• Journal of the Korean Geotechnical Society
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• v.39 no.4
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• pp.45-54
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• 2023

The settlement prediction during the design phase is primarily conducted using theoretical methods. However, measurement-based settlement prediction methods that predict future settlements based on measured settlement data over time are primarily used during construction due to accuracy issues. Among these methods, the hyperbolic method is commonly used. However, the existing hyperbolic method has accuracy issues and statistical limitations. Therefore, a weighted nonlinear regression hyperbolic method has been proposed. In this study, two weighting methods were applied to the weighted nonlinear regression hyperbolic method to compare and analyze the accuracy of settlement prediction. Measured settlement plate data from two sites located in Busan New Port were used. The settlement of the remaining sections was predicted by setting the regression analysis section to 30%, 50%, and 70% of the total data. Thus, regardless of the weight assignment method, the settlement prediction based on the hyperbolic method demonstrated a remarkable increase in accuracy as the regression analysis section increased. The weighted nonlinear regression hyperbolic method predicted settlement more accurately than the existing linear regression hyperbolic method. In particular, despite a smaller regression analysis section, the weighted nonlinear regression hyperbolic method showed higher settlement prediction performance than the existing linear regression hyperbolic method. Thus, it was confirmed that the weighted nonlinear regression hyperbolic method could predict settlement much faster and more accurately.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.173-195
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• 2021

A new implicit discontinuous Galerkin spectral element method (DGSEM) based on the first order hyperbolic system(FOHS) is presented for solving elliptic type partial different equations, such as the Poisson problems. By utilizing the idea of hyperbolic formulation of Nishikawa[1], the original Poisson equation was reformulated in the first-order hyperbolic system. Such hyperbolic system is solved implicitly by the collocation type DGSEM. The steady state solution in pseudo-time, which is the solution of the original Poisson problem, was obtained by the implicit solution of the global linear system. The optimal polynomial orders of 𝒪(𝒽^𝑝+1)) are obtained for both the solution and gradient variables from the test cases in 1D and 2D regular grids. Spectral accuracy of the solution and gradient variables are confirmed from all test cases of using the uniform grids in 2D.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.309-322
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• 2021

A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.

• Geotechnical Engineering
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• v.13 no.6
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• pp.5-12
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• 1997

Predictions of settlements under preloading for the improvement of soft soil is a very important element of construction management. Due to the non uniformity, difficulty of estimating resonable soil properties, predictions of settlements and settlement velocities at the design stage seldom agree with the actual future settlements. To overcome this problem, the prediction methods based on the settlement observation of initial preloading stage such as hyperbolic method and Asaoka method have been employed frequently. However the estimating method for the reliability of these predictions at the time of prediction has not been suggested. In this study, comparisons of predicted settlements by hyperbolic met hed and observed settlements are explored through case studies. And a stratagem of estimating reliability of settlement predictions by hyperbolic method is suggested as the result of investigation on the relationship between the initial observed time and error of settlement prediction by hyperbolic method.

• Proceedings of the Korean Geotechical Society Conference
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• 2010.03a
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• pp.457-467
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• 2010

The settlement prediction is very important to preloading method for a construction site on a soft ground. At the design stage, however, it is hard to predict the settlement exactly due to limitations of the site survey. Most of the settlement prediction is performed by a regression settlement curve based on the field data during a construction. In Korea, hyperbolic method has been most commonly used to align the settlement curve with the field data, because of its simplicity and many application cases. The results from hyperbolic method, however, may be differed by data selections or data fitting methods. In this study, the analyses using hyperbolic method were performed about the field data of $\bigcirc\bigcirc$ site in Pusan. Two data fitting methods, using an axis transformation or an alternative method, were applied with the various data group. If data was used only after the ground water level being stabilized, fitting results using both methods were in good agreement with the measured data. Without the information about the ground water level, the alternative method gives better results with the field data than the method using an axis transformation.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.29-40
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• 2016

In this paper, we consider the nonlinear hyperbolic equations with forcing term. Some suffcient conditions for the oscillation are derived by using integral averaging method and a generalized Riccati technique.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1998.10a
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• pp.425-430
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• 1998

The theory of consolidation has been achieved remarkable development, but associated properties are very difficult to determine in the laboratory. The theoretical shortcomings of those consolidation theories and uncertainties of associated properties make inevitably some discrepancy between theoretical and field settlements. Field settlement measurement by settlement plate is, therefore, widely used to overcome the discrepancy. Among the various methods of ultimate settlement predictions using field settlement data, hyperbolic method and Asaoka's method are most commonly used because of their simplicity and ability to give a reasonable estimate of consolidation settlement. In this paper, the applicability of hyperbolic method and Asaoka's method has been estimated by the analysis of the laboratory consolidation test and field measured data. It is shown that both hyperbolic method and Asaoka's method are significantly affected by the direction of drainage, and Asaoka's method is better to reflect the properties of the soft foundation than hyperbolic method.

• Magazine of the Korean Society of Agricultural Engineers
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• v.45 no.5
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• pp.140-150
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• 2003

Observational methods such as the Asaoka's method and the hyperbolic method are widely applied on the settlement analysis using observed settlement. The most unreliable aspects in those methods is arose from the subjective discretion of initial non-linearity on linear regression. The initial non-linearity is inevitable due to the settlement behaviour itself. Therefore an objective method is essential to achieve more reliable results on settlement analysis. It was found that the initial non-linear data are statistical outliers. New automation algorithms of the hyperbolic and the Asaoka's method were developed based on outlier detection method. The methods are a successive detection of outliers and a searching method of suitable hyperbolic range for the Asaoka's and the hyperbolic method respectively. Applicability of the algorithms was verified through case studies.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.481-493
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• 2007

We will construct several types of semi-regular tilings of a hyperbolic unit disk model by defining geometric features of the definition of distance in a hyperbolic plane, area of triangle, and isometry of inversions. We researched the method of regular tilings and semi-regular tilings of hyperbolic unit disk model and wrote an semi-regular tiling construction algorithm using Cabri2 program and Cinderella program. Lastly, We want to make a product related to traditional heritage cultural patterns using Photoshop, so we'll model the advertising photos of cites; Seoul, Gwangju.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.799-807
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• 2013

We defined and studied a naturally extended hyperbolic space (see [1] and [2]). In this study, we describe Sforza's formula [7] and Santal$\acute{o}$'s formula [6], which were rediscovered and later discussed by many mathematicians (Milnor [4], Su$\acute{a}$rez-Peir$\acute{o}$ [8], J. Murakami and Ushijima [5], and Mednykh [3]) in the spherical space in an elementary way. Thereafter, using the extended hyperbolic space, we apply the same method to prove their results in the hyperbolic space.