• 대한수학회보
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• 제25권2호
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• pp.243-246
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• 1988

Let M(z)=exp (-1+z/1-z) be the unit singular inner function. See [1] or [2] for the basic facts about inner functions. We define the iterations of M9z) as (Fig.) Since the composition M$_{2}$(z)=M.M(z) is known (see [5] for example) to be singular inner function it has the "cannonical" representation (Fig.) where .mu. is a finite, positive singular Borel measure on the unit circle T. In section 2, we have explicit cannonical representation of M$_{2}$(z) by determining the singular measure .mu. In section 3 we show that (Fig.) These facts might have been known but could not be found in the literature.iterature.

• 대한수학회지
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• 제48권2호
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.

• 대한수학회지
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• 제33권1호
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• pp.39-46
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• 1996

Let $\alpha > 0$ and $\zeta$ be a point on the unit circle $T= {$\mid$z$\mid$ = 1}$ of the complex plane C.

• 대한수학회지
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• 제36권4호
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• pp.787-811
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• 1999

Let M be the maximal ideal space of the Banach algebra $H^{\infty}$ of bounded analytic functions on the open unit disc $\triangle$. For a positive singular measure ${\mu}\;on\;{\partial\triangle},\;let\;{L_{+}}^1(\mu)$ be the set of measures v with $0\;{\leq}\;{\nu}\;{\ll}\;{\mu}\;and\;{{\psi}_{\nu}}$ the associated singular inner functions. Let $R(\mu)\;and\;R_0(\mu)$ be the union sets of $\{$\mid$\psiv$\mid$\;<\;1\}\;and\;\{$\mid${\psi}_{\nu}$\mid$\;<\;0\}\;in\;M\;{\setminus}\;{\triangle},\;{\nu}\;\in\;{L_{+}}^1(\mu)$, respectively. It is proved that if $S(\mu)\;=\;{\partial\triangle}$, where $S(\mu)$ is the closed support set of $\mu$, then $R(\mu)\;=\;R0(\mu)\;=\;M{\setminus}({\triangle}\;{\cup}\;M(L^{\infty}(\partial\triangle)))$ is generated by $H^{\infty}\;and\;\overline{\psi_{\nu}},\;{\nu}\;{\in}\;{L_1}^{+}(\mu)$. It is proved that %d{\theta}(S(\mu))\;=\;0$ if and only if there exists as Blaschke product b with zeros $\{Zn\}_n$ such that $R(\mu)\;{\subset}\;{$\mid$b$\mid$\;<\;1}\;and\;S(\mu)$ coincides with the set of cluster points of $\{Zn\}_n$. While, we proved that $\mu$ is a sum of finitely many point measure such that $R(\mu)\;{\subset}\;\{$\mid${\psi}_{\lambda}$\mid$\;<\;1}\;and\;S(\lambda)\;=\;S(\mu)$. Also it is studied conditions on \mu for which $R(\mu)\;=\;R0(\mu)$.

• 조형예술학연구
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• 제4권
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• pp.67-90
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• 2002

What is the semantic function of visual image in Contemporary art? This article proposes that representation is semantically still important in post-modernism as well as in modernism. The semantic function of representation has been changed by keeping pace with times. In modernism the 'outer representation' changed to 'inner representation', and in postmodernism the 'inner representation' changed to 'metaphorical representation'. The 'outer representation' means that image indicates a certain object or subject as the classical realism. In this case, the meaning of image is subordinate to an object, and a one-to-one correspond existed between the image and the object. Because this 'outer representation' is focused on an object but subject's intention, the indicative function of meaning is definite and singular. The 'inner representation' means that image exposes the fundamentals or process of an object. In this case, the meaning of image resolves itself into an absolute fundamental, and one-to-many correspond existed between the image and the object. Because this 'inner representation' is focused on essence and substance but an external form, the indicative function of meaning is inclusive and general. The 'metaphorical representation' means that image critically relates social constraint and condition as metaphor and allegory. In this case, the meaning of image is not subordinate to an object and a subject, and the image and the object indicate interactively. Because this 'metaphorical representation' is focused on interaction between subject, object, and interpreter, the indicative function of meaning is differant and ecological. This article focused on the representation because I believe that continuous thinking of totality can be opened by cognitive mapping, even though we never understand the world totally in the chaotic post modern age.

• Journal of Welding and Joining
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• 제29권2호
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• pp.64-71
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• 2011

In this paper, crack propagation analyses in the inner diameter (ID) repair weld of the dissimilar metal weldment of a nozzle were performed using a finite element alternating method (FEAM). To calculate the theoretical solution for the crack tip stress intensity factor, a weak type singular integral equation consisted of crack surface traction and dislocation density function was constructed and solved in conjunction with the FEAM. A two-dimensional axisymmetric finite element nozzle model was prepared and ID repair welding was simulated. An initial crack, 10% depth of weld thickness, was assumed and crack propagation trajectory from the initial crack to the 75% depth of thickness was calculated using the FEAM. Crack growth versus time curve was also calculated and compared with the curves obtained from ASME code method. With the method constructed in this paper, crack propagation trajectory and crack growth time were calculated automatically and effectively.

• 한국과학교육학회지
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• 제34권2호
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• pp.55-62
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• 2014

본 연구는 1960년대 이후 과학적 소양을 정의하고 분류를 시도했던 연구자들의 분류 결과를 3가지 분류 기준에 의하여 재분류하고, 과학적 소양의 정의 분류의 경향을 파악하는데 목적이 있다. 과학적 소양이 과학교육의 주요 목표를 대변하는 개념이므로 그 정의에 따른 분류는 과학교육의 목적에 대한 동향을 검토할 수 있는 주요자료가 될 수 있다. 분류 기준은 1) "literate"의 의미로서 '학습됨', '능력 있음', '사회에서 최소 기능을 할 수 있음', 2) 과학적 소양을 표현하는 방식으로서 용어와 서술, 3) 과학적 소양의 내부 구조로서 '단일 구조', '직렬식 위계구조', '병렬식 수평구조'이다. 분류 결과와 해석은 다음과 같다. 첫째, 과학적 소양의 구조로서 위계 구조는 90년대 후반부터 표현방식으로서 용어를 사용하는 정의와 함께 나타나고 있으며, 학습과 능력사이에서만 위계를 인정하고 사회적 기능으로서의 과학적 소양의 의미는 수용하지 않고 있다. 수평구조는 과학적 소양의 하위 요소 간의 위계 구조를 보이지 않는 대신 사회적 기능으로서 과학적 소양의 의미를 전반적으로 수용하고 있다. 또, 단일 구조는 대부분 과학적 소양을 새로운 시각에서 제안하는 연구에서 나타나고 있으며, 소양의 의미도 최근으로 오면서 학습에서 능력을 거쳐 사회적 기능을 강조하는 특성이 있다. 둘째, 근래로 오면서 과학적 소양을 용어 형식으로 정의하려는 연구가 증가하고, 이들 사이에도 위계를 설정하는 분류가 주도하고 있다. 또한 소양의 세 가지 의미인 학습, 능력, 사회적 기능을 전반적으로 수용하는 분류가 빈번해졌으나, 이들 간에는 위계 구조보다는 오히려 수평 구조를 설정하는 경향이 있다. 위와 같은 분석 결과를 토대로 살펴 볼 때, 과학 교육의 목표로서 과학적 소양의 의미는 학습이나 과제 해결 능력뿐만 아니라, 근래에는 사회적 맥락에서 어떤 역할을 하는 개인을 육성하려는 목표로서 인정되고 있다는 점이다. 또한 주목할 것은 과학적 소양의 이러한 사회적 기능 측면은 위계적이 아닌 독립적인 목표로서의 특성을 견지하고 있다는 점이다. 이러한 변화에 능동적으로 대처하기 위해서는 과학교육이 교과 내 개념학습에서 벗어나 다양한 맥락에서의 적용과 사회적 역할을 중시하는 목표로 전환할 준비를 해야 할 것으로 보인다.