• 대한수학회지
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• 제58권5호
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• pp.1279-1298
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• 2021

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

• Bulletin of the Korean Chemical Society
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• 제20권1호
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• pp.35-41
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• 1999

Stability characteristics of hyperbolic reaction-diffusion equations with a reversible Brusselator model are investigated as an extension of the previous work. Intensive stability analysis is performed for three important parameters, Nrd, β and Dx, where Nrd is the reaction-diffusion number which is a measure of hyperbolicity, β is a measure of reversibility of autocatalytic reaction and Dx is a diffusion coefficient of intermediate X. Especially, the dependence on Nrd of stability exhibits some interesting features, such as hyperbolicity in the small Nrd region and parabolicity in the large Nrd region. The hyperbolic reaction-diffusion equations are solved numerically by a spectral method which is modified and adjusted to hyperbolic partial differential equations. The numerical method gives good accuracy and efficiency even in a stiff region in the case of small Nrd, and it can be extended to a two-dimensional system. Four types of solution, spatially homogeneous, spatially oscillatory, spatio-temporally oscillatory and chaotic can be obtained. Entropy productions for reaction are also calculated to get some crucial information related to the bifurcation of the system. At the bifurcation point, entropy production changes discontinuously and it shows that different structures of the system have different modes in the dissipative process required to maintain the structure of the system. But it appears that magnitude of entropy production in each structure give no important information related for states of system itself.

• 산업기술연구
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• 제28권B호
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• pp.91-99
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• 2008

Applicability of existing methods of predicting consolidation settlement was assessed by analyzing results of centrifuge tests modelling self-weight consolidation of soft marine clay. From extensive literature review about self-weight consolidation of soft marine clays located in southern coast in Korea, constitutive relationships of void ratio-effective stress-permeability and typical self-weight consolidation curves with time were obtained by centrifuge model experiments. For the condition of surcharge loading, exact solution of consolidation settlement curve was obtained by Terzaghi's consolidation theory and was compared with the results predicted by currently available methods such as Hyperbolic method, Asaoka's method, Hoshino's method and ${\sqrt{S}}$ method. All methods were found to have their own inherent error to predict final consolidation settlement. From results of analyzing the self-weight consolidation with time by using those methods, Asaoka's method predicted the best. Hyperbolic method predicted relatively well in error range of 2~24% for the case of showing the linearity in the relationship between T vs T/S in the stage of consolidation degree of 60~90 %. For the case of relation curve of T vs $T/S^2$ showing the lineality after the middle stage, error range from Hoshino method was close to those from Hyperbolic method. However, Hoshino method is not able to predict the final settlement in the case of relation curve of T vs $T/S^2$ being horizontal. For the given data about self-weight consolidation after the middle stage, relation curve of T vs T/S from ${\sqrt{S}}$ method shows the better linearity than that of T vs $T/{\sqrt{s}}$ from Hyperbolic method.

• 한국정보과학회논문지:시스템및이론
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• 제30권5_6호
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• pp.213-222
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• 2003

일반적으로 하이퍼볼릭 공간상에서 대칭 패턴을 생성하는 알고리즘은 벡터표현 방식에 기반한 포워드 매핑 알고리즘을 사용한다. 기존의 알고리즘에서는 복사한 대칭 패턴을 표현하는 레이어의 증가에 따라 메모리의 사용이 기하급수적으로 증가한다 이러한 문제점으로 인해 전체 패턴의 정밀한 표현이 불가능하다. 또한 기본 패턴으로 비트맵 이미지를 사용하기 어렵고 벡터형태의 결과를 이미지로 변환하는 추가의 처리를 필요로 한다. 본 논문에서는 하이퍼볼릭 공간에서 대칭 패턴을 생성하는데 있어 정밀하고도 효율적인 계산 방법인 백워드 매핑 알고리즘을 제안한다.

• 한국지반공학회논문집
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• 제38권12호
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• pp.103-112
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• 2022

본 연구에서는 시간-침하량 계측 데이터를 기반으로 한 기존 침하 예측 이론식을 확인하였다. 기존 계측 기반 침하 예측 이론식 중 쌍곡선법 및 Asaoka법이 정확도가 높게 나타났으며, 이외 방법은 정확도가 낮은 것으로 확인되었다. 이러한 분석 결과를 토대로 기존 침하 예측 방법의 한계점을 도출하였으며, 이러한 한계점을 보완할 수 있는 개선방안으로써 가중 비선형 회귀분석을 통한 침하 예측 방법을 제시하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.31-40
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• 1998

Spectral analysis by energy method is given for a fully discrete methods for hyperbolic integro-differential equations with a weakly singular kernel. Stability and error estimates in $H^1$-norm are derived.

• International Journal of Aerospace System Engineering
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• 제3권1호
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• pp.1-4
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• 2016

Functionally graded materials (FGMs) are becoming very popular in various industries due to their effectiveness of the utilization of their constituent elements. However, the modelling of these materials is difficult due to the complex nature of variation of material properties across the thickness. Many shear deformation theories have been developed and employed for the analysis of such functionally graded plates (FGPs). A recently developed inverse hyperbolic shear deformation theory has been successfully employed by Grover et al. [1] for the analysis of laminated composites and sandwich plates. The objective of the study is to obtain finite element solution for the structural analysis of functionally graded plates using inverse hyperbolic shear deformation theory. Finite element analysis facilitates the analysis of complex problems such as functionally graded plates with different boundary conditions and different loadings.

• 분석과 대안
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• 제4권1호
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• pp.105-123
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• 2020

This study analyzes the risk selection behavior of Japanese households. The study approaches the view of 'the hyperbolic discount' which is used in behavioral economics based on the rise in mortgage lending by low-income households in the late 2000s. The study focuses on how households risk preferences vary by income levels. The study analyzes the relationship of attitude of household interest rate risk using Binomial Logistic and Heckman two-step estimation method assuming that there are only two types of Adjustable-Rate Mortgage and Fixed-Rate Mortgage. As a result of the empirical analysis, low-income households annual income tend to have a higher proportion of housing debt as same as higher interest rate risk preferences households in proportion to income growth and interest rate risk preferences. Those results indicate that there is possibility of a hyperbolic discount on low-income households in Japan, and support the hypothesis that low-income households are relatively higher household debt ratio because of high utility due to home purchase in the near future (short-term).

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.623-646
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• 2023

In this article, we introduce the hyperbolic space version of a faster iterative algorithm. The proposed iterative algorithm is used to approximate the common fixed point of three multi-valued almost contraction mappings and three multi-valued mappings satisfying condition (E) in hyperbolic spaces. The concepts weak w²-stability involving three multi-valued almost contraction mappings are considered. Several strong and △-convergence theorems of the suggested algorithm are proved in hyperbolic spaces. We provide an example to compare the performance of the proposed method with some well-known methods in the literature.

• 대한수학회논문집
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• 제38권1호
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• pp.243-256
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• 2023

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C¹ generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.