• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.101-108
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• 1998

For a smoothly bounded n-connected domain $\Omega$ in C, we get a formula representing the relation between the Szego" kernel associated with $\Omega$ and holomorphic mappings obtained from harmonic measure functions. By using it, we show that the coefficient of the above holomorphic map is zero in doubly connected domains.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.1039-1044
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• 2000

We investigate the projectively flat warped product manifolds and study the geometric structure of the base space and its fibre. Specifically we find the conditions that the scalar curvature of the base space (B,g) vanishes if and only if f is harmonic on (B,g) and the fibre (F,$\bar{g}$) is a space of constant curvature.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.157-168
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• 2015

In this paper, we prove that every f-biharmonic map from a complete Riemannian manifold into a Riemannian manifold with non-positive sectional curvature,satisfying some condition, is f-harmonic. Also we present some properties for the f-biharmonicity of submanifolds of $\mathbb{S}^n$, and we give the classification of f-biharmonic curves in 3-dimensional sphere.

• East Asian mathematical journal
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• v.29 no.1
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• pp.91-99
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• 2013

In this paper, we prove that the BMO norm and the Garsia norm are equivalent on a bounded domain in $\mathbb{R}^N$. Also, we investigate the equivalent relation between the Lipschitz norm and the Garsia-type norm for harmonic functions.

• The Journal of Engineering Research
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• v.5 no.1
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• pp.37-44
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• 2004

n this paper, an efficient LP method for discrete harmonic spectra is proposed and discussed. A new efficient LP method is a combination of recursive and frequency selective LP. While the recursive LP provides better spectral matching in spectral hill, frequency selective LP eliminates numerical instability and improves spectral matching when the harmonics are confined in the low frequency region. The proposed LP method is applied to the HILN coder. Simulation results using a verification model(VM) software for real audio signals show a definite trend of significant improvement.

• 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.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.911-920
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• 2019

In this paper we characterize semiconformally flat spacetimes and a spacetime with harmonic semiconformal curvature tensor. At first in a semiconformally flat perfect fluid spacetime we obtain a state equation and prove that in particular for dimension n = 4, the spacetime represents a model for incoherent radiation. Next we prove that perfect fluid spacetime with harmonic semiconformal curvature tensor is of Petrov type I, D or O and the spacetime is a GRW spacetime. As a consequence we obtain several corollaries.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.859-867
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• 2002

In this paper, we get a necessary and sufficient condition for an inner automorphism between compact connected semisimple Lie groups to be an atone transformation, and obtain atone transformations of (SU(n),g) with some left invariant metric g.

• East Asian mathematical journal
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• v.40 no.5
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• pp.515-526
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• 2024

We consider the initial value problem of the Schrödinger equation for an Euler operator 𝓡 on ℂⁿ that is an analogue of the harmonic oscillator in ℝⁿ. We get some regularity results of the Schrödinger equation on Fock spaces.

• Journal of Power Electronics
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• v.9 no.3
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• pp.403-409
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• 2009

Automatically tuned passive filters can improve power quality to a great extent in power systems. A novel three-phase shunt auto-tuned filter is designed to effectively compensate source current harmonics and to provide reactive power required by the non-linear load, which draws a highly reactive, harmonic-rich current from the supply. An artificial neural network (ANN) based controller selects filter component values in accordance with reactive power requirement and harmonic compensation. Traditional passive filters are permanently connected to the system and draw large amounts of source current even under light load conditions. By using auto-tuned filters, the passive filter components can be controlled according to load variations and, hence, draw only required source currents. The selection is done by the ANN with the help of a properly tuned knowledge base to provide instantaneous compensation using a digital controller.