• Journal of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.73-75
• /
• 1973

• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1207-1220
• /
• 2018

The generalized hyperharmonic numbers $h^{(m)}_n(k)$ are defined by means of the multiple harmonic numbers. We show that the hyperharmonic numbers $h^{(m)}_n(k)$ satisfy certain recurrence relation which allow us to write them in terms of classical harmonic numbers. Moreover, we prove that the Euler-type sums with hyperharmonic numbers: $$S(k,m;p):=\sum\limits_{n=1}^{{\infty}}\frac{h^{(m)}_n(k)}{n^p}(p{\geq}m+1,\;k=1,2,3)$$ can be expressed as a rational linear combination of products of Riemann zeta values and harmonic numbers. This is an extension of the results of Dil [10] and $Mez{\ddot{o}}$ [19]. Some interesting new consequences and illustrative examples are considered.

• Journal of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.659-670
• /
• 2012

For any $K$ > $2/{\pi}$ we determine the optimal constant $L(K)$ for which the following holds. If $u$, $tilde{u}$ are conjugate harmonic functions on the unit disc with $\tilde{u}(0)=0$, then $$ {\int}_{-\pi}^{\pi}{\mid}\tilde{u}(e^{i\phi}){\mid}\frac{d{\phi}}{2{\pi}}{\leq}K{\int}_{-\pi}^{\pi}{\mid}u(e^{i{\phi}}){\mid}{\log}^+{\mid}u(e^{i{\phi}}){\mid}\frac{d{\phi}}{2{\pi}}+L(K).$$ We also establish a related estimate for orthogonal harmonic functions given on Euclidean domains as well as an extension concerning orthogonal martingales under differential subordination.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.10 s.181
• /
• pp.2413-2419
• /
• 2000

Harmonic resonances in a continuous rotating shaft with distributed mass are discussed. The restoring force of the shaft has geometric stiffening nonlinearity due to the extension of the shaft centerline. The effect of a distributed lateral force, such as the gravity, is assumed. The possibility of the occurrences of harmonic resonances, the shapes of resonance curves, and internal resonance phenomena are investigated.

• Journal of the Korean Society of Industry Convergence
• /
• v.4 no.4
• /
• pp.379-386
• /
• 2001

The lower toughness or brittle materials for mechanical test lead to the additional requirement that applied displacements be controlled with high resolution. Biaxial tension and shear tester using stepper motor with harmonic driver is shown. The device had to be high resolution so that the crack initiation process of slow extension and steady growth could be examined, Grip plates were connected to a linear bearing and actuator. The actuators consisted of stepper motors with harmonic driver connected to pre-loaded ball screw and nut assemblies. The encoders and motor controllers were connected to a personal computer so that arbitrary displacements histories could he prescribed in normal and tangential directions. The linear bearings were used to react loads perpendicular to their axes while allowing low friction, parallel movement of the attached grips. Load cells measured the reactions normal and tangential. the loads measured the reactions were recorded by the computer.

• The Transactions of the Korean Institute of Electrical Engineers B
• /
• v.52 no.2
• /
• pp.68-79
• /
• 2003

We estimated harmonics on power system of AC railway based on quantitatively measured harmonics and investigated the need of facilities for harmonics reduction. In order to analysis harmonics which inflow into power system due to increase in collector voltages and harmonic currents generated from the train when the railway is in operation, the railway system Is sectioned into power supply, railway line, AT, sectioning Post and subsectioning post. For analysis of extension of currents resulting from the railway loads, PWM converter, VVVF inverter and the feeder system are modeled based on the dynamic node technique(DNT). In order to test the usefulness of the DNT for analysis of harmonic effects, the measured harmonic currents and harmonic magnification ratios at the S/K substation are compared with simulation results using DNT modelling, which include the results for two cases with and without filters for suppression of harmonic currents. When 8 cars(4M4T) are in operation, the total sum of harmonic currents resulting from the train at M and T phases, which inflow into the substation along with the railway line, is calculated. Using the harmonics analysis program for railway feeder system with these data, the total harmonic distortion factor(710) at the outgoing point of KEPCO substation is computed. The calculation shows that when the maximum THD at the receiving point of H/K substation was 0.0443% which is much lower than 1.5% which is the allowable value of KEPCO at 154kV as well as IEEE-519 above 132kV This result indicates that any measure for harmonics reduction in Incheon International Airport Railway is not needed.

• Journal of the Optical Society of Korea
• /
• v.13 no.1
• /
• pp.15-21
• /
• 2009

High-order harmonic generation from a solid surface affected by the contrast of a laser pulse was studied using an oscillating mirror model. High-order harmonics generated from solid surfaces have unusual properties such as spectral redshift, and an intensity difference between even- and odd-order harmonics which is not reported for high-order harmonics generated by a gas medium. We confirmed that high-order harmonics from solid surfaces have selectivity of polarization as well as cut-off extension and the enhancement of conversion efficiency proportional to laser intensity. And the principle of operation and the characteristics of a plasma mirror system developed for achieving high contrast laser pulses to pursue the experimental realization of high-harmonic generation from solid surfaces are reported. Energy fluence on the plasma mirrors is tunable between $10\;J/cm^2$ and $1000\;J/cm^2$ and around 1000 shots are available before the plasma mirrors require replacement.

• Journal of Power Electronics
• /
• v.12 no.3
• /
• pp.477-486
• /
• 2012

This paper proposes a novel current control scheme for vector-controlled induction machine (IM) drives in the overmodulation (OVM) range, with which the voltage utilization of the voltage-source inverter (VSI) can be maximized. In the OVM region, the original voltage reference is modified by changing its magnitude and angle, which causes the motor current to be distorted, resulting in a deterioration of the current control performance. To meet with this situation, the harmonic components in the feedback currents should be eliminated before being input to the PI current controllers. For this, a composite observer is applied to extract the fundamental and harmonic components from the distorted currents, which gives a good performance without a delay and the effect of a fundamental frequency variation. In addition, through a detailed analysis of the response of the PI current controllers in the OVM range, the effectiveness of using the composite observer is demonstrated. Simulation and experimental results for a 3-kW induction motor drive are shown to verify the validity of the proposed method.

• Proceedings of the KSR Conference
• /
• 2005.11a
• /
• pp.754-764
• /
• 2005

This paper presents the RC-Bank installation by its optimal location and design to reduce harmonics on the Korean high-speed railway system. The system model of the Korean high-speed railway system is based on 8-port representation, which is an extension of 2-port network theory. A new proposed model is for harmonic analysis in $2\times27.5kV$ traction power supply system including feeders, contact lines, rails and autotransformers. The proposed model is developed by combining fundamental element models of the Korean high-speed railway system, and it is verified by comparing simulation results with measurement data regarding the amplification rate of harmonic currents.

• Proceedings of the KSR Conference
• /
• 2000.05a
• /
• pp.100-107
• /
• 2000

This paper proposes a new model for harmonic analysis in 2${\times}$25㎸ traction power supply system including inverted feeder, contact line, rails and auto-transformer. The system model is based on four-port representation which is an extension of two-port network theory. In order to verify the proposed approach, we have analysed and tested real traction power feeding system focused on the amplification of harmonic current. The calculation results front tile proposed approach and the measurement data from the test are widely described in the paper.