• 호남수학학술지
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• 제33권4호
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• pp.557-573
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• 2011

Let G be a compact and connected semisimple Lie group, H a closed subgroup, g (resp. h) the Lie algebra of G (resp. H), B the Killing form of g, g the normal metric on the homogeneous space G/H which is induced by -B. Let D be an invarint connection with Weyl structure (D, g, ${\omega}$) in the tangent bundle over the normal homogeneous Riemannian manifold (G/H, g) which is projectively flat. Then, the affine connection D on (G/H, g) is a Yang-Mills connection if and only if D is the Levi-Civita connection on (G/H, g).

• 대한수학회논문집
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• 제30권3호
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• pp.209-219
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• 2015

In this article, we first give metric version of an iteration scheme of Agarwal et al. [1] and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.

• 대한수학회보
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• 제42권4호
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• pp.757-776
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• 2005

In this paper we establish the stability of a Jensen type functional equation, namely f(xy) - f($xy^{-1}$) = 2f(y), on some classes of groups. We prove that any group A can be embedded into some group G such that the Jensen type functional equation is stable on G. We also prove that the Jensen type functional equation is stable on any metabelian group, GL(n, $\mathbb{C}$), SL(n, $\mathbb{C}$), and T(n, $\mathbb{C}$).

• 대한수학회논문집
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• 제9권4호
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• pp.927-931
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• 1994

Let G be a cyclic group of order 2 and let $S^1$ denote the unit circle in $R^2$ with the standard metric. We consider smooth G-vector bundles over $S^1$ when G acts on $S^1$ by reflection. Then the fixed point set of G on $S^1$ is two points ${z_0, z_1}$. Let $E$\mid$_{z_0} and E$\mid$_{z_1}$ be the fiber G-representation spaces at $z_0$ and $z_1$ respectively. We associate an orthogonal G-representation $\rho_i : G \to O(n)$ to $E$\mid$_{z_i}, i = 0, 1$. Let det $p\rho_i(g), g \neq 1$, be denoted by det $E$\mid$_{z_i}$ since det $\rho_i(g)$ is independent of choice of $\rho_i$.

• 대한수학회논문집
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• 제26권1호
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• pp.115-124
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• 2011

In this paper, some fuzzy fixed point theorems for fuzzy mappings are established by considering the nonempty closed $\alpha$-cut sets. Some importance observations are also discussed. Our results clearly extend, generalize and improve the corresponding results in the literatures, which have given most of their attention to the class of fuzzy sets with nonempty compact or closed and bounded $\alpha$-cut sets.

• 대한수학회지
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• 제57권6호
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• pp.1471-1484
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• 2020

It may very well be difficult to prove an eigenvalue inequality of Payne-Pólya-Weinberger type for the bi-drifting Laplacian on the bounded domain of the general complete metric measure spaces. Even though we suppose that the differential operator is bi-harmonic on the standard Euclidean sphere, this problem still remains open. However, under certain condition, a general inequality for the eigenvalues of bi-drifting Laplacian is established in this paper, which enables us to prove an eigenvalue inequality of Ashbaugh-Cheng-Ichikawa-Mametsuka type (which is also called an eigenvalue inequality of Payne-Pólya-Weinberger type) for the eigenvalues with lower order of bi-drifting Laplacian on the Gaussian shrinking soliton.

• 대한수학회보
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• 제46권6호
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• pp.1099-1133
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• 2009

We study the hyperbolic cosine and sine laws in the extended hyperbolic space which contains hyperbolic space as a subset and is an analytic continuation of the hyperbolic space. And we also study the spherical cosine and sine laws in the extended de Sitter space which contains de Sitter space S$^n_1$ as a subset and is also an analytic continuation of de Sitter space. In fact, the extended hyperbolic space and extended de Sitter space are the same space only differ by -1 multiple in the metric. Hence these two extended spaces clearly show and apparently explain that why many corresponding formulas in hyperbolic and spherical space are very similar each other. From these extended trigonometry laws, we can give a coherent and geometrically simple explanation for the various relations between the lengths and angles of hyperbolic polygons, and relations on de Sitter polygons which lie on S$^2_1$, and tangent laws for various polyhedra.

• Journal of the Optical Society of Korea
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• 제20권2호
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• pp.321-324
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• 2016

Transformation optics methodology provides a new pathway for designing novel devices. It is based on changing a material’s permittivity and permeability. A design for changing the appearance of an object by transformation optics methodology is proposed here. Through a certain transformation, the relations of the metric spaces and the calculation of the material parameters are derived, and the aim of changing the apparent size of an object can be realized. Full wave simulations are performed to validate the proposed device’s performance. It is possible to think that the methodology will improve the flexibility of designing interesting applications in microwave and optical regimes.

• 대한수학회지
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• 제60권2호
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• pp.341-358
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• 2023

Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with 𝛽-Kenmotsu structure. It is proven that a (2n + 1)-dimensional generalized Sasakian-space-form with 𝛽-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with 𝛽-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either ψ∖T^k × M^2n+1-k or gradient 𝜂-Yamabe soliton.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.839-853
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• 2022

We define the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property in terms of the topology of the phase space. Secondly we define these notions in terms of the compatible uniformity of the phase space. When the phase space is a compact Hausdorff space, we establish the equivalence of the corresponding definitions of the topological approach and the uniformity approach. In case the phase space is a compact metric space, the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property defined in terms of topology and uniformity are equivalent to their respective standard definitions.