• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.365-374
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• 1995

On a compact manifold without conjugate points, the volume entropy can be obtained as the average mean curvature of the horospheres in the universal covering space. In the case when the volume entropy is zero, we prove that the universal covering space is diffeomorphic to a product space with a line factor. This fact can be considered as a surporting evidence for the Mane's conjecture, which claims the flatness of the mainfold.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.259-269
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• 2021

We shall study the following. Let 𝜙 be an expansive flow on a compact TVS-cone metric space (X, d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that lim sup ${\frac{1}{t}}$ log v(t) ≤ h(𝜙), where v(t) denotes the number of closed orbits of 𝜙 with a period 𝜏 ∈ [0, t] and h(𝜙) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space [?].

• Journal of Space Technology and Applications
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• v.1 no.1
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• pp.104-120
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• 2021

Some optical schemes of lenses for spacecraft developed by the author are considered. The main optical characteristics of telescope lenses of various architectures are compared. We propose compact solutions of mirror, lens-mirror, and lens systems with maximum available angular resolutions and other parameters. Examples of calculating the optical systems of lenses used for various tasks both in the field of astronomy and in the field of remote sensing of the Earth and other planets are given. The example of onboard computer system is discussed. Practical recommendations on the development and use of telescope lenses are given.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.447-452
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• 2005

Given operators X and Y on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. Let L be a subspace lattice acting on a separable complex Hilbert space H and Alg L be a tridiagonal algebra. Let X = $(x_{ij})\;and\;Y\;=\;(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a compact operator A = $(x_{ij})$ in AlgL such that AX = Y. (2) There is a sequence {$\alpha_n$} in $\mathbb{C}$ such that {$\alpha_n$} converges to zero and $$y_1\;_j=\alpha_1x_1\;_j+\alpha_2x_2\;_j\;y_{2k}\;_j=\alpha_{4k-1}x_{2k\;j}\;y_{2k+1\;j}=\alpha_{4k}x_{2k\;j}+\alpha_{4k+1}x_{2k+1\;j}+\alpha_{4k+2}x_{2k+2\;j\;for\;all\;k\;\epsilon\;\mathbb{N}$$.

• Journal of the Korean Society of Combustion
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• v.18 no.2
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• pp.23-31
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• 2013

Compact steam boiler is a useful heat exchanger in a space-intensive system. There are some constraints in terms of sizing and designing the space confined in the system which is usually used in vessels. In this study, design considerations for heavy duty heat exchangers of compact steam boilers are presented and evaluated. Especially, evaporator tubes of marine boiler which are exposed to a high temperature environment are considered. Also, extended surface designs with a high temperature are examined. In order to determine the criteria with considerations of both heat transfer rate and pressure drop in the heat exchanger, they are evaluated with major variables, such as the tube diameter, the number of tubes, and the tube length. Finally, the design parameters are estimated as the bare tubes are installed instead of the finned tubes.

• Korean Journal of Computational Design and Engineering
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• v.14 no.4
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• pp.217-224
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• 2009

Most divide-and-conquer implementations for Delaunay triangulation utilize quad-edge or winged-edge data structure since triangles are frequently deleted and created during the merge process. How-ever, the proposed divide-and-conquer algorithm utilizes the array based data structure that is much simpler than the quad-edge data structure and requires less memory allocation. The proposed algorithm has two important features. Firstly, the information of space partitioning is represented as a permutation vector sequence in a vertices array, thus no additional data is required for the space partitioning. The permutation vector represents adaptively divided regions in two dimensions. The two-dimensional partitioning of the space is more efficient than one-dimensional partitioning in the merge process. Secondly, there is no deletion of edge in merge process and thus no bookkeeping of complex intermediate state for topology change is necessary. The algorithm is described in a compact manner with the proposed data structures and operators so that it can be easily implemented with computational efficiency.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.397-409
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• 1996

Let X be a connected compact polyhedron and $f : X \to X$ a selfmap of X. The Reidemeister number of f is denoted by R(f).

• Archives of design research
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• v.13 no.2
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• pp.25-32
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• 2000

The body proportion of a passenger car has been changed by the demand of consumer and the market. Now the interior space proportion on a passenger car become to have the importance as the passenger space and this proportion has been changed as the new models have been developed. It didn't seems to had a unified direction or strategy in the dimensions of the domestic passenger cars on the early models, but they had a specific changes in dimensions on the later models. The proportion of the wheelbase and greenhouse can be calculated into as about 58% and 57% on the compact and sub-compact passenger cars while it is about 56% on mid-size sedan type passenger cars for thier 3-box structure body concept. The overrall proportion of the interior space is bigger on the compact and the sub-compact passenger cars than the mid-size passenger cars as the calculation shows. It can be concluded that the interior space proportion on the compact passenger cars would become larger, which is closed to 60%. And this trend would be appear on the mid-size passenger cars.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.735-747
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• 2018

Let M be a real hypersurface of a complex space form with constant curvature c. In this paper, we study the hypersurface M admitting Miao-Tam critical metric, i.e., the induced metric g on M satisfies the equation: $-({\Delta}_g{\lambda})g+{\nabla}^2_g{\lambda}-{\lambda}Ric=g$, where ${\lambda}$ is a smooth function on M. At first, for the case where M is Hopf, c = 0 and $c{\neq}0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with ${\lambda}$ > 0 or ${\lambda}$ < 0 is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.357-375
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• 2023

In this paper, we introduce the concept of bipolar soft supra topological space and provide a characterization of the related concepts of bipolar soft supra closure and bipolar soft supra interior. We also establish a connection between bipolar soft supra topology and bipolar soft topology. Additionally, we present the concept of bipolar soft supra continuous mapping and examine the concept of bipolar soft supra compact topological space. A related result concerning the image of the bipolar soft supra compact space is proved. Finally, we identify the concepts of disconnected (connected) and strongly disconnected (strongly connected) space and derive several results linking them together. Relationships among these concepts are clarified with the aid of examples.