• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.221-229
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• 1989

• Journal of the Korean Geotechnical Society
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• v.38 no.12
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• pp.103-112
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• 2022

The existing subsidence prediction method based on the measurement data were confirmed in this study through literature research. It was confirmed that the hyperbolic method and the Asaoka method showed high accuracy, while the other prediction methods showed significantly low accuracy. Based on the analysis results, the limitations of the existing prediction equations were derived, and the improvement method of the settlement prediction equations was suggested. In this study, a weighted nonlinear regression analysis method that gives higher weight to the later data was proposed to improve the existing hyperbolic method.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.

• Journal of information and communication convergence engineering
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• v.12 no.1
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• pp.39-45
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• 2014

A numerical method for solving Hamiltonian equations is said to be symplectic if it preserves the symplectic structure associated with the equations. Various symplectic methods are widely used in many fields of science and technology. A symplectic method preserves an approximate Hamiltonian perturbed from the original Hamiltonian. It theoretically supports the effectiveness of symplectic methods for long-term integration. Although it is also related to long-term integration, numerical stability of symplectic methods have received little attention. In this paper, we consider explicit symplectic methods defined for Hamiltonian equations with Hamiltonians of the special form, and study their numerical stability using the harmonic oscillator as a test equation. We propose a new stability criterion and clarify the stability of some existing methods that are visually based on the criterion. We also derive a new method that is better than the existing methods with respect to a Courant-Friedrichs-Lewy condition for hyperbolic equations; this new method is tested through a numerical experiment with a nonlinear wave equation.

• Wind and Structures
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• v.26 no.6
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• pp.355-367
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• 2018

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction. Considering flow separation, the wind field around membrane structure is simulated as the superposition of a uniform flow and a continuous vortex layer. By the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics, aerodynamic pressure acting on membrane surface can be determined. And based on the large amplitude theory of membrane and D'Alembert's principle, interaction governing equations of wind-structure are established. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction governing equations into a system of second-order nonlinear differential equation with constant coefficients. Through judging the frequency characteristic of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy, geometrical nonlinearity and scantling of structure is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the model without considering flow separation, it's basically consistent about the divergence instability regularities in the flow separation model.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.247-259
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• 2011

In this paper, the $(\frac{G'}{G})$-expansion method is used to construct new exact travelling wave solutions of some nonlinear evolution equations. The travelling wave solutions in general form are expressed by the hyperbolic functions, the trigonometric functions and the rational functions, as a result many previously known solitary waves are recovered as special cases. The $(\frac{G'}{G})$-expansion method is direct, concise, and effective, and can be applied to man other nonlinear evolution equations arising in mathematical physics.

• Bulletin of the Korean Mathematical Society
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• v.27 no.2
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• pp.165-172
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• 1990

In this paper, we study a method which speeds up the convergence of monotone iterations and give some numerical examples of the types (2) and (3). In [2] this method has been applied to a system of hyperbolic differential equations with initial and boundary conditions.

• Earthquakes and Structures
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• v.13 no.3
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• pp.241-253
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• 2017

In this paper, dynamic response of the horizontal nanofiber reinforced polymer (NFRP) strengthened concrete beam subjected to seismic ground excitation is investigated. The concrete beam is modeled using hyperbolic shear deformation beam theory (HSDBT) and the mathematical formulation is applied to determine the governing equations of the structure. Distribution type and agglomeration effects of carbon nanofibers are considered by Mori-Tanaka model. Using the nonlinear strain-displacement relations, stress-strain relations and Hamilton's principle (virtual work method), the governing equations are derived. To obtain the dynamic response of the structure, harmonic differential quadrature method (HDQM) along with Newmark method is applied. The aim of this study is to investigate the effect of NFRP layer, geometrical parameters of beam, volume fraction and agglomeration of nanofibers and boundary conditions on the dynamic response of the structure. The results indicated that applied NFRP layer decreases the maximum dynamic displacement of the structure up to 91 percent. In addition, using nanofibers as reinforcement leads a 35 percent reduction in the maximum dynamic displacement of the structure.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.04a
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• pp.501-506
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• 2000

An iterative numerical computational algorithm is presented to design a plate or shell element subjected to membrane and flexural forces. Based on equilibrium consideration, equations for capacities of top and bottom reinforcements in two orthogonal directions have been derived. The amount of reinforcement is determined locally, i.e., for each sampling point, from the equilibrium between applied and internal forces. Based on nonlinear analyses performed in a hyperbolic cooling tower, the analytically calculated ultimate load exceeded the design ultimate load from 50% to 55% for an analysis with relatively low to high tension stiffening, cases $\gamma$=10 and 15. For these cases, the design method gives a lower bound on the ultimate load with respect to Lower bound theorem, This shows the adequacy of th current practice at least for this cooling tower shell case studied. To generalize the conclusion more designs - analyses should be reformed with different shell configurations.

• Environmental Engineering Research
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• v.14 no.2
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• pp.102-110
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• 2009

Application of artificial intelligence (AI) approaches in eco-environmental modeling has gradually increased for the last decade. Comprehensive understanding and evaluation on the applicability of this approach to eco-environmental modeling are needed. In this study, we reviewed the previous studies that used AI-techniques in eco-environmental modeling. Decision Tree (DT) and Artificial Neural Network (ANN) were found to be major AI algorithms preferred by researchers in ecological and environmental modeling areas. When the effect of the size of training data on model prediction accuracy was explored using the data from the previous studies, the prediction accuracy and the size of training data showed nonlinear correlation, which was best-described by hyperbolic saturation function among the tested nonlinear functions including power and logarithmic functions. The hyperbolic saturation equations were proposed to be used as a guideline for optimizing the size of training data set, which is critically important in designing the field experiments required for training AI-based eco-environmental modeling.