• Communications of the Korean Mathematical Society
• /
• v.9 no.4
• /
• pp.927-931
• /
• 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 $\rho_i$.

• Journal of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.341-358
• /
• 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.

• Journal of the Optical Society of Korea
• /
• v.20 no.2
• /
• pp.321-324
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.4
• /
• pp.757-776
• /
• 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, $\mathbb{C}$).

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.6
• /
• pp.1099-1133
• /
• 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 Digital Contents Society
• /
• v.16 no.2
• /
• pp.335-343
• /
• 2015

This paper describes a quantitative approach to the BIM-enabled assessment of building circulation by using quantitative data and applying its weight. Assessment of building circulation plays an important role before construction stage because of related requirements regulated by design guide, building codes, etc. and design decision making as well. In this paper, Qualitative issue is mainly dealt with that are usually excluded from rule checking objects due to their implicit definition such as 'comfortable circulation'. A weighting framework is suggested using weighted data of circulation properties such as 1) metric distance, 2) number of passing spaces, 3) number of turning spaces, 4) window area of passing space, etc.

• Journal of Biosystems Engineering
• /
• v.3 no.1
• /
• pp.33-46
• /
• 1978

To get the goal of self-supply of food grain, improvement of post-harvest grain operations in rural area is under consideration as an important task of agriculture in Korea. This is study is focused on elimination of losses and deteriorations of grain and reduction of labour requirements and funds for post-harvest grain operations. The purpose of this study are presentation of basic data referring to conventional post-harvest grain operations in rural area and suggestion of improving methods for the operations, and also finding out reasonable operating processes of the operations. The result of this study are follows; 1. Grain drying in-the-filed which is performed before threshing has major factors of grain loss during drying, and so should be restrained as possible. Combine harvesting system is recommended among other king of mechanized harvesting systems for restraining in-the-field drying and securing available labors for drying. 2. It is predicted that mechanical grain drying could be prevalent when combine harvesting is taken place. Recommended grain drier for pre-combine harvesting system and for combine harvesting system is batch-type drier and circulating -type drier, respectively. 3. As existing farm storages for grain have insufficient spaces and offer poor conditions for grain storing , it is greatly needed to build up new storage which store only grains. And it is concluded that storing grain in community common storages in desirable. 4. Power supplying system for milling machinery in local milling plants, that a large capacity prime mover supplies power to 4 to 6 kinds of milling machinery simultaeously, should be converted to a system of several small capacity prime movers supplying power to each machiner y for the purpose of reducing extra consumption of energy. 5. Governmental grain, of which Korean farms produced, should be milled and stored in the local milling plant successively for the purpose of reducing transportation fee and stroing facilities. 6. Furture post-havest grain operations-drying, storing and milling should be periormed successively in he community common plant. And average optimum processing capacity of the plant is estimated about 300 metric ton of grain every year.