• 대한수학회논문집
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• 제34권1호
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• pp.279-286
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• 2019

Complex Grassmann manifolds $G_{n,k}$ are a generalization of complex projective spaces and have many important features some of which are captured by the $Pl{\ddot{u}}cker$ embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$ where $N=\(^n_k\)$. The problem of existence of cross sections of fibrations can be studied using the Gottlieb group. In a more generalized context one can use the relative evaluation subgroup of a map to describe the cohomology of smooth fiber bundles with fiber the (complex) Grassmann manifold $G_{n,k}$. Our interest lies in making use of techniques of rational homotopy theory to address problems and questions involving applications of Gottlieb groups in general. In this paper, we construct the Sullivan minimal model of the (complex) Grassmann manifold $G_{n,k}$ for $2{\leq}k<n$, and we compute the rational evaluation subgroup of the embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$. We show that, for the Sullivan model ${\phi}:A{\rightarrow}B$, where A and B are the Sullivan minimal models of ${\mathbb{C}}P^{N-1}$ and $G_{n,k}$ respectively, the evaluation subgroup $G_n(A,B;{\phi})$ of ${\phi}$ is generated by a single element and the relative evaluation subgroup $G^{rel}_n(A,B;{\phi})$ is zero. The triviality of the relative evaluation subgroup has its application in studying fibrations with fibre the (complex) Grassmann manifold.

• 대한수학회논문집
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• 제29권4호
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• pp.569-579
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• 2014

We consider a condition under which the projectivization $P(E^k)$ of a complex k-bundle $E^k{\rightarrow}M$ over an even-dimensional manifold M can have the hard Lefschetz property, affected by [10]. It depends strongly on the rank k of the bundle $E^k$. Our approach is purely algebraic by using rational Sullivan minimal models [5]. We will give some examples.

• 대한수학회논문집
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• 제36권4호
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• pp.835-840
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• 2021

In this paper, we compute the rational evaluation subgroup of the Hopf fibration S²ⁿ⁺¹ ↪ ℂP(n). We show that, for the Sullivan model 𝜙 : A → B, where A and B are the minimal Sullivan models of ℂP(n) and S²ⁿ⁺¹ respectively, the evaluation subgroup G_n(A, B; 𝜙) and the relative evaluation subgroup G^rel_n (A, B; 𝜙) of 𝜙 are generated by single elements.

• Kyungpook Mathematical Journal
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• 제63권1호
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• pp.131-139
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• 2023

Let V_k,n (ℂ) denote the complex Steifel and Gr_k,n (ℂ) the Grassmann manifolds for 1 ≤ k < n. In this paper, we compute, in terms of the Sullivan minimal models, the evaluation subgroups and, more generally, the relative evaluation subgroups of the fibration p : V_k,k+n (ℂ) → Gr_k,k+n (ℂ). In particular, we prove that G_* (Gr_k,k+n (ℂ), V_k,k+n (ℂ) ; p) is isomorphic to G^rel_* (Gr_k,k+n (ℂ), V_k,k+n (ℂ) ; p) ⊕ G_* (V_k,k+n (ℂ)).

• 대한수학회논문집
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• 제38권2호
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• pp.643-648
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• 2023

Let X be a simply connected rationally elliptic space such that H²(X; ℚ) ≠ 0. In this paper, we show that if H²ⁿ(X^[2n-2]; ℚ) = 0 or if π_2n(X²ⁿ) ⊗ ℚ = 0 for all n, then X is an F₀-space.

• 대한불안의학회지
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• 제1권1호
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• pp.14-17
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• 2005

By the influence of the descriptive approach of DSM-III, the anxiety became the same thing as the anxiety disorder to the clinicians. This unfortunate result sacrificed psychodynamic model of symptom formations and simplified the anxiety as one of the disease entity not as the overdetermined symptoms. These phenomenon awakened the psychoanalytic interest which was in sleep. Freud was the first major articulator of the basic significance of anxiety in human behavior. He attributed the particular quality of the anxiety experience to the trauma of birth, and subsequently to the fear of castration. Such classification of the anxiety according to the psychosexual development is helpful for the clinicians in understanding the origin of anxiety which the patient shows during the psychotherapy. The other analytical view of interpersonal psychoanalysis came from Sullivan. A large part of his therapy is taken up with recognizing and correcting parataxic distortions that interfere with realistic self-appraisal of events and of oneself in relation to others. Perhaps no explanation is the 'most basic' explanation for human anxiety. Anxiety is a multifaceted entity consisting of aspects of realm of discourse. Existential anxiety is inescapable in Western culture but it can be transcended by the cultivation of mind in Eastern culture. The analysts need to stay attuned to their own propensities for anxiety and must permit their own experiences with anxiety to be the grist for the psychotherapeutic mill.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.313-318
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• 1998

In this paper we prove two independent theorems concerning formality of a nilmanifold and a differential graded algebra using the well-known theorem of Deligne-Griffiths-Morgan-Sullivan. We first give a rational homotopy theoretic proof to the statement that a nilmanifold is formal if and only if it is a torus. And then we study some conditions with which formality of one dga implies formality of the other in an extension of dga's.

• 대한수학회보
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• 제58권2호
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• pp.445-449
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• 2021

We define the relative self-closeness number N��(g) of a map g : X → Y, which is a generalization of the self-closeness number N��(X) of a connected CW complex X defined by Choi and Lee [1]. Then we compare N��(p) with N��(X) for a fibration $X{\rightarrow}E{\rightarrow\limits^p}Y$. Furthermore we obtain its rationalized result.

• 응용통계연구
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• 제30권3호
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• pp.475-486
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• 2017

국민 건강의 향상 및 복지의 선진화를 위해 객관적이고 정확한 건강기대수명의 필요성이 대두되었다. 또한 건강기대수명은 삶의 질을 평가하는 주요한 지표이기 때문에 기대수명 및 건강기대수명에 근거한 사회계층간의 삶의 질의 불평등에 대한 논의는 이미 여러 해외연구에서 계속되어 왔다. 이에 본 논문에서는 우리나라 유병률과 사망률에서 모집단에 대한 대표성을 갖고 있는 표본코호트DB를 통해 건강기대수명을 도출하였다. 본 논문에서는 건강기대수명의 산출을 위해 Sullivan (1971)의 단일상태 접근법을 이용하였다. 이때, 사망률과 유병률이 관측되지 않은 연령대의 경우에는 Greville (1945)의 9-order correction factor 방법과 Brass (1971)의 Brass-logit 모형을 통하여 보정하여 주었다. 그 결과 2013년 기준 한국여성의 기대수명은 87세, 남성은 80세 였으나 여성의 경우는 60년, 남성은 61년 동안만 질병이 없는 '건강한 삶'을 영위하는 것으로 나타났다. 본 연구에서는 또한 2003년부터 2013년까지 한국인의 특정 질병으로부터의 건강한 삶의 영위기간을 성별, 소득수준별, 건강보험가입 구분별로 산출하였다. 그 결과 건강기대수명 측면에서 한국의 성별, 소득수준별, 건강보험 가입 구분별 삶의 질의 불평등을 확인하였다.

• 대한수학회논문집
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• 제34권3호
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• pp.991-1004
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• 2019

Firstly we consider preorders (not necessarily partial orders) on a canonical quotient of the set of the homotopy classes of continuous maps between two spaces induced by a certain equivalence relation ${\sim}_{{\varepsilon}R}$. Secondly we apply it to a classification of orientable fibrations over Y with fibre X. In the classification theorem of J. Stasheff [22] and G. Allaud [3], they use the set $[Y,\;Baut_1X]$ of homotopy classes of continuous maps from Y to $Baut_1X$, which is the classifying space for fibrations with fibre X due to A. Dold and R. Lashof [11]. In this paper we give a classification of fibrations using a preordered set (abbr., proset) structure induced by $[Y,\;Baut_1X]_{{\varepsilon}R}:=[Y,\;Baut_1X]/{\sim}_{{\varepsilon}R}$.