• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.217-220
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• 2008

In this paper, we investigate the harmonic mappings that arise in connection with Scherk's surface and helicoid.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1419-1431
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• 2018

Let $f=h+{\bar{g}}$ be a harmonic mapping of the unit disk ${\mathbb{D}}$ with the holomorphic part h satisfying that h is injective and $h({\mathbb{D}})$ is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.865-869
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• 2012

In [2], D. Gaier has given an estimates of harmonic measure. In this paper, we generalize for the K-quasiconformal mapping the corresponding result.

• Progress in Superconductivity and Cryogenics
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• v.14 no.1
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• pp.14-19
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• 2012

Shimming, active and/or passive, is indispensable for most MR (magnetic resonance) magnets where homogeneous magnetic fields are required within target spaces. Generally, shimming consists of two steps, field mapping and correcting of fields, and they are recursively repeated until the target field homogeneity is reached. Thus, accuracy of the field mapping is crucial for fast and efficient shimming of MR magnets. For an accurate shimming, a "magnetic" center, which is a mathematical origin for harmonic analysis, must be carefully defined, Although the magnetic center is in general identical to the physical center of a magnet, it is not rare that both centers are different particularly in HTS (high temperature superconducting) magnets of which harmonic field errors, especially high orders, are significantly dependent on a location of the magnetic center. This paper presents a new algorithm, based on a field mapping theory with harmonic analysis, to define the best magnetic center of an MR magnet in terms of minimization of pre-shimming field errors. And the proposed algorithm is tested with simulation under gaussian noise environment.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1591-1603
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• 2014

In this paper, we investigate maximum principle, convergence of sequences and angular limits for harmonic Bloch mappings. First, we give the maximum principle of harmonic Bloch mappings, which is a generalization of the classical maximum principle for harmonic mappings. Second, by using the maximum principle of harmonic Bloch mappings, we investigate the convergence of sequences for harmonic Bloch mappings. Finally, we discuss the angular limits of harmonic Bloch mappings. We show that the asymptotic values and angular limits are identical for harmonic Bloch mappings, and we further prove a result that applies also if there is no asymptotic value. A sufficient condition for a harmonic Bloch mapping has a finite angular limit is also given.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1377-1387
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• 2013

Let $f$ be a harmonic mapping on the unit disc ${\Delta}$ in $\mathbb{C}$. We give some condition for $f$ to be a quasiconformal homeomorphism on ${\Delta}$ and to have a quasiconformal extension to the whole plane $\bar{\mathbb{C}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order ${\alpha}{\in}(0,1)$.

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

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.369-374
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• 2016

In this paper, we study the hereditary convex radius of convex harmonic mapping $f(z)=f_1(z)+{\bar{f_x(z)}}$ under the integral operator $I_f(z)={\int_{o}^{z}}{\frac{f_1(u)}{u}}du+{\bar{{\int_{o}^{z}}{\frac{f_x(u)}{u}}}}$ and obtain the sharp constant ${\frac{{\sqrt[4]{6}}-{\sqrt[]{15}}}{9}}$, which generalized the result corresponding to the class of analytic functions given by Nash.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.803-814
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• 1995

Let $\Sigma$ be the class of all complex-valued, harmonic, orientation-preserving, univalent mappings defined on $\Delta = {z : $\mid$z$\mid$ > 1}$ that map $\infty$ to $\infty$.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.1-3
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• 2002

In this paper, we obtain some coefficient bounds of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$.