• 대한수학회보
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• 제60권4호
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• pp.933-955
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• 2023

For any prime number p, let J(p) be the set of positive integers n such that the numerator of the n^th harmonic number in the lowest terms is divisible by this prime number p. We consider an extension of this set to the generalized harmonic numbers, which are a natural extension of the harmonic numbers. Then, we present an upper bound for the number of elements in this set. Moreover, we state an explicit condition to show the finiteness of our set, together with relations to Bernoulli and Euler numbers.

• 대한수학회논문집
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• 제33권1호
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• pp.13-36
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• 2018

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.

• 대한수학회보
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• 제58권6호
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• pp.1463-1481
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• 2021

Divisibility properties of harmonic numbers by a prime number p have been a recurrent topic. However, finding the exact p-adic orders of them is not easy. Using class numbers of number fields and Bernoulli numbers, we compute the exact p-adic orders of harmonic type sums. Moreover, we obtain an asymptotic formula for generalized harmonic numbers whose p-adic orders are exactly one.

• Journal of Electrical Engineering and Technology
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• 제13권2호
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• pp.711-721
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• 2018

This paper presents a single-phase asymmetric half-bridge cascaded multilevel inverter based series active power filter (SAPF) for harmonic voltage compensation. The effect of level number on performance of the proposed SAPF is examined in terms of total harmonic distortion (THD) and system efficiency. Besides, the relationship between the level number and the number of switching device are compared with the other multilevel inverter topologies used in APF applications. The paper is also aimed to demonstrate the capability of the SAPF for compensating harmonic voltages alone, without using a passive power filter (PPF). To obtain the required output voltage, a new switching algorithm is developed. The proposed SAPF with levels of 7, 15 and 31 is used in both simulation and experimental studies and the harmonic voltages of the load connected to the point of common coupling (PCC) is compensated under two different loading conditions. Furthermore, very high system efficiency values such as 98.74% and 96.84% are measured in the experimental studies and all THD values are brought into compliance with the IEEE-519 Standard. As a result, by increasing the level number of the inverter, lower THD values can be obtained even under high harmonic distortion levels while system efficiency almost remains the same.

• Journal of Power Electronics
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• 제15권4호
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• pp.964-973
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• 2015

This paper presents a simple approach for the selective harmonic elimination (SHE) of multilevel inverter based on the transistor-clamped H-bridge (TCHB) family. The SHE modulation is derived from the sinusoidal voltage-angle equal criteria corresponding to the optimized switching angles. The switching angles are computed offline by solving transcendental non-linear equations characterizing the harmonic contents using the Newton-Raphson method to produce an optimum stepped output. Simulation and experimental tests are conducted for verification of the analytical solutions. An Altera DE2 field-programmable gate array (FPGA) board is used as the digital controller device in order to verify the proposed SHE modulation in real-time applications. An analysis of the voltage total harmonic distortion (THD) has been obtained for multiple output voltage cases. In terms of the THD, the results showed that the higher the number of output levels, the lower the THD due to an increase number of harmonic orders being eliminated.

• 대한수학회지
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• 제44권2호
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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.

• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.545-555
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• 2009

In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.

• 대한수학회보
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• 제42권2호
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• pp.421-432
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• 2005

Suppose that an infinite graph G of bounded degree has finite number of ends, each of which is p-regular, where $1. Then we can identify all the positive (bounded, respectively) p-harmonic functions on G.

• 한국전산유체공학회지
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• 제15권4호
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• pp.76-84
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• 2010

In order to analyze the periodic unsteady flow problem efficiently the partially implicit harmonic balance (PIHB) method was developed. Contrary to the existing harmonic balance method, this method handles the harmonic source term explicitly and deals with flux terms implicitly. This method has a good convergence in comparison with the full explicit harmonic method and it is easy to apply this method because there is no need to calculate the complicated flux Jacobian term by comparing with the full implicit harmonic method. With the multigrid method about the each harmonic it turns out that this method has a good convergence regardless of the number of harmonics. The oscillating flows over NACA0012 airfoil is considered to verify this method then the result correponsed to both the result of dual time stepping and explicit Runge-Kutta method.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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• pp.834-839
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• 2007

This paper investigates the distortion of magnetic field of a brushless DC (BLDC) motor due to deformed rubber magnet. Global or local deformation of rubber magnet in the BLDC motor is mathematically modeled by using the Fourier series. Distorted magnetic field is calculated by using the finite element method, and unbalanced magnetic force are calculated by using the Maxwell stress tensor. The first harmonic deformation in the global deformation of rubber magnet generates the first harmonic driving frequency of the unbalanced magnetic force, and the rest harmonic deformations of rubber magnet except the harmonic deformation with multiple of common divisor of pole and slot introduces the driving frequencies with multiple of slot number ${\pm}1$ to the unbalanced magnetic force. However, the harmonic deformation with multiple of common divisor of pole and slot does not generate unbalanced magnetic force due to the rotational symmetry. When the rubber magnet is locally deformed, the unbalanced magnetic force has the first harmonic driving frequency and the driving frequencies with multiples of slot number ${\pm}1$.