• Journal of Korean Association for Spatial Structures
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• v.13 no.1
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• pp.51-57
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• 2013

There can be diverse causes in the destruction of a large space structure by strong wind such as characteristics of construction materials and changes in internal and external wind pressure of the structure. To evaluate the wind pressure of roof against the large space structure, wind pressure experiment is performed. However, in this wind pressure experiment, peak internal pressure coefficient is set according to the opening of the roof in Korea wind code. In this article, it was tried to identify the change of internal pressure coefficient and the characteristics of wind pressure coefficient acting on the roof by two kinds of opening on the side of the structure with Hyperbolic Paraboloid Spatial Structures roof. When analyzing internal pressure coefficient according to roof shape, it was found that minimum (52%) and maximum (30%~80%) overestimation was made comparing to partial opening type proposed in the current wind load. It is judged that evaluation according to the opening rate of the structure should be made to evaluate the internal pressure coefficient according to load.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.967-970
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• 2018

The aim of this paper is to show that there exists a weakly quasisymmetric homeomorphism $f:(X,d){\rightarrow}(Y,d^{\prime})$ between two locally compact non-complete metric spaces such that $f:(X,d_h){\rightarrow}(Y,d^{\prime}_h)$ is not quasi-isometric, where dh denotes the Gromov hyperbolic metric with respect to the metric d introduced by Ibragimov in 2011. This result shows that the answer to the related question asked by Ibragimov in 2013 is negative.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.835-848
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• 1995

Let $M_n$(c) be an n-dimensional complete and simply connected Kahlerian manifold of constant holomorphic sectional curvature c, which is called a complex space form. Then according to c > 0, c = 0 or c < 0 it is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.369-383
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• 1994

A complex n-dimensional Kahler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_{n}$ (c). A complete and simply connected complex space form consists of a complex projective space $P_{n}$ C, a complex Euclidean space $C^{n}$ or a complex hyperbolic space $H_{n}$ C, according as c > 0, c = 0 or c < 0.(omitted)

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.161-170
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• 1995

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. Takagi [12] and Berndt [2] classified all homogeneous real hypersufaces of $P_nC$ and $H_nC$.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.709-721
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• 2004

A punctured torus ${\Sigma}$(1, 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of elements of the Teichmuller space of a punctured torus using the matrix presentations of a pair of pants ${\Sigma}$(0, 3) and the gluing method.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.345-358
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• 1998

Let (p/q,n) denote the orbifold with its underlying space $S^3$ and a rational knot or link p/q as its singular set with a cyclic isotropy group of order n. In this paper we shall show the geometrical realization for the case (7/3,n) for all $n \geq 3$.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.423-428
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• 1998

This paper studies the regional identifiability of spatially-varying parameters in distributed parameter systems of hyperbolic type. Let Ω be a bounded domain of R$^n$and let Ωo be a subregion of the closed domain Ω. The distributed parameter systems having unknown parameters defined on Ω are described by the second order evolution equations in the filbert space L$^2$(Ω) and the observations are made on the subregion Ωo ⊂ Ω. The regional identifiability is formulated as the uniqueness of parameters by the identity of solutions on the subregion. Several regional identifiability results of the spatially-varying parameters of hyperbolic distributed parameter systems are established by means of the Riesz spectral representations.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.1-14
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• 2024

In this paper, we establish strong and ∆-convergence theorems for new iteration process namely S-R iteration process for a generalized α-nonexpansive mappings in a uniformly convex hyperbolic space and also we show that our iteration process is faster than other iteration processes appear in the current literature's. Our results extend the corresponding results of Ullah et al. [5], Imdad et al. [16] in the setting of uniformly convex hyperbolic spaces and many more in this direction.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.301-327
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• 2019

The proper orthogonal decomposition (POD) method for time-dependent problems significantly reduces the computational time as it reduces the original problem to the lower dimensional space. Even a higher degree of reduction can be reached if the solution is smooth in space and time. However, if the solution is discontinuous and the discontinuity is parameterized e.g. with time, the POD approximations are not accurate in the reduced space due to the lack of ability to represent the discontinuous solution as a finite linear combination of smooth bases. In this paper, we propose to post-process the sample solutions and re-initialize the POD approximations to deal with discontinuous solutions and provide accurate approximations while the computational time is reduced. For the post-processing, we use the Gegenbauer reconstruction method. Then we regularize the Gegenbauer reconstruction for the construction of POD bases. With the constructed POD bases, we solve the given PDE in the reduced space. For the POD approximation, we re-initialize the POD solution so that the post-processed sample solution is used as the initial condition at each sampling time. As a proof-of-concept, we solve both one-dimensional linear and nonlinear hyperbolic problems. The numerical results show that the proposed method is efficient and accurate.