• 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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.199-214
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• 2017

We consider fixed-point iterations constructed by simple transforming from a quadratic matrix equation to equivalent fixed-point equations and assume that the iterations are well-defined at some solutions. In that case, we suggest real valued functions. These functions provide radii at the solution, which guarantee the local convergence and the uniqueness of the solutions. Moreover, these radii obtained by simple calculations of some constants. We get the constants by arbitrary matrix norm for coefficient matrices and solution. In numerical experiments, the examples show that the functions give suitable boundaries which guarantee the local convergence and the uniqueness of the solutions for the given equations.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.327-344
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• 2005

The first part of the paper deals with a brief introduction of the plant-herbivore model system along with deterministic analysis of local stability and Hopf-bifurcations. The second part consists of stability analysis of the limit cycle arising from Hopf-bifurcation and uniqueness of limit cycle. The third part deals with the study of global stability of the model system under consideration.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.509-517
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• 2005

We shall prove the existence and uniqueness theorem of a solution to the non local fuzzy differential equation using the contraction mapping principle.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.355-366
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• 2018

Let R be a commutative ring with identity and let M be a finitely generated module over a Noetherian local ring R. Then it is well-known that M has a minimal projective resolution, which is unique up to isomorphisms of exact sequences. We provide a new proof of its uniqueness. Moreover, we deal with the cohomologies of (M, R/m).

• Journal of the Economic Geographical Society of Korea
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• v.26 no.1
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• pp.23-39
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• 2023

Due to the recent population decrease and urban decline, it has become increasingly important to induce qualitative changes in the city itself and create a differentiated development model. Local culture, based on its uniqueness and diversity, generates the expansion and ripple effect of various contents through creative utilization. In this study, we examine a new local content approach called "town-stay (village hotel)" that develops cultural content and creates a place-making in terms of creating a sustainable ecosystem with cultural vitality. While the uniqueness and creativity of individual content can make a region's attractiveness stand out, we have seen in the case of small-sized cities in Korea and Japan that content elements (place, story, people) can be materialized into area-level content called town-stay(village hotel). The local contents are densely presented in a specific area to increase visibility and expand into a variety of content that reveals regional connections. Local creators, who are the core actors, understand locality, induce active activities, and pursue sustainable development that promotes not only economic value but also community solidarity.

• Journal of the Korean Society of Clothing and Textiles
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• v.42 no.4
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• pp.689-707
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• 2018

This study reviewed the differences among Onggis made in Jeju and other areas, developed creative textile designs and cultural products, and conducted the consumer evaluation of developed products. First, the 1,063 photos of Onggis made before the first part of the 20th century were collected and the unique differences of Jeju Onggis were confirmed through the observation of collected photos. Second, based on the uniqueness of Jeju Onggis, the eight pieces of Jeju Onggis were selected from the photos and used as pattern design motifs. Nine basic patterns were drawn and ten textile designs were created using the basic patterns. Third, the 16 pieces of textile products were made with cotton fabrics on which the textile designs were printed. Four mugs and four tumblers with printed patterns were also made. Finally, 64 students evaluated the developed products using a 7-point scale. As a result, folksy atmosphere, uniqueness, usage as a Jeju souvenir and at local restaurants, and the role of fostering concern for Jeju Onggi were highly evaluated but aesthetics was rated relatively low. Most of the developed products were highly preferred and recommended as Jeju souvenirs or for local restaurants.

• Proceedings of the National Institute of Ecology of the Republic of Korea
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• v.3 no.2
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• pp.122-128
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• 2022

To present the spatial variation of fish assemblages in the Geum River in Korea, the concept of beta diversity (β-diversity) estimates based on the variance of the community data table was applied. Fish communities and environmental variables were collected from 13 sampling sites along the in mid-low reaches of the River. We calculated the β-diversity and local contribution to beta diversity (LCBD) values at each site depending on the two types of data, 'occurrence' with Jaccard and Sørensen dissimilarity coefficients, and 'abundance' with Hellinger distance. Multivariate and correlation analyses were also performed to determine the relationships between LCBD and other variables, such as community indices and physicochemical and hydrological factors. The β-diversity values of fish communities in the River were estimated as 0.218 and 0.145 for occurrence data table with Jaccard and Sørensen respectively, and 0.268 for abundance data. Similar patterns of LCBD along the sampling sites were detected in two dissimilarity measurements of occurrence table, and LCBD values with abundance data were slightly different. The LCBD values are strongly correlated with community indices, and also suitable for indicating the uniqueness of fish assemblages. However, further research is needed to determine the LCBD value as an indicator of environmental variability.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.35-64
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• 2021

In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.