• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.487-498
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• 2007

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.

• Proceedings of the KIEE Conference
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• 2005.07b
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• pp.1687-1689
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• 2005

In this paper, novel concept of a photovoltaic(PV) power generation system adding the function of active filter(AF) is proposed. Even PV power generation system can be treated to a harmonics source for the power distribution system, it is necessary that the function of AF system in grid connected PV power generation system. Active Filters intended for harmonic solutions are expending their functions from harmonic compensation of nonlinear loads into harmonic isolation between utilities and consumer, and harmonic damping throughout power distribution system. So, the PV system combined the function of AF system can be usefully applied in power distribution system. Here, the control strategy of PV-AF system is introduced.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1255-1280
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• 2017

In this paper we present a new family of identities for parametric Euler sums which generalize a result of David Borwein et al. [2]. We then apply it to obtain a family of identities relating quadratic and cubic sums to linear sums and zeta values. Furthermore, we also evaluate several other series involving harmonic numbers and alternating harmonic numbers, and give explicit formulas.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.319-329
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• 2012

For a norm 1 function ${\sigma}$ in the Fourier-Stieltjes algebra of a locally compact group we define the space of ${\sigma}$-harmonic operators in the non-commutative $L^p$-space associated to the group von Neumann algebra of G. We will investigate some properties of the space and will obtain a precise description of it.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.377-393
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• 2024

In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in ℤ^d. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.3 s.258
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• pp.300-305
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• 2007

Many practical flow problems are defined with the circular boundary. Fluid flows within a circular boundary are however susceptible to a singularity problem when the cylindrical coordinates are employed. To remove this singularity a method has been developed in this study which uses the local harmonic functions in discretization of derivatives as well as interpolation. This paper describes the basic reason for introducing the harmonic functions and the overall numerical methods. The numerical methods are evaluated in terms of the accuracy and the stability. The Lamb-dipole flow is selected as a test flow. We will see that the harmonic-function method indeed gives more accurate solutions than the conventional methods in which the polynomial functions are utilized.

• Journal of Power Electronics
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• v.16 no.6
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• pp.2284-2293
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• 2016

With the rapid development of clean energy, photovoltaic (PV) generation has been utilized in the harmonic compensation of power systems. This paper presents a novel multi-function PV micro-inverter with three stages (pseudo-two-stage). It can inject active power and compensate harmonic currents in the power grid at the same time. In order to keep the micro-inverter working under the maximum allowable output power, an optimized capacity limitation strategy is presented. Moreover, the harmonic compensation can be adjusted according to the customized requirements of power quality. Additionally, a phase shedding strategy in the DC/DC stage is introduced to improve the efficiency of parallel Boost converters in a wide range. Compared with existing capacity limitation methods, the proposed strategy shows better performance and energy efficiency. Simulations and experiments verify the feasibility of the micro-inverter and the effectiveness of the strategy.

• Proceedings of the KIEE Conference
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• 2002.04a
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• pp.225-227
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• 2002

In this paper, novel concept of a photovoltaic(PV) power generation system adding the function of active filter(AF) is proposed. Even PV power generation system can be treated to a harmonics source for the power distribution system, it is necessary that the function of AF system in grid connected PV power generation system. Active Filters intended for harmonic solutions are expending their functions from harmonic compensation of nonlinear loads into harmonic isolation between utilities and consumer, and harmonic damping throughout power distribution system. So, the PV system combined the function of AF system can be usefully applied in power distribution system. Here, the control strategy of PV-AF system is introduced.

• Structural Engineering and Mechanics
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• v.44 no.5
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• pp.681-704
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• 2012

The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.771-776
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• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).