• Honam Mathematical Journal
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• v.24 no.1
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• pp.25-33
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• 2002

In this paper we have shown conditions of R for the existence of the solution to the problem of the type $-u''=ue^{{\varepsilon}u}$ on the interval (0, R) with boundary and other conditions as in $(1-{\varepsilon})-(4)$ for various ${\varepsilon}$.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.549-555
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• 2021

We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.439-451
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• 2000

To compute derivatives using matrix vector multiplication method, new algorithms were introduced in [1.2]n By these algorithms, we reduced roundoff error in computing derivative using Chebyshev collocation methods (CCM). In this paper, some applications of these algorithms ar presented.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.231-238
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• 2019

We obtain ordinary differential equations related with some nonlocal Schr$Schr{\ddot{o}}dinger$dinger equations. As applications, we prove finite time blow-up or extinction of solutions.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Advances in Computational Design
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• v.5 no.1
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• pp.55-89
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• 2020

For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.

• Advances in Computational Design
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• v.7 no.1
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• pp.1-17
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• 2022

In this study, a new strategy is presented to transmit the fundamental elastic beam problem into the modern optimization platform and solve it by using artificial intelligence (AI) tools. As a practical example, deflection of Euler-Bernoulli beam is mathematically formulated by 2nd-order ordinary differential equations (ODEs) in accordance to the classical beam theory. This fundamental engineer problem is then transmitted from classic formulation to its artificial-intelligence presentation where the behavior of the beam is simulated by using neural networks (NNs). The supervised training strategy is employed in the developed NNs implemented in the heuristic optimization algorithms as the fitness function. Different evolutionary optimization tools such as genetic algorithm (GA) and particle swarm optimization (PSO) are used to solve this non-linear optimization problem. The step-by-step procedure of the proposed method is presented in the form of a practical flowchart. The results indicate that the proposed method of using AI toolsin solving beam ODEs can efficiently lead to accurate solutions with low computational costs, and should prove useful to solve more complex practical applications.

• Journal of the Korean Vacuum Society
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• v.20 no.5
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• pp.313-321
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• 2011

The Korea Research Institute of Standards and Science (KRISS) has three major vacuum systems: an ultrasonic interferometer manometer (UIM), a static volume expansion system (SVES), and an orifice-type dynamic expansion system (ODES). For each system explict measurement model equations with multiple variables are respectively given. According to ISO standards, all these system variables errors were used to calculate the expanded uncertainty (U).

• Cross-Cultural Studies
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• v.46
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• pp.227-251
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• 2017

This article is designed to study the conceptualization process of one of the ancient Chinese classical literature heritages, the so-called, the Triple Virtue(三達尊). By showing the principle meanings and the newly embodied symbolism of this Triple Virtue, this article is prepared to encourage revitalization of the moral virtues and self-identical pride among the elderly and to promote the young people's social consciousness of respecting the elderly. The author identifies the philosophical origins of the Triple Virtue, implying that the virtuous trinity is composed of morality, position and age, by analyzing poems in "Daya(大雅)", "Xiaoya(小雅)" of the Book of Odes and archives in "Zhoushu(周書)" of the Book of Documents(尙書). The author especially emphasizes that the concept of Triple Virtue was created by governing classes for meeting the political needs in the Zhou Dynasty. Moreover, by regarding King Wen of the Zhou Dynasty as the symbolic representation in the beginning era of the Western Zhou Dynasty and Shao BoHu as the embodiness representation in the end of the Western Zhou Dynasty, the author performs an in-depth study related to the above two great men. Finally, the author sheds lights on how symbolic and embodiness representations had played significant roles in formulating a typical model of the Triple Virtue in the following generations.

• Cross-Cultural Studies
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• v.19
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• pp.7-24
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• 2010

This paper is to survey a serise for The Red Cliff which is depicted The Former and Latter Odes on the Red Cliff written by Su Shi. This subject was mainly painted by the literati painters and consistently represented. In format of The Red Cliff, there are basically a types of pictorial depicton in accordance with their contents. Describing the whole scenes and the part of the story. Others is painted which bring from one scene of describing the whole scenes of the story.