• 대한수학회지
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• 제36권3호
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• pp.581-592
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• 1999

Let M be a properly immersed timelike hypersurface of $\overline{M}$. If M is a diagonal type, M satisfies the generic condition under the certain conditions of the eigenvalues of the shape operator. Moreover, applying them to Raychaudhuri equation, we can show that M satisfies the generic condition. Thus, by these results, we establish the singularity theorem for M in $\overline{M}$.

• 대한수학회논문집
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• 제36권2호
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• pp.361-375
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• 2021

The object of the present paper is to deduce some important results on generic submanifolds and also generic product of LP-Sasakian manifolds with concurrent vector fields. Also, we provide a necessary and sufficient condition for which the invariant distribution D and anti-invariant distribution D^⊥ of M are Einstein. Also, we deduce an interesting necessary and sufficient condition for submanifolds of LP-Sasakian manifolds to be totally umbilical submanifolds. Especially we deal with the generic submanifolds admitting a Ricci soliton in LP-Sasakian manifolds endowed with concurrent vector fields.

• 대한수학회논문집
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• 제31권2호
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• pp.389-394
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• 2016

Let $f:M{\rightarrow}M$ be a diffeomorphism on a closed $C^{\infty}\;d({\geq}2)$ dimensional manifold M. For $C^1$-generic f, if a diffeomorphism f satisfies the local star condition on a transitive set, then it is hyperbolic.

• 대한수학회논문집
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• 제11권3호
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• pp.743-756
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• 1996

The purpose of this paper is to compute the covariant derivative of a shape operator of a generic submanifold of a complex space form without using the Green-Stoke's theorem. In particular, we classify complete generic submanifolds of a complex number space $C^m$ with parallel mean curvature vector satisfying a certain condition.

• 충청수학회지
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• 제19권4호
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• pp.427-435
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• 2006

In this paper, we are to study the generic submanifold M of a Kenmotsu manifold and consider the integrability condition of the almost complex structure induced on the even-dimensional product manifold $M{\times}R^p{\times}R^1$ where p is the codimension.

• 충청수학회지
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• 제28권1호
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• pp.119-125
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• 2015

We find a necessary and sufficient condition for which a point star-configuration in $\mathbb{P}^n$ has generic Hilbert function. More precisely, a point star-configuration in $\mathbb{P}^n$ defined by general forms of degrees $d_1,{\ldots},d_s$ with $3{\leq}n{\leq}s$ has generic Hilbert function if and only if $d_1={\cdots}=d_{s-1}=1$ and $d_s=1,2$. Otherwise, the Hilbert function of a point star-configuration in $\mathbb{P}^n$ is NEVER generic.

• 한국수학교육학회지시리즈A:수학교육
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• 제23권2호
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• pp.61-66
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• 1985

• 충청수학회지
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• 제25권3호
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• pp.553-562
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• 2012

It has been proved that the union of two linear star-configurations in $\mathbb{P}^2$ of type $t{\times}s$ for $3{\leq}t{\leq}9$ and $3{\leq}t{\leq}s$ has generic Hilbert function. We extend the condition to $t$ = 10, so that it is true for $3{\leq}t{\leq}10$, which generalizes the result of [7].

• 정보보호학회논문지
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• 제13권5호
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• pp.169-177
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• 2003

본 논문에서는 DPA와 Goubin의 공격을 동시에 방어하도록 하는 타원곡선 스칼라 곱셈 알고리듬의 일반적인 조건을 제시하며, 제시된 조건을 만족하면 두 공격 모두를 방지할 수 있음을 보인다. 이러한 조건을 만족하는 것으로는 Ha-Moon의 재부호화 방법을 이용한 랜덤 스칼라 곱셈 알고리듬이 있음을 보이고, 또한 Ha-Moon의 재부호 방법을 변형하여 두 공격을 방지하는 새로운 재부호화 알고리듬을 제안한다. 효율성 면에서 제안하는 스칼라 곱셈 방식은 Izu-Takagi의 스칼라 곱셈방법(y-좌표를 계산하지 않고 Montgomery-ladder를 사용)과 비교될 만큼 효율적이다. 제안하는 스칼라 곱셈은 랜덤화된 사영좌표와 기저점 은닉(bsae point blinding) 또는 isogeny 함수를 결합한 방법보다 빠르다. 또한 Izu-Takagi의 경우 은닉 또는 isogeny 함수 방법을 이용하면 상당량의 시스템 파라미터를 EEPROM에 저장해야 하는 단점이 있지만 이것은 제안하는 스칼라 곱셈 방법에는 해당되지 않는다.

• 한국안전학회지
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• 제18권4호
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• pp.164-168
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• 2003

Bayes theorem, suggested by the British Mathematician Bayes (18th century), enables the prior estimate of the probability of an event under the condition given by a specific This theorem has been frequently used to revise the failure probability of a component or system. 2-Stage Bayesian procedure was firstly published by Shultis et al. (1981) and Kaplan (1983), and was further developed based on the studies of Hora & Iman (1990) Papazpgolou et al., Porn(1993). For a small observed failure number (below 12), the estimated reliability of a system or component is not reliable. In the case in which the reliability data of the corresponding system or component can be found in a generic reliability reference book, however, a reliable estimation of the failure probability can be realized by using Bayes theorem, which jointly makes use of the observed data (specific data) and the data found in reference book (generic data).