• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.359-376
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• 2002

We give a new interpretation of Darboux transforms in the context of orthogonal polynomials and find conditions in or-der for any Darboux transform to yield a new set of orthogonal polynomials. We also discuss connections between Darboux trans-forms and factorization of linear differential operators which have orthogonal polynomial eigenfunctions.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1149-1156
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• 2016

In this paper, we introduce the degenerate Carlitz q-Bernoulli numbers and polynomials and give some interesting identities and properties of these numbers and polynomials which are derived from the generating functions and p-adic integral equations.

• Journal for History of Mathematics
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• v.33 no.6
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• pp.303-314
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• 2020

Extending the method of extractions of square and cube roots in Jiuzhang Suanshu, Jia Xian introduced zengcheng kaifangfa in the 11th century. The process of zengcheng kaifangfa is exactly the same with that in Ruffini-Horner method introduced in the 19th century. The latter is based on the synthetic divisions, but zengcheng kaifangfa uses the binomial expansions. Since zengcheng kaifangfa is based on binomial expansions, traditional mathematicians in East Asia could not relate the fact that solutions of polynomial equation p(x) = 0 are determined by the linear factorization of p(x). The purpose of this paper is to reveal the difference between the mathematical structures of zengcheng kaifangfa and Ruffini-Honer method. For this object, we first discuss the reasons for zengcheng kaifangfa having difficulties to connect solutions with linear factors. Furthermore, investigating multiple solutions of equations constructed by tianyuanshu, we show differences between two methods and the structure of word problems in the East Asian mathematics.

• Geomechanics and Engineering
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• v.30 no.6
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• pp.551-564
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• 2022

Fragmenting the rock mass is considered as the most important work in open-pit mines. Ground vibration is the most hazardous issue of blasting which can cause critical damage to the surrounding structures. This paper focuses on developing an explicit model to predict the ground vibration through an multi objective evolutionary polynomial regression (MOGA-EPR). To this end, a database including 79 sets of data related to a quarry site in Malaysia were used. In addition, a gene expression programming (GEP) model and several empirical equations were employed to predict ground vibration, and their performances were then compared with the MOGA-EPR model using the mean absolute error (MAE), root mean square error (RMSE), mean (𝜇), standard deviation of the mean (𝜎), coefficient of determination (R²) and a20-index. Comparing the results, it was found that the MOGA-EPR model predicted the ground vibration more precisely than the GEP model and the empirical equations, where the MOGA-EPR scored lower MAE and RMSE, 𝜇 and 𝜎 closer to the optimum value, and higher R² and a20-index. Accordingly, the proposed MOGA-EPR model can be introduced as a useful method to predict ground vibration and has the capacity to be generalized to predict other blasting effects.

• Journal of the Korean Society of Clothing and Textiles
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• v.14 no.2
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• pp.152-163
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• 1990

The purpose of this study is to experimentally analyze the relationship between structural characteristics of cotton fabrics and their cool-and-warm felling in order to develop more comfortable fabrics. Comfort in textile products has been emphasized as consumers preferred performance to fashion of clothing. Thermal comfort of clothing is a basic parameter of the comfort sensation which is usually represented by the cool-and-warm feeling felt by human skin. Cloo-and-warm feeling is perceived by the heat flux which transfers heat energy stored in an object to skin. We feel warm (cool) if the temperature of nerve extremity in skin ascends (descends). As cool-and-warm feeling determines the comfort sensation of clothing, it is important to develop new comfort fabrics. Although considerable works have been made on the body, clothing, and environment, there has been no research study on the structural characteristics of fabrics and their cool and warm feeling. Cool-and-warm feeling is closely related to the transient heat transfer property. This research study used the cotton fabrics manufactured in Korea as sample and measured $q_{max}$ value with thermal property measuring instrument (Thermo-Labo II type). $q_{max}$ values estimated by polynomial regression equation were compared with those observed in this study. This study also identified the structural parameters of cotton fabrics for a specific range of $q_{max}$ values. The findings of this study can be summarized as follows: 1) As the thickness, porosity and air permeability of cotton fabrics increase, $q_{max}$ value decreases. 2) As the fabric count and over factor of cotton fabrics increase, $q_{max}$ value also increases. 3) $q_{max}$ values have been estimated by simple and polynomial regression equations developed in this study. Regression curves which have been plotted by polynomial regression equations also provided with the range of structural parameters for a specific range of $q_{max}$ values of cotton fabrics. This study would be significant in that it has identified the structural Parameters for the cool-and-warm feeling of cotton fabric at $65\%$ relative humidity.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.1326-1333
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• 2006

Purpose of this research is a development for the curve fitted equations that can improve practical calculation and work application when seismic performance has been evaluated and this work has been made a study of the dynamic response under various boundary conditions of buried pipelines to compare the dynamic behavior of concrete pipe and steel pipe, FRP pipe. This research have been developed curve fitted equations that can be improving efficiency and practicality. Using a nonlinear least square method, and after testing several different exponential equations, Proposed the curve fitted equations to give the best result and constant value by the propagation velocities. With these results, dynamic response analysis and seismic performance evaluation have been achieved on concrete pipe, steel pipe and FRP pipe that have a various boundary conditions. Degree of a polynomial expression and coefficient value by propagation velocity have been calculated when using the curve fitting equations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.9 s.180
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• pp.2292-2301
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• 2000

We propose an accurate and efficient estimation method of transverse shear stresses for analysis and design of laminated composite structures by 4-node quadrilateral degenerated shell elements. To get proper distributions of transverse shear stresses in each layer, we use 3-dimensional equilibrium equations instead of constitutive equations with shear correction factors which vary diversely according to the shapes of shell sections. Three dimensional equilibrium equations are integrated through the thickness direction with complete polynomial membrane stress fields, which are recovered by REP (Recovery by Equilibrium in Patches) recovery method. The 4-node quadrilateral degenerated shell element used in this paper has drilling degrees of freedom and shear stresses derived from assumed strain fields that are set up at natural coordinate systems. The numerical results demonstrate that the proposed estimation method attains reasonable accuracy and efficiency compared with other methods and FE analysis using 4-node degenerated shell elements.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1049-1070
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• 2004

We classify all partial differential equations with polynomial coefficients in $\chi$ and y of the form A($\chi$) $u_{{\chi}{\chi}}$ ＋ 2B($\chi$, y) $u_{{\chi}y}$ ＋ C(y) $u_{yy}$ ＋ D($\chi$) $u_{{\chi}}$ ＋ E(y) $u_{y}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.

• Advances in materials Research
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• v.4 no.1
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• pp.31-44
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• 2015

This paper presents a simple n-order four variable refined theory for buckling analysis of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and eliminates the shear stresses at the top and bottom surfaces. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present n-order refined theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.