• 대한수학회보
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• 제56권6호
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• pp.1525-1537
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• 2019

Let ${\tilde{M}}$ be a Riemannian manifold equipped with a concircular vector field ${\tilde{X}}$ and M a submanifold (with its induced metric) of ${\tilde{M}}$. Denote by X the restriction of ${\tilde{X}}$ on M and by $X^T$ the tangential component of X, called the canonical field of M. In this article we study submanifolds of ${\tilde{M}}$ whose canonical field $X^T$ is also concircular. Several characterizations and classification results in this respect are obtained.

• 대한수학회논문집
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• 제36권3호
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• pp.575-592
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• 2021

In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle T^*M over an anti-paraKähler manifold (M, 𝜑, g) as a new natural metric with respect to g non-rigid on T^*M. Firstly, we investigate the Levi-Civita connection of this metric. Secondly, we study the curvature tensor and also we characterize the scalar curvature.

• 한국산업융합학회 논문집
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• 제6권1호
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• pp.11-15
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• 2003

There are various method for the LEV(Low Emission Vehicle) regulation, but 2-catalyst system using one catalyst near exhaust manifold and another catalyst underfloor, is the most popular. This system uses the proven catalyst technology and doesn't use energy. But it is difficult to determine capacity of the two catalysts. So an optimization method to determine the capacity has been proposed by other researcher. It uses the fact that emission decreases with capacity increasing, but the decreasing ratio slows down in high capacity range. It means that the emission and capacity of catalyst is exponentially decreasing relation. In this paper this method will be verified with various experiments. And this method was proven to be very useful to determine the capacity of two catalysts system.

• 대한수학회지
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• 제59권1호
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• pp.13-33
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• 2022

The quaternionic Calabi conjecture was introduced by Alesker-Verbitsky, analogous to the Kähler case which was raised by Calabi. On a compact connected hypercomplex manifold, when there exists a flat hyperKähler metric which is compatible with the underlying hypercomplex structure, we will consider the parabolic quaternionic Monge-Ampère equation. Our goal is to prove the long time existence and C^∞ convergence for normalized solutions as t → ∞. As a consequence, we show that the limit function is exactly the solution of quaternionic Monge-Ampère equation, this gives a parabolic proof for the quaternionic Calabi conjecture in this special setting.

• 대한수학회논문집
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• 제38권1호
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• pp.223-234
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• 2023

The main purpose of this paper is to study the lightlike hypersurface (M, $\overline{g}$) of cosymplectic space form $\overline{M}$(c). In this paper, we computed the Gauss and Codazzi formulae of (M, $\overline{g}$) of cosymplectic manifold ($\overline{M}$, g). We showed that we can't obtain screen semi-invariant lightlike hypersurface (SCI-LH) of $\overline{M}$(c) with parallel second fundamental form h, parallel screen distribution and c ≠ 0. We showed that if second fundamental form h and local second fundamental form B are parallel, then (M, $\overline{g}$) is totally geodesic. Finally we showed that if (M, $\overline{g}$) is umbilical, then cosymplectic manifold ($\overline{M}$, g) is flat.

• 대한수학회논문집
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• 제19권1호
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• pp.135-141
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• 2004

We studied the relation between the tangential Cauchy-Riemann operator ${\={\partial}}_b$ CR-manifolds and the derivation $d^{{\pi}^{0,\;1}}$ associated to the natural projection map ${\pi}^{0.1}\;:\;TM\;{\bigotimes}\;{\mathbb{C}}\;=\;T^{1,0}\;{\bigoplus}\;T^{0,\;1}\;{\rightarrow}\;T^{0,\;1}$. We found that these two differential operators agree only on the space of functions ${\Omega}^0(M),\;unless\;T^{1,\;0}$ is involutive as well. We showed that the difference is a derivation, which vanishes on ${\Omega}^0(M)$, and it is induced by the Nijenhuis tensor associated to ${\pi}^{0.1}$.

• 대한수학회보
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• 제25권2호
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• pp.175-178
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• 1988

Let .SIGMA. be a smooth compact manifold without boundary having the same homotopy type as a sphere, which is called a homotopy sphere. Supose a group G acts smoothly on .SIGMA. with the fixed point set .SIGMA.$^{G}$ consists of two isolated fixed points p and q. In this case, tangent spaces $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA. at isolated fixed points, as isotropy representations of G are called Smith equivalent. Moreover .SIGMA. is called a supporting homotopy sphere of Smith equivalent representations $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA.. The study on Smith equivalence has rich history, and for this we refer the reader to [P] or [Su]. The following question of pp.A.Smith [S] motivates the study on Smith equivalence.e.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권2호
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• pp.109-129
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• 2023

In this paper, we introduce a second order linear differential operator ^T□: C^∞ (M) → C^∞ (M) as a natural generalization of Cheng-Yau operator, [8], where T is a (1, 1)-tensor on Riemannian manifold (M, h), and then we show on compact Riemannian manifolds, divT = divT^t, and if divT = 0, and f be a smooth function on M, the condition ^T□ f = 0 implies that f is constant. Hereafter, we introduce T-energy functionals and by deriving variations of these functionals, we define T-harmonic maps between Riemannian manifolds, which is a generalization of L_k-harmonic maps introduced in [3]. Also we have studied fT-harmonic maps for conformal immersions and as application of it, we consider fL_k-harmonic hypersurfaces in space forms, and after that we classify complete fL₁-harmonic surfaces, some fL_k-harmonic isoparametric hypersurfaces, fL_k-harmonic weakly convex hypersurfaces, and we show that there exists no compact fL_k-harmonic hypersurface either in the Euclidean space or in the hyperbolic space or in the Euclidean hemisphere. As well, some properties and examples of these definitions are given.

• 한국자동차공학회논문집
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• 제1권3호
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• pp.1-11
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• 1993

An experimental study was carried out to evaluate the characteristics of transient performance of carburettered gasoline engine under rapid accelerating transient driving conditions. In order to evaluate the characteristics of transient performance quantitatively, the concept of dead time $t_d$ response delay time $t_r$ are introduced. Performance parameters such as air mass fiowrate Gat, engine speed N, manifold boost pressure Pb, and output torque T are measured simultaneously during the rapid opening of the throttle valve by the stepping motor. During the rapid opening of the throttle valve, air mass fiowrate Gat is increased immediately without delay time, but response of engine revolution N, and output torque T are delayed. Therefore hesitation, and stumble phenomena are occurred. Dead time $t_d$ and response delay time $t_r$ of engine revolution N, which is extremely delayed comparing to other performance parameters, are respectively 0.2-0.3sec., 3.0-4.6sec., and dead time rate $t_d/{\Delta}t$ and response delay time rate $t_r/{\Delta}t$ are linearly increased with the throttle valve opening rate ${\theta}$ during the acceleration from 12 degree to 20 degree at 1250rpm.

• 응용통계연구
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• 제36권2호
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• pp.167-173
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• 2023

본 논문에서는 고차원의 자료를 저차원으로 변환시켜 시각화하는 다양한 방법들을 소개하였다. 차원 축소는 크게 선형 방법과 비선형 방법으로 나눌 수 있는데 선형 방법으로 주성분 분석, 다차원 척도 등을 간략하게 소개하였고 비선형 방법으로 커널 주성분 분석, 자기조직도, 국소 선형 사상, Isomap, 국소 다차원 척도 등을 간략하게 소개하였으며, 가장 최근에 제안되었으며 매우 널리 사용되고 있지만 통계학 분야에는 비교적 생소한 t-SNE에 대하여 자세히 소개하였다. t-SNE를 이용한 간단한 예제를 제시하고 t-SNE의 장단점을 지적한 최근 연구 논문을 소개하고 제시된 향후 연구 과제들을 살펴보았다.