• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.625-635
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• 2016

In this paper, we study certain doubly-warped products which admit gradient Ricci solitons with harmonic Weyl curvature and non-constant soliton function. The metric is of the form $g=dx^2_1+p(x_1)^2dx^2_2+h(x_1)^2\;{\tilde{g}}$ on ${\mathbb{R}}^2{\times}N$, where $x_1$, $x_2$ are the local coordinates on ${\mathbb{R}}^2$ and ${\tilde{g}}$ is an Einstein metric on the manifold N. We obtained a full description of all the possible local gradient Ricci solitons.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.103-114
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• 1997

The asymptotic Dirichlet problem for harmonic functions on a noncompact complete Riemannian manifold has a long history. It is to find the harmonic function satisfying the given Dirichlet boundary condition at infinity. By now, it is well understood [A, AS, Ch, S], when M is a Cartan-Hadamard manifold with sectional curvature $-b^2 \leq K_M \leq -a^2 < 0$. (By a Cartan-Hadamard manifold, we mean a complete simply connected manifold of non-positive sectional curvature.)

• Journal of Magnetics
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• v.12 no.3
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• pp.113-117
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• 2007

Here we report a theoretical description of ferromagnetic vortex dynamics. Based on Thiele's formulation of the Landau-Lifshitz-Gilbert equation, the motion of the vortex core could be described by a function of the vortex core position. Under a parabolic potential generated in the circular magnetic patterns, the vortex core showed a circular rotation-namely the gyrotropic motion, which could be described by a 2-dimensional simple harmonic oscillator. The gyrotropic frequency and apparent damping constant were predicted and compared with the values obtained micromagnetic calculation.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.781-789
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• 2003

Formal manipulations of double series are useful in getting some other identities from given ones and evaluating certain summations, involving double series. The main object of this note is to summarize rather useful double series manipulations scattered in the literature and give their generalized formulas, for convenience and easier reference in their future use. An application of such manipulations to an evaluation for Euler sums (in itself, interesting), among other things, will also be presented to show usefulness of such manipulative techniques.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.215-227
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• 2011

In this paper we introduce a class $h^{-\infty}_{\Phi}(\mathbb{B})$ of weighted spaces of harmonic functions in the unit ball $\mathbb{B}$ of $\mathbb{R}^n$. We dene weakly sufficient sets in this space and give an explicit construction of countable sets of such a type. Various examples of weight functions are also discussed.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.253-266
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• 2021

This work is devoted to the study of a q-harmonic analysis related to the q-analog of the Bessel-Wright integral transform [6]. We establish some important properties of this transform and we focalise our attention in studying the associated transmutation operator.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.559-572
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• 2021

It is well known that every invariant harmonic function on the unit ball of the multi-dimensional complex space has the volume version of the invariant mean value property. In 1993 Ahern, Flores and Rudin first observed that the validity of the converse depends on the dimension of the underlying complex space. Later Lie and Shi obtained the analogues on the unit ball of multi-dimensional real space. In this paper we obtain the half-space analogues of the results of Liu and Shi.

• Proceedings of the KIPE Conference
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• 2004.07b
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• pp.515-518
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• 2004

Increasing of the nonlinear power electronics equipments, power conditioning systems have been researched and developed for many years to compensate the harmonic disturbances and the reactive power. The main function of power conditioning systems is to reduce harmonic distortions, since extensive surveys quantify the problems associated with electric networks having non-linear loads. The main function of power conditioner compensates the current instead of the voltage. Therefore the inverter used in power conditioner is mostly the current controlled type. In this paper, we propose the power conditioner using photovoltaic system, which is operated by the PRT(Polarized Ramp Time) current control algorithm. The proposed system could also achieve Demand Side Management's function and Uninterruptible Power Supply's function simultaneously. To verify the proposed current controlled inverter for improved quality of the grid, the detail simulation and experiment results indicate that operation PCS, DSM and UPS can be achieved.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.37 no.5
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• pp.16-22
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• 2000

This paper presents a compression algorithm applicable for transmitting a HPO hologram data. The proposed algorithm exploits a modulating function to compress the bandwidth of the hologram pattern, resulting in decimation due to relaxed Nyquist sampling constraints. At the receiver, the compressed data will be interpolated and compensated via being divided by the modulating function. We also present compression rate and analyze the resolution of a reconstructed image and the periodicity of harmonic interferences. Finally, we shows the validity of the proposed algorithm by simulation where a reconstructed image from undersampled data is compared with a reconstructed image obtained through decimatioin by modulating function, interpolation and compensation.

• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.97-104
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• 2016

We give representations of differential operators and rules for addition and multiplication of dual quaternions. Also, we research the notions and properties of a regular function and a corresponding harmonic function with values in dual quaternions of Clifford analysis.