• International Journal of Naval Architecture and Ocean Engineering
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• 제13권1호
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• pp.35-49
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• 2021

This paper presents a direct numerical simulation of turbulent flows over a bump in an open channel to examine the turbulence characteristics near divergent waves emanating from the bump and to investigate the interaction of the turbulences with the divergent waves. To verify the reliability of the simulations, the mean velocity profile and root-mean-square of velocity fluctuations are compared with previous data. The anisotropic invariant maps show that the ratio of the streamwise to spanwise velocity fluctuations plays an important role in characterizing the anisotropic nature of the separated shear layer behind the bump in the vicinity of the free surface. The vortex identification discloses a large-scale streamwise vortical structure from the mean velocity field and a cluster of small coherent structures from the instantaneous velocity field, which are responsible for the anisotropic characteristics of the turbulence beneath the free surface.

• 대한수학회지
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• 제60권1호
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• pp.115-141
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• 2023

We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup {exp tX} is a normal nilpotent subgroup commuting with {exp tX}, and X is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-Kähler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension 5 and those of dimension 7 whose Kähler reduction in the above sense is abelian.

• Journal of the Korean Statistical Society
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• 제7권2호
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• pp.131-142
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• 1978

This study aims to find out a suitable mathematical models for the estimation of population size and improve it for the estimation of social increase of population at urban areas. This study shows that Model (I) is obtained by the generalization of Kabak's Wild Life Management Model together with some other useful results as follows: a) By the transition matrix P, it is known that the interregional migrations have shown greater rise than those of five years ago. b) The invariant population vector $\alpha$ predicts that the Kyonggi area will have a share of 48%, the Choongcheong area of 10%, the Honam area of 12%, and the Youngnam area of 17% of the total population of Korea. c) The estimated population of the Special City of Seoul (Metropolitan) will be above ten millon in 1983. d) The estimated optmum population of Korea will be 53,850,000 in 2000 A.D.

• 대한수학회보
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• 제24권1호
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• pp.31-37
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• 1987

I want to focus on developments in the areas of general relativity and gauge theory. The topics to be considered are the singularity theorms of Hawking and Penrose, the positivity of mass, instantons on the four-dimensional sphere, and the string picture of quantum gravity. I should mention that I will not have time do discuss either classical mechanics or symplectic structures. This is especially unfortunate, because one of the roots of differential geometry is planted firmly in mechanics, Cf. [GS]. The French geometer Elie Cartan first formulated his invariant approach to geometry in a series of papers on affine connections and general relativity, Cf. [C]. Cartan was trying to recast the Newtonian theory of gravity in the same framework as Einstein's theory. From the historical perspective it is significant that Cartan found relativity a convenient framework for his ideas. As about the same time Hermann Weyl in troduced the idea of gauge theory into geometry for purposes much different than those for which it would ultimately prove successful, Cf. [W]. Weyl wanted to unify gravity with electromagnetism and though that a conformal structure would fulfill thel task but Einstein rebutted this approach.

• 대한수학회지
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• 제60권6호
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• pp.1303-1336
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• 2023

In this paper, we study the 𝜂-parallelism of the Ricci operator of almost Kenmotsu 3-manifolds. First, we prove that an almost Kenmotsu 3-manifold M satisfying ∇_𝜉h = -2𝛼h𝜑 for some constant 𝛼 has dominantly 𝜂-parallel Ricci operator if and only if it is locally symmetric. Next, we show that if M is an H-almost Kenmotsu 3-manifold satisfying ∇_𝜉h = -2𝛼h𝜑 for a constant 𝛼, then M is a Kenmotsu 3-manifold or it is locally isomorphic to certain non-unimodular Lie group equipped with a left invariant almost Kenmotsu structure. The dominantly 𝜂-parallelism of the Ricci operator is equivalent to the local symmetry on homogeneous almost Kenmotsu 3-manifolds.

• 대한수학회지
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• 제61권3호
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• pp.547-564
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• 2024

We study totally real and complex subsets of a right quarternionic vector space of dimension n + 1 with a Hermitian form of signature (n, 1) and extend these notions to right quaternionic projective space. Then we give a necessary and sufficient condition for a subset of a right quaternionic projective space to be totally real or complex in terms of the quaternionic Hermitian triple product. As an application, we show that the limit set of a non-elementary quaternionic Kleinian group 𝚪 is totally real (resp. commutative) with respect to the quaternionic Hermitian triple product if and only if 𝚪 leaves a real (resp. complex) hyperbolic subspace invariant.

• 대한수학회지
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• 제61권4호
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• pp.743-760
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• 2024

In this paper, we are devoted to study a forth order curve flow for a smooth closed curve in centro-affine geometry. Firstly, a new evolutionary equation about this curve flow is proposed. Then the related geometric quantities and some meaningful conclusions are obtained through the equation. Next, we obtain finite order differential inequalities for energy by applying interpolation inequalities, Cauchy-Schwartz inequalities, etc. After using a completely new symbolic expression, the n-order differential inequality for energy is considered. Finally, by the means of energy estimation, we prove that the forth order curve flow has a smooth solution all the time for any closed smooth initial curve.

• 대한수학회지
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• 제53권4호
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• pp.795-834
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• 2016

The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group $Homeo^{\Omega}$ ($D^2$, ${\partial}D^2$) of area preserving homeomorphisms of the 2-disc $D^2$. We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : $Diff^{\Omega}$ ($D^1$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to a homomorphism ${\bar{Cal}}$ : Hameo($D^2$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to that of the vanishing of the basic phase function $f_{\underline{F}}$, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian ${\underline{F}}$ on $S^2$ that is obtained via the natural embedding $D^2{\hookrightarrow}S^2$. Here Hameo($D^2$, ${\partial}D^2$) is the group of Hamiltonian homeomorphisms introduced by $M{\ddot{u}}ller$ and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on $D^2$ via a study of the associated Hamiton-Jacobi equation.

• 제어로봇시스템학회논문지
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• 제20권11호
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• pp.1098-1102
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• 2014

Localization of aerial vehicles and map building of flight environments are key technologies for the autonomous flight of small UAVs. In outdoor environments, an unmanned aircraft can easily use a GPS (Global Positioning System) for its localization with acceptable accuracy. However, as the GPS is not available for use in indoor environments, the development of a SLAM (Simultaneous Localization and Mapping) system that is suitable for small UAVs is therefore needed. In this paper, we suggest a vision-based SLAM system that uses vision sensors and an AHRS (Attitude Heading Reference System) sensor. Feature points in images captured from the vision sensor are obtained by using GPU (Graphics Process Unit) based SIFT (Scale-invariant Feature Transform) algorithm. Those feature points are then combined with attitude information obtained from the AHRS to estimate the position of the small UAV. Based on the location information and color distribution, a Gaussian process model is generated, which could be a map. The experimental results show that the position of a small unmanned aircraft is estimated properly and the map of the environment is constructed by using the proposed method. Finally, the reliability of the proposed method is verified by comparing the difference between the estimated values and the actual values.

• Journal of Computational Design and Engineering
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• 제2권1호
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• pp.26-37
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• 2015

A lot of researchers have been investigating interactive portable projection systems such as a mini-projector. In addition, in exhibition halls and museums, there is a trend toward using interactive projection systems to make viewing more exciting and impressive. They can also be applied in the field of art, for example, in creating shadow plays. The key idea of the interactive portable projection systems is to recognize the user's gesture in real-time. In this paper, a vision-based shadow gesture recognition method is proposed for interactive projection systems. The gesture recognition method is based on the screen image obtained by a single web camera. The method separates only the shadow area by combining the binary image with an input image using a learning algorithm that isolates the background from the input image. The region of interest is recognized with labeling the shadow of separated regions, and then hand shadows are isolated using the defect, convex hull, and moment of each region. To distinguish hand gestures, Hu's invariant moment method is used. An optical flow algorithm is used for tracking the fingertip. Using this method, a few interactive applications are developed, which are presented in this paper.