• 대한화학회지
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• 제52권3호
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• pp.223-238
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• 2008

이 논문에 화학반응식 균형을 맞추기 위한 새로운 유사 역행렬법이 기술되었다. 여기에 제공된 방법은 Moore-Penrose 유사 역행렬을 사용한 Diophantin 행렬식의 해에 기초를 둔다. 방법은 전형적인 여러 화학반응식에 시험적용되었고 폭넓은 균형연구에서 모든 반응식에 매우 성공적이었다. 이 방법은 아무 제한없이 성공적으로 적용되고, 또한 새로운 화학반응식의 타당성에 대한 검증력도 있고, 만일 새식이 타당하다면 화학식 균형을 이룰 것이다. 여기서 다루어진 화학반응식들은 소수산화수를 지닌 원자를 포함하고 있다. 또한, 화학반응식의 확장된 행렬의 안정성에 대한 화학반응식의 안정성의 필요충분조건을 이 연구에 소개하였다.

• Structural Engineering and Mechanics
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• 제55권3호
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• 대한기계학회논문집A
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• 제26권3호
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• pp.514-520
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• 2002

A new non-linear modelling of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends. Using the Euler-Bernoulli beam theory and the non-linear Lagrange strain theory, from the extended Hamilton's principle are derived the coupled non-linear equations of motion for the longitudinal and transverse displacements. These equations of motion are discretized by using the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. On the other hand, the time histories for the displacements are also obtained by applying the generalized-$\alpha$ time integration method to the non-linear discretized equations. The validity of the new modelling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by Paidoussis.

• Journal of Nutrition and Health
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• 제23권2호
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• pp.93-107
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• 1990

The purposes of this investigation were to determine the validity of various methods (available anthropometric equations and near-infrared light interactance) for estimating body fat and to develop multiple regression equations for the prediction of body fat. Thirty-eight healthy males(age: 20.87$\pm$7.17 yrs) and 12 females(19.58$\pm$2.19 yrs) underwent hydrostatic weighing to determine body fat. Anthropometric measurements were taken of height, weight, nin skinfolds and thirteen circumferences. The results obtained are summarized as follows: 1) Relative body fat determined by underwater weighing was 12.08$\pm$5.21% for the males and 17.97$\pm$5.75% for the females. 2) Circumference and skin fold that had the highest correlation with the body fat were waist girth in males and females(r=0.60, r=0.96, respectively), and subscapular in males(r=0.68) and triceps in females(r=0.96). 3) Corss-validation of 18 selected equations on males revealed total errors ranging from 3.76% to 5.06%. Among these equations, M3(Pollock et al.) demonstrated the least total error. Total error of estimation by near-infrared(NIR) was less than that of available anthropometric measurement equations. The results of the cross-validation of 12 equations on females revealed that F3(Sloan et al.) was clearly superior in accuracy of prediction. 4) Correlational analyses showed that estimation of body fat by NIR measurement seemed to be more closely associated with body fat determined by underwater weighing in women than men, in older subjects than younger ones, and in fatter subjects than leaner ones.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 추계학술대회 논문집 학회본부 D
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• pp.765-768
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• 2000

Linearization of the biped dynamic equations and design of linear controller for the linearized equations are studied in this paper. The biped robot with inverted pendulum type trunk, used to stabilize the dynamic balancing of the biped robot during dynamic walking period, is modelled with 14 DOF and simulated. Despite of well defined linear control theories so far, the linear control methods was limited to the applications for a walking robot, because they have been inherently strong nonlinear properties, such as a modeling parameter uncertainties, external forces as noise, inertial and Coriolis terms by three dimensional modeling and so on. To linearize the nonlinear equations of motion of biped robot on MIMO and time varying linear equations of motion, 1st order Taylor series is used to formulate the linear equation. And a 2nd order numerical perturbation method Is used to approximate partial differential equations. Using the linearized equations of motion, a linear controller is designed by pole placement method with feed forward compensation. Using the obtained linearized equations and linear controller, the continuous walking simulation is performed.

• Journal of Biosystems Engineering
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• 제22권1호
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• pp.11-20
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• 1997

Thin layer drying tests of short gain rough rice were conducted in an experimental dryer equiped with air conditioning unit. The drying tests were performed in triplicate at three air temperatures of $35^circ$, $45^circ$, $55^circ$, and three relative humidities of 40%, 55%, 70%, respectively. Previously published thin layer equations were reviewed and four different models widely used as thin layer drying equations for cereal grains were selected. The selected four models were Pages, simplified diffusion, Lewis's and Thompson's models. Experimental data were fitted to these equations using stepwise multiple regression analysis. The experimental constants involved in tow equations were represented as a function of temperature and relative humidity of drying air. The results of comparing coefficients of determination and root mean square errors of miosture ratio for low equations showed that Page's and Thompsons models were found to fit adequately to all drying test data with coefficient of determination of 0.99 or better and root mean square error of moisture ratio of 0.025.

• 한국수학사학회지
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• 제27권3호
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• pp.165-182
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• 2014

After algebraic expressions for the roots of 3rd and 4th degree polynomial equations were given in the mid 16th century, seeking such a formula for the 5th and greater degree equations had been one main problem for algebraists for almost 200 years. Lagrange made careful and thorough investigation of various solving methods for equations with the purpose of finding a principle which could be applicable to general equations. In the process of doing this, he found a relation between the roots of the original equation and its auxiliary equation using permutations of the roots. Lagrange's ingenious idea of using permutations of roots of the original equation is regarded as the key factor of the Abel's proof of unsolvability by radicals of general 5th degree equations and of Galois' theory as well. This paper intends to examine Lagrange's contribution in the theory of polynomial equations, providing a detailed analysis of various solving methods of Lagrange and others before him.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집B
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• pp.372-377
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• 2001

A new non-linear of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends. Using the Euler-Bernoulli beam theory and the non-linear Lagrange strain theory, from the extended Hamilton's principle are derived the coupled non-linear equations of motion for the longitudinal and transverse displacements. These equations of motion for are discretized by using the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. On the other hand, the time histories for the displacements are also obtained by applying the $generalized-{\alpha}$ time integration method to the non-linear discretized equations. The validity of the new modeling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by $Pa{\ddot{i}}dousis$.

• Nuclear Engineering and Technology
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• 제49권4호
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• pp.838-849
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• 2017

This paper proposes penalty factor equations that take into consideration the weld strength over-match given in the classified form similar to the revised equations presented in the Code Case N-779 via cyclic elastic-plastic finite element analysis. It was found that the $K_e$ analysis data reflecting elastic follow-up can be consolidated by normalizing the primary-plus-secondary stress intensity ranges excluding the nonlinear thermal stress intensity component, $S_n$ to over-match degree of yield strength, $M_F$. For the effect of over-match on $K_n{\times}K_{\nu}$, dispersion of the $K_n{\times}K_{\nu}$ analysis data can be sharply reduced by dividing total stress intensity range, excluding local thermal stresses, $S_{p-lt}$ by $M_F$. Finally, the proposed equations were applied to the weld between the safe end and the piping of a pressurizer surge nozzle in pressurized water reactors in order to calculate a cumulative usage factor. The cumulative usage factor was then compared with those derived by the previous $K_e$ factor equations. The result shows that application of the proposed equations can significantly reduce conservatism of fatigue assessment using the previous $K_e$ factor equations.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.73-116
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• 2020

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.