• Journal for History of Mathematics
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• v.19 no.2
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• pp.115-124
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• 2006

Functions of bounded variation were discovered by Jordan in 1881 while working out the proof of Dirichlet concerning the convergence of Fourier series. Here, we investigate Waterman's study with respect to bounded variation and its application on a closed bounded interval. The value of his study is whether Dirichlet-Jordan theorem holds in which function classes or not and summability method is what modifies its Fourier coefficients to make resulting series converge to the associated function. We have a view that the directions of future research with respect to bounded variation are two things; one is to find the function spaces which are larger than HBV and smaller than ${\phi}BV$, and the other is to find a fields of applications.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.9
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• pp.801-808
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• 1991

Volume holographic interconnection scheme for photonic sitching and optical neural network has been presented. Theoretical formulation for photorefative space-change fields generated by the illumination of multiple noncollinear plane light interferenc pattens was achieved by substituting the complex Fourier series of the space-chage field and freecarrier density into Kukhtarev's nonlinear diffeential equations.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.12
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• pp.1216-1222
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• 2009

This article describes a simple method for generating the walking trajectory for the biped humanoid robot. The method used a simple inverted model instead of complex multi-mass model and a reasonable explanation for the model simplification is included. The problem of gait trajectory generation is to find the solution from the desired ZMP trajectory to CoG trajectory. This article presents the analytic solution for the bipedal gait generation on the bases of ZMP trajectory. The presented ZMP trajectory has Fourier series form, which has finite or infinite summation of sine and cosine functions, and ZMP trajectory can be designed by calculating the coefficients. From the designed ZMP trajectory, this article focuses on how to find the CoG trajectory with analytical way from the simplified inverted pendulum model. Time segmentation based approach is adopted for generating the trajectories. The coefficients of the function should be designed to be continuous between the segments, and the solution is found by calculating the coefficients with this connectivity conditions. This article also has the proof and the condition of solution existence.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.13 no.1
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• pp.59-65
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• 2014

To obtain an elliptical trajectory at the cutting edge during elliptical vibration cutting, sinusoidal voltage excitations of two piezoelectric actuators have commonly been used. In this study, PWM excitation, which is relatively simple to generate, was employed and its characteristics were investigated. In experimental and analytical analyses, we found that for PWM excitation, the integer-multiple frequencies of the excitation voltage distorted the shape of the elliptical trajectory, whereas at a duty ratio(DR) of 50%, the distortion of the elliptical trajectory was minimized due to disappearance of the first overtone. When the magnitude of the maximum excitation voltage was maintained at the same level for both PWM and sinusoidal excitation, PWM (DR=50%) excitation produced a greater vibration amplitude than sinusoidal excitation but resulted in more rapid saturation of a high-frequency power amplifier.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.67-96
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• 2008

In the 19th century Fourier and Dirichlet studied the expansion of "arbitrary" functions into the trigonometric series and this led to the development of the Riemann's definition of the integral. Riemann's integral was considered to be of the highest generality and was discussed intensively. As a result, some weak points were found but, at least at the beginning, these were not considered as the criticism of the Riemann's integral. But after Jordan introduced the theory of content and measure-theoretic approach to the concept of the integral, and after Borel developed the Jordan's theory of content to a theory of measure, Lebesgue joined these two concepts together and obtained a new theory of integral, now known as the "Lebesgue integral".

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2001.05a
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• pp.437-442
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• 2001

Recently, transformerless inverters have been studied to reduce sizes and costs of utility-connected PV systems. This paper presents a transformerless PV inverter using a two-phase boost converter of reduced ripples in input current and output voltage, low voltage stress of semiconductor device and reduced size of input reactor. And new PWM method is introduced, whose on-off time is calculated from simultaneous equation induced by fourier series. To verify a validity of the proposed transformerless inverter, computer simulation has been carried out.

• The Transactions of the Korean Institute of Power Electronics
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• v.16 no.3
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• pp.234-241
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• 2011

This paper proposes a simple static overmodulation strategy that extends the linearity of the inverter output voltage. The proposed method obtains the reference vector having the instantaneous value directly from the modulation index based on the magnitude of fundamental voltage, and has a simplified form of phase command. This method does not need trigonometric functions for calculating the magnitude of the reference vector. The magnitude of reference voltage and holding angle in the overmodulation region corresponding to the modulation index are determined in advance to have the same fundamental voltage magnitude by using the result of Fourier series expansion.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.1
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• pp.123-130
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• 2008

An analytical method for the free vibration of a flexible rectangular plate in contact with water is developed by the Rayleigh-Ritz method. The plate clamped along the edges is partially contacted with water at both sides. It is assumed that the contained water is incompressible and inviscid. The wet mode shape of the plate is assumed as a combination of the dry mode shapes of a clamped beam. The liquid motion is described by using the liquid displacement potential and determined by using the compatibility conditions along the liquid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict excellently the fluid-coupled natural frequencies comparing with the finite element analysis result.

• Atmosphere
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• v.33 no.4
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• pp.387-398
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• 2023

The double Fourier series (DFS) spectral dynamical core is evaluated for the two idealized test cases in comparison with the spherical harmonics (SPH) spectral dynamical core. A new approach in calculating the meridional expansion coefficients of DFS, which was recently developed to alleviate a computational error but only applied to the 2D spherical shallow water equation, is also tested. In the 3D deformational tracer transport test, the difference is not conspicuous between SPH and DFS simulations, with a slight outperformance of the new DFS approach in terms of undershooting problem. In the baroclinic wave development test, the DFS-simulated wave pattern is quantitatively similar to the SPH-simulated one at high resolutions, but with a substantially lower computational cost. The new DFS approach does not offer a salient advantage compared to the original DFS while computation cost slightly increases. This result suggests that the current DFS spectral method can be a practical and alternative dynamical core for high-resolution global modeling.

• Journal of IKEEE
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• v.28 no.3
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• pp.432-439
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• 2024

This paper introduces an enhanced Selective Harmonic Elimination (SHE) technique of a single-phase Cascaded H-Bridge (CHB) Multilevel Inverter (MLI) for improving the reliability and power quality of a second life battery energy storage system (ESS). The technique involves solving non-linear transcendental equations derived from Fourier series offline to determine the optimal switching angles for the proposed SHE-PWM implementation. These angles are then applied in real-time via a Look-Up Table (LUT). The Levenberg-Marquardt algorithm, an iterative method, is employed in MATLAB to solve the equations and obtain the switching angles. The effectiveness of the proposed method is validated using PLECS simulation software and is compared with other conventional PWM techniques for MLIs.