• Journal for History of Mathematics
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• v.28 no.4
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• pp.167-179
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• 2015

We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

• Journal of the Korean Statistical Society
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• v.10
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• pp.140-144
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• 1981

This paper approximates to a kernel density estimate by a truncated series of expansion involving Hermite polynomials, since this could ease the computing burden involved in the kernel-based density estimation. However, this truncated series may give a multimodal estimate when we are estiamting unimodal density. In this paper we will show a way to insure the truncated series to be positive and unimodal so that the approximation to a kernel density estimator would be maeningful.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.1018-1021
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• 1988

This study is concerned with modeling an elastomer constitutive relation by utilizing the truncated Volterra series. Actual experimental data from the Instron Tester are obtained for combined input, i.e. constant strain rate followed by a constant strain input. These data are then estimated for step inputs and utilized for the truncated Volterra series models. One second order and one third order truncated Volterra series models have been employed to estimated the force-displacement relation which is one of the prominent properities to characterize the viscoelastic material. The third order Volterra series model has better results, compared with those of the second order Volterra series model.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.6
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• pp.71-78
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• 1989

The imput-output relations for nonlinear systems can be explicitly represented by the Volterra series and they can be characterized by the Volterra kernels. This study is concerned with modeling an elastomer force-displacement relation due to step inputs by utilizing the truncated Volterra series. Since it is practically impossible to apply step inputs that have infinite slope at zero time, the loads due to constant penetration(displacement) rate followed by constant penetration inputs are measured as an alternative approach and estimated for step inputs and then utilized for the truncated Volterra series models. One second order and one third order truncated Volterra series models have been employed to model the force-displacement relation which is one of the prominent properties to characterize the viscoelastic material. The third order truncated Volterra series model has better results, compared with those of the second order truncated Volterra series model.

• Proceedings of the Acoustical Society of Korea Conference
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• 1987.11a
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• pp.93-97
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• 1987

In this paper a SAW based AWZPSK modulator using the classical truncated cosine series functoins as a baseband pulse is described. A SAW AWQPSK modulator has been designed and fabricated on YZ-LINBO3 substrates. Measured responses meet the theoretical values with tolerable amounts of deviation. This SAW-based device shows good performance as a simple AWQPSK modulator.

• Journal of Ocean Engineering and Technology
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• v.37 no.6
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• pp.225-237
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• 2023

In this study, numerical simulations for a single fixed truncated circular cylinder in regular waves were conducted to investigate the nonlinear wave run-up under various dampers and wave period conditions. The present study used the volume of fluid (VOF) technique to capture the air-water interface. The unsteady Reynolds-averaged Navier-Stokes (URANS) equation with the k- 𝜖 turbulence model was solved using the commercial computational fluid dynamics (CFD) software STAR-CCM+. First, a systematic spatial convergence study was conducted to assess the performance and precision of the present numerical wave tank. The numerical scheme was validated by comparing the numerical results of wave run-up on a bare truncated cylinder with the experimental results, and a good agreement was achieved. Then, a series of parametric studies were carried out to examine the wave run-up time series around the truncated cylinder with single and dual dampers in terms of the first- and second-order harmonic and mean set-up components. Additionally, the local wave field and the flow velocity vectors adjacent to the cylinder were evaluated. It was confirmed that under short wave conditions, the high position of the damper led to a noticeable increase in the wave run-ups with significant changes in the first- and second-order harmonic components.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.55-60
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• 2011

The aim of the paper is to apply Homotopy Perturbation Method (HPM) for the solution of a nonlinear fractional differential equation. Finally, the solution obtained by the Homotopy perturbation method has been numerically evaluated and presented in the form of tables and then compared with those obtained by truncated series method. A good agreement of the results is observed.

• Journal of the Korean Statistical Society
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• v.11 no.2
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• pp.131-138
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• 1982

Analogous to Singh's (1978) characterization of positive-Poisson distributioin and Shanmugam and Singh's (1992) characterization of logarithmic series distribution, a characterization and its statistical application of the negative binomial distribution truncated at zero are given in this paper. While it is known that under certain conditions the negative binomial distribution truncted at zero approaches the positive-Poisson and the logarithmic series distributions, we show here that the results of this paper approach in limit the results of Singh, and Shanmugam and Singh, respectively. Using the biologicla data from Sampford (1955), we illusrate our results. Also, expressions are explicitly given to test the hypothesis whether a random sample is indeed from a geometric distribution.

• Journal of Korean Society for Quality Management
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• v.17 no.1
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• pp.19-34
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• 1989

In this paper, we propose the Bayes estimators of the reliability for a system consisting of the left-truncated exponential components under the truncated normal distribution as a conjugate prior distribution and squared - error loss function on the series, parallel and k-out-of-m : G system. And we compare the proposed Bayes estimators of the system reliability each other in terms of MSE performances and stabilities by the Monte Carlo simulation.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.2
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• pp.952-969
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• 2019

This study develops new analytical solutions to water wave diffraction by vertical truncated cylinders in the context of linear potential theory. Three typical truncated surface-piercing cylinders, a submerged bottom-standing cylinder and a submerged floating cylinder are examined. The analytical solutions utilize the multi-term Galerkin method, which is able to model the cube-root singularity of fluid velocity near the edges of the truncated cylinders by expanding the fluid velocity into a set of basis function involving the Gegenbauer polynomials. The convergence of the present analytical solution is rapid, and a few truncated numbers in the series of the basis function can yield results of six-figure accuracy for wave forces and moments. The present solutions are in good agreement with those by a higher-order BEM (boundary element method) model. Comparisons between present results and experimental results in literature and results by Froude-Krylov theory are conducted. The variation of wave forces and moments with different parameters are presented. This study not only gives a new analytical approach to wave diffraction by truncated cylinders but also provides a reliable benchmark for numerical investigations of wave diffraction by structures.