem posed by Dorff et al. in [7].

• 대한수학회논문집
• /
• 제34권3호
• /
• pp.841-854
• /
• 2019

In this article, a subclass of univalent harmonic mapping is introduced by restricting its analytic part to lie in the class $S^{\delta}[{\alpha}]$, $0{\leq}{\alpha}<1$, $-{\infty}<{\delta}<{\infty}$ which has been introduced and studied by Kumar [17] (see also [20], [21], [22], [23]). Coefficient estimations, growth and distortion properties, area theorem and covering estimates of functions in the newly defined class have been established. Furthermore, we also found bound for the Bloch's constant for all functions in that family.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1998년도 추계학술대회 논문집 학회본부A
• /
• pp.58-60
• /
• 1998

This paper analyzes the torque characteristics with the structure of harmonic side drive motor using by F.E.M and conformal mapping method. F.E.M and conformal analysis result are almost same. Through the results, we investigate how do design parameters variation affect torque characteristics.

• Investigative Magnetic Resonance Imaging
• /
• 제22권1호
• /
• pp.37-49
• /
• 2018

Purpose: The effect of global inhomogeneity on quantitative susceptibility mapping (QSM) was investigated. A technique referred to as Simultaneous Unwrapping Phase with Error Recovery from inhomogeneity (SUPER) is suggested as a preprocessing to QSM to remove global field inhomogeneity-induced phase by polynomial fitting. Materials and Methods: The effect of global inhomogeneity on QSM was investigated by numerical simulations. Three types of global inhomogeneity were added to the tissue susceptibility phase, and the root mean square error (RMSE) in the susceptibility map was evaluated. In-vivo QSM imaging with volunteers was carried out for 3.0T and 7.0T MRI systems to demonstrate the efficacy of the proposed method. Results: The SUPER technique removed harmonic and non-harmonic global phases. Previously only the harmonic phase was removed by the background phase removal method. The global phase contained a non-harmonic phase due to various experimental and physiological causes, which degraded a susceptibility map. The RMSE in the susceptibility map increased under the influence of global inhomogeneity; while the error was consistent, irrespective of the global inhomogeneity, if the inhomogeneity was corrected by the SUPER technique. In-vivo QSM imaging with volunteers at 3.0T and 7.0T MRI systems showed better definition in small vascular structures and reduced fluctuation and non-uniformity in the frontal lobes, where field inhomogeneity was more severe. Conclusion: Correcting global inhomogeneity using the SUPER technique is an effective way to obtain an accurate susceptibility map on QSM method. Since the susceptibility variations are small quantities in the brain tissue, correction of the inhomogeneity is an essential element for obtaining an accurate QSM.

• 한국콘텐츠학회논문지
• /
• 제10권4호
• /
• pp.106-114
• /
• 2010

메쉬 파라메터화는 입력으로 들어온 메쉬와 파라메터 영역 사이의 부드러운 일대일 대응함수를 구하는 것으로, 삼차원 스캐너를 통해 획득한 디지털 형상을 여러 가지 응용문제에 활용하기 위해 필요한 디지털 형상 처리의 핵심기반기술이다. 본 논문에서는 구형 위상구조를 가지는 삼차원 물체에 대해, 표면뿐만 아니라 내부를 포함한 물체 전체를 단일 입방정육면체로 하모닉 매핑하는 새로운 삼차원 볼륨파라메터화 방법을 제안한다. 제안하는 방법은 입력으로 들어온 볼륨메쉬의 표면을 정육면체와 동일한 위상구조를 가지는 여섯 개의 영역으로 나누고, 이를 이용하여 볼륨 파라메터화의 경계조건을 계산한다. 이후 경계조건을 만족하며 볼륨 내부의 하모닉 에너지를 최소화하는 하모닉 매핑을 계산하여 물체 내부까지 왜곡이 적은 삼차원 파라메터화 결과를 얻어낸다. 실험결과를 통해, 본 논문에서 제안하는 방법을 통해 다양한 구형 삼차원 모델에 대해 삼차원 볼륨파라메터화 결과를 효과적으로 얻을 수 있음을 확인하였다.

• 호남수학학술지
• /
• 제27권2호
• /
• pp.195-203
• /
• 2005

We show that the exact Bergman kernel function associated to a $C^{\infty}$ bounded domain in the plane relates the derivatives of the Ahlfors map in an explicit way. And we find several formulas relating the exact Bergman kernel to classical kernel functions in potential theory.

• 전력전자학회:학술대회논문집
• /
• 전력전자학회 2000년도 전력전자학술대회 논문집
• /
• pp.237-240
• /
• 2000

A new control method using average comparison strategy have been proposed in this paper. This control method realizes sinusoidal input and output current. unity input displacement factor regardless of load power factor. Moreover compensation of the asymmetrical and harmonic containing input voltage is sautomatically realized and calculation time of control function is reduced.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2005년도 제36회 하계학술대회 논문집 B
• /
• pp.1204-1206
• /
• 2005

This paper deals with magnetic field analysis and computation of cogging torque in IPM motor with an analytical method, which is based on the Conformal Mapping technique. The magnetic field is analyzed by solving space harmonic field analysis due to inserted PM magnetizing distribution. Conformal Mapping method is then used for considering the slot opening effect and rotor saliency effect on the air-gap field magnetic distribution. Then, by integrating the field over the stator surface, cogging torque is calculated. The validity of the proposed analytical method is confirmed by comparing the results with 2-D FEA results.