• 대한수학회보
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• 제57권2호
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• pp.489-508
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• 2020

This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.

• 대한수학회논문집
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• 제31권3호
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• pp.625-635
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• 2016

In this paper, we study certain doubly-warped products which admit gradient Ricci solitons with harmonic Weyl curvature and non-constant soliton function. The metric is of the form $g=dx^2_1+p(x_1)^2dx^2_2+h(x_1)^2\;{\tilde{g}}$ on ${\mathbb{R}}^2{\times}N$, where $x_1$, $x_2$ are the local coordinates on ${\mathbb{R}}^2$ and ${\tilde{g}}$ is an Einstein metric on the manifold N. We obtained a full description of all the possible local gradient Ricci solitons.

• Bulletin of the Korean Chemical Society
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• 제19권1호
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• pp.93-98
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• 1998

The molecular geometries and harmonic vibrational frequencies of biphenyl in the ground and the first excited triplet states have been calculated using the Hartree-Fock and Becke-3-Lee-Yang-Parr (B3LYP) density functional methods with 6-31G* basis set. Structural change occurs from a twisted benzene-like to a planar quinone-like form upon the excitation to the first excited state. Scaled harmonic vibrational frequencies for the ground state obtained from the B3LYP calculation show good agreement with the available experimental data. A few vibrational fundamentals for both states are newly assigned based on the B3LYP results.

• 대한수학회보
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• 제59권3호
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• pp.709-723
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• 2022

In this note, we revise some vanishing and finiteness results on hypersurfaces with finite index in ℝⁿ⁺¹. When the hypersurface is stable minimal, we show that there is no nontrivial L^2p harmonic 1-form for some p. The our range of p is better than those in [7]. With the same range of p, we also give finiteness results on minimal hypersurfaces with finite index.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.2283-2286
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• 2003

This paper presents conservation of electrical energy in building with harmonics analysis and compensation which occur in electrical system. We use load controlling and management system in order to adjust load factor of system.The maximum demand limiting and controlling are used ,then the system can acquire the prediction and compare it to the maximum demand set point.The electrical signal analysis based on FFT technique. The harmonics are compensated by using harmonic filters.This system consists computer which works as controller, processor , analysis and database unit together with digital power meter in form of multidrop network through serial communication via RS-485.The load control system uses PLC to control load via serial communication RS-485. The A/D converter is used for sampling the electrical signals via parallel port of computer.The harmonic filters are controlled by a computer.The data of measurement such as voltage, current, power, power factor, total harmonic distortion, energy, etc., can be saved as database and analysis. The load factor is adjusted by limiting and controlling maximum demand. The load factor adjustment can reduce the cost of electric consumption and energy generation together with harmonics compensation in order to increase high efficiency of electrical system.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 하계종합학술대회 논문집(4)
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• pp.151-154
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• 2001

In this Paper, a new harmonic imaging technique is proposed and evaluated experimentally. In the proposed method, a weighted chin signal with a hanning window is transmitted. The RF samples obtained on each array element are individually compressed by correlating with the reference signal defined as the 2nd harmonic (2f0) component of a transmitted chirp signal generated in a square-law system. The proposed method uses the compressed 2f0 component to form an image, for which the crosscorrelation term with f0 component should be suppressed below at least -60dB. After experiment, the 6dB pulse width and peak sidelobe level of the compressed 2f0 component were 0.7us and -60dB, respectively. This result shows that the proposed method can successfully eliminate the f0 component with a single transmit-receive event and therefore is more efficient than the conventional pulse inversion (PI) method in terms of frame rate. We also observed that the 2nd harmonic compont starts to decrease for source pressure higher than 210kPa in water, which implies that SNR of the 2nd harmonic imaging using short pulses cnanot be incresed beyond a certain limit.

• 전기학회논문지
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• 제58권10호
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• pp.1930-1935
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• 2009

This paper deals with the torque ripple reduction of permanent magnet synchronous motor using harmonic current injection. Torque ripple of electric motor reduces system stability and performances, therefore efforts to reduce torque ripple are exerted in the design process. Torque ripple can be reduced by appropriate pole/slot combination, skew of rotor or stator, design of magnetic circuit, etc. In addition, torque ripple can be also reduced by input voltage and current, and many researches have been conducted to reduce torque ripple for six-step drive. Torque ripple reduction for current vector controlled permanent magnet synchronous motor also have been conducted and verified by investigating back emf wave form. Torque ripple reduction in this paper started from getting torque profile according to input current and electrical angle calculated by FEA, then instantaneous currents at each electrical angles for constant torque are calculated and applied to experiments. Therefore, 0% of torque ripple can be obtained theoretically with harmonic current injection. In order to maximize the effect of torque ripple reduction, a BLDC motor having high harmonic component of back emf is chosen. With sinusoidal current drive, over 100% of torque ripple is obtained initially, then 0.5 % of torque ripple is obtained by FEA using harmonic current injection. The effect is verified by experiment and the presented method can be effectively applicable to Electric Power Steering(EPS).

• 대한수학회지
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• 제26권2호
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• pp.311-322
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• 1989

• Smart Structures and Systems
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• 제9권2호
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• pp.165-188
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• 2012

In the first part of the paper, the optimal design parameters for tuned liquid column dampers (TLCD) in harmonic pitching motion were investigated. The configurations in design tables include uniform and non-uniform TLCDs with cross-sectional ratios of 0.3, 0.6, 1, 2 and 3 for the design in different situations. A closed-form solution of the structural response was used for performing numerical optimization. The results from optimization indicate that the optimal structural response always occurs when the two resonant peaks along the frequency axis are equal. The optimal frequency tuning ratio, optimal head loss coefficient, the corresponding response and other useful quantities are constructed in design tables as a guideline for practitioners. As the value of the head loss coefficient is only available through experiments, in the second part of the paper, the prediction of head loss coefficients in the form of a design chart are proposed based on a series of large scale tests in pitching base motions, aiming to ease the predicament of lacking the information of head loss for those who wishes to make designs without going through experimentation. A large extent of TLCDs with cross-sectional ratios of 0.3, 0.6, 1, 2 and 3 and orifice blocking ratios ranging from 0%, 20%, 40%, 60% to 80% were inspected by means of a closed-form solution under harmonic base motion for identification. For the convenience of practical use, the corresponding empirical formulas for predicting head loss coefficients of TLCDs in relation to the cross-sectional ratio and the orifice blocking ratio were also proposed. For supplemental information to horizontal base motion, the relation of head loss values versus blocking ratios and the corresponding empirical formulas were also presented in the end.

• Coupled systems mechanics
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• 제1권2호
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.