• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.471-484
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• 2005

We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1475-1488
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• 2019

In this paper, we firstly define the Ricci mean value along the gradient vector field of the Ricci potential function and show that it is non-negative on a compact Ricci soliton. Furthermore a Ricci soliton is Einstein if and only if its Ricci mean value is vanishing. Finally, we obtain a compact Ricci soliton $(M^n,g)(n{\geq}3)$ is Einstein if its Weyl curvature tensor and the Kulkarni-Nomizu product of Ricci curvature are orthogonal.

• The Korean Journal of Food & Health Convergence
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• v.10 no.2
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• pp.1-5
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• 2024

This study aims to investigate the impact of character collaboration product characteristics on brand awareness and purchase intention within the food and beverage (F&B) industry, with a special focus on Generation MZ's growing interest in such products. The methodology involves a comprehensive review of existing literature on character marketing, brand awareness, and consumer purchase intention, supplemented by case studies of successful character collaborations in the F&B sector. The findings reveal that character collaborations significantly impact brand awareness and purchase intentions, particularly among younger consumers like Generation MZ. These collaborations not only rekindle nostalgia but also introduce new and exciting consumer experiences, effectively attracting a wide demographic. The success of character-themed products, from Pokémon bread to Coca-Cola's League of Legends collaboration, underscores the strategy's effectiveness in boosting brand recognition and consumer engagement. The implications of this research are manifold for the F&B industry. Firstly, it highlights the importance of leveraging popular characters to forge emotional connections with consumers. Secondly, it suggests that product development should closely align with consumer preferences and market trends to maximize appeal. Lastly, it positions character collaboration as a strategic marketing tool that not only enhances product sales but also strengthens brand loyalty and facilitates sustained brand growth.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1101-1110
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• 2005

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.799-808
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• 1999

We investigate when the .product of two smooth manifolds admits a weakly Lagrangian embedding. Assume M, N are oriented smooth manifolds of dimension m and n,. respectively, which admit weakly Lagrangian immersions into $C^m$ and $C^n$. If m and n are odd, then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$ In the case when m is odd and n is even, we assume further that $\chi$(N) is an even integer. Then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$. As a corollary, we obtain the result that $S^n_1\;{\times}\;S^n_2\;{\times}\;...{\times}\;S^n_k$, $\kappa$>1, admits a weakly Lagrang.ian embedding into $C^n_1+^n_2+...+^n_k$ if and only if some ni is odd.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1887-1892
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• 2016

It is well known that the helicoids are the only ruled minimal surfaces in ${\mathbb{R}}^3$. The similar characterization for ruled minimal surfaces can be given in many other 3-dimensional homogeneous spaces. In this note we consider the product space $M{\times}{\mathbb{R}}$ for a 2-dimensional manifold M and prove that $M{\times}{\mathbb{R}}$ has a nontrivial minimal surface ruled by horizontal geodesics only when M has a Clairaut parametrization. Moreover such minimal surface is the trace of the longitude rotating in M while translating vertically in constant speed in the direction of ${\mathbb{R}}$.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1255-1274
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• 2008

The purpose of this paper is to discuss the constant term appearing in the BFK-gluing formula for the zeta-determinants of Laplacians on a complete Riemannian manifold when the warped product metric is given on a collar neighborhood of a cutting compact hypersurface. If the dimension of a hypersurface is odd, generally this constant is known to be zero. In this paper we describe this constant by using the heat kernel asymptotics and compute it explicitly when the dimension of a hypersurface is 2 and 4. As a byproduct we obtain some results for the value of relative zeta functions at s=0.

• Korean Journal of Computational Design and Engineering
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• v.7 no.3
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• pp.170-176
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• 2002

To exchange CAD data between heterogeneous CAD systems, we generally use a neutral format especially STEP, which is the international standard (ISO-10303) for product model data exchange. AP214 (Application Protocol) for the automotive industry not only takes into account geometry and organizational data, but also provides a classification mechanism for product modeling. When reading a STEP file during a design process that is exported from other CAD systems, it is a burden to a designer to go through the tedious process of removing duplicate or non-manifold entities, adjusting parts, and rearranging text. We analyze the structure of AP214 and develop a healing tool to solve the following problem. Without the assembly information in the Master workspace of CATIA, or to read a STEP file from Pro/Engineer, a designer should do a repetitive process of disintegrating an assembly into parts one by one. We have developed a post-processing tool for STEP AP214 that separates out a part from an assembly model and adjusts superfluous or useless entities using the ACIS kernel.

• Journal of Welding and Joining
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• v.33 no.6
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• pp.6-12
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• 2015

Thermal fatigue life of the automobile exhaust manifold is directly affected by the restraint force according to the structure of exhaust system and bead shape of the welded joints. In the present study, the microstructural changes and precipitation behavior during thermal fatigue cycle of the 18wt% Cr ferritic stainless steel weld heat affected zone (HAZ) considering restraint stress were investigated. The simulation of weld HAZ and thermal fatigue test were carried out using a metal thermal cycle simulator under complete constraint force in the static jig. The change of the restraint stress on the weld HAZ was simulated by changing the shape of notch in the specimen considering the stress concentration factor. Thermal fatigue properties of the weld HAZ were deteriorated during cyclic heating and cooling in the temperature range of $200^{\circ}C$ to $900^{\circ}C$ due to the decrease of Nb content in solid solution and coarsening of MX type precipitates, laves phase, $M_6C$ with coarsening of grain and softening of the matrix. As the restraint stress on the specimen increased, the thermal fatigue life was decreased by dynamic precipitation and rapid coarsening of the precipitates.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.409-421
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• 2018

Let X be a complex manifold of dimension n $n{\geqslant}2$ and let ${\Omega}{\Subset}X$ be a weakly q-convex domain with smooth boundary. Assume that E is a holomorphic line bundle over X and $E^{{\otimes}m}$ is the m-times tensor product of E for positive integer m. If there exists a strongly plurisubharmonic function on a neighborhood of $b{\Omega}$, then we solve the ${\bar{\partial}}$-problem with support condition in ${\Omega}$ for forms of type (r, s), $s{\geqslant}q$ with values in $E^{{\otimes}m}$. Moreover, the solvability of the ${\bar{\partial}}_b$-problem on boundaries of weakly q-convex domains with smooth boundary in $K{\ddot{a}}hler$ manifolds are given. Furthermore, we shall establish an extension theorem for the ${\bar{\partial}}_b$-closed forms.