• Journal of Power Electronics
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• v.12 no.5
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• pp.830-841
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• 2012

Active power filters (APF) can be employed for harmonic compensation in power systems. In this paper, a fuzzy based method is proposed for identification of probable APF nodes of a radial distribution system. The modified adaptive particle swarm optimization (MAPSO) technique is used for final selection of the APFs size. A combination of Fuzzy-MAPSO method is implemented to determine the optimal allocation and size of APFs. New fuzzy membership functions are formulated where the harmonic current membership is an exponential function of the nodal injecting harmonic current. Harmonic voltage membership has been formulated as a function of the node harmonic voltage. The product operator shows better performance than the AND operator because all harmonics are considered in computing membership function. For evaluating the proposed method, it has been applied to the 5-bus and 18-bus test systems, respectively, which the results appear satisfactorily. The proposed membership functions are new at the APF placement problem so that weighting factors can be changed proportional to objective function.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.129-147
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• 2011

In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on $\mathbb{R}^2$. By using change of variables we reduce the harmonic oscillators having general quadratic potentials to the standard harmonic oscillators and compute their spectra and eigenfunctions. We then discuss their zeta functions and zeta-determinants. In some special cases we compute the zeta-determinants of harmonic oscillators concretely by using the Riemann zeta function, Hurwitz zeta function and Gamma function.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.360-369
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• 2022

The aim of this study is to establish some new Jensen and Lazhar type inequalities for p-convex function that is a generalization of convex and harmonic convex functions. The results obtained here are reduced to the results obtained earlier in the literature for convex and harmonic convex functions in special cases.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.449-457
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• 2003

On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.155-161
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• 2014

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that $Ric^M{\geq}-\frac{4(p-1)}{p^2}{\mu}_0$ at all $x{\in}M$ and Vol(M) is infinite, where ${\mu}_0$ > 0 is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on M. Then any p-harmonic map ${\phi}:M{\rightarrow}N$ of finite p-energy is constant Also, we study Liouville type theorem for p-harmonic morphism.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.521-540
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• 2004

In this paper, we give a sharp estimate on the cardinality of the set generating the convex hull containing the image of harmonic maps with polynomial growth rate on a certain class of manifolds into a Cartan-Hadamard manifold with sectional curvature bounded by two negative constants. We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifold into a regular ball in terms of massive subsets, in the case when the space of bounded harmonic functions on the manifold is finite dimensional.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.73-95
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• 1999

We prove that if a given complete Riemannian manifold is roughly isometric to a complete Riemannian manifold satisfying the volume doubling condition, the Poincar inequality and the finite covering condition at infinity on each end, then every positive harmonic function on the manifold is asymptotically constant at infinity on each end. This result is a direct generalization of those of Yau and of Li and Tam.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.243-256
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• 2022

In 1914, Bohr proved that there is an r₀ ∈ (0, 1) such that if a power series ∑^∞_m=0 c_mz^m is convergent in the open unit disc and |∑^∞_m=0 c_mz^m| < 1 then, ∑^∞_m=0 |c_mz^m| < 1 for |z| < r₀. The largest value of such r₀ is called the Bohr radius. In this article, we find Bohr radius for some univalent harmonic mappings having different dilatations. We also compute the Bohr radius for functions that are convex in one direction.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.51-58
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• 1997

On the setting of the upper half-space, H of the euclidean n-space, we consider the question of when the Poisson integral of a function on the boundary of H is a harmonic Bergman function and here we give a partial answer.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.31-41
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• 2003

In this paper, we will show that the bounds for coefficients of harmonic, orientation-preserving, univalent mappings f defined on ${\Delta}$ = {z : |z| > 1} with $f({\Delta})={\Delta}$ are sharp by finding extremal functions.