• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.593-606
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• 2002

We prove local existence and global uniqueness in one dimensional nonlinear hyperbolic inverse problems. The basic key for showing the local existence of inverse solution is the principle of contracted mapping. As an application, we consider a hyperbolic inverse problem with damping term.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.621-631
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• 1999

In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.631-638
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• 2011

In this paper, we prove that for $C^1$ generically, if every hyperbolic periodic point in a chain component is uniformly far away from being nonhyperbolic, and it is $C^1$-robustly average shadowable, then the chain component is hyperbolic.

• The Journal of Engineering Geology
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• v.30 no.1
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• pp.1-15
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• 2020

The Mohr-Coulomb model is mainly used in evaluating the behavior of the ground in numerical analyses of domestic ground excavation. This study analyzes its limitations and compares its numerical results with the hyperbolic model, a model that closely follows actual ground behavior during excavation. Recent applications of the Mohr-Coulomb model in Korea have tended to impose arbitrary special boundary conditions to control the problem of excessive heaving of the ground excavation surface. This adjustment only controls the size of the heaving of the excavation surface, implying that the ground behavior is distorted from the actual behavior. This study compares results from the hyperbolic model (hardening soil model) and the Mohr-Coulomb model, and confirms that the hyperbolic model provides both a more-suitable solution to the problem of heaving during excavation and the actual stress-strain behavior. In numerical analyses of ground excavation, the hyperbolic model is expected to give results consistent with the actual ground behavior.

• 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.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.375-385
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• 2020

Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1143-1158
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• 2006

We consider the projectivization of Minkowski space with the analytic continuation of the hyperbolic metric and call this an extended hyperbolic space. We can measure the volume of a domain lying across the boundary of the hyperbolic space using an analytic continuation argument. In this paper we show this method can be further generalized to find the volume of a domain with smooth boundary with suitable regularity in dimension 2 and 3. We also discuss that this volume is invariant under the group of hyperbolic isometries and that this regularity condition is sharp.

• Current Optics and Photonics
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• v.1 no.4
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• pp.336-343
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• 2017

A wide field-of-view (FOV) image contains more visual information than a conventional image. This study proposes a new type of hyperbolic mirror for wide FOV image acquisition. The proposed mirror consists of a hyperbolic cylindrical section and a bowl-shaped hyperbolic omnidirectional section. Using an imaging system with this mirror, it is possible to achieve a $213.8^{\circ}$ horizontal and a $126.94^{\circ}$ vertical maximum FOV. Parameters of each section of the mirror are designed to be continuous at the junction of the two parts, and the resultant image is seamless. The image-acquisition model is obtained using ray-tracing optics. To rectify the geometrical distortion of the original image due to the mirror, an image-restoration algorithm based on conformal projection is presented in this study. The performance of the proposed imaging system with the hyperbolic mirror and its image-restoration algorithm are verified by experiments.

• 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.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.735-749
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• 2000

The multiplicity if periodic sloutions of semilinear dissipative hyperbolic equations is treated