• 대한수학회보
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• 제37권4호
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• pp.675-683
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• 2000

As a by-product of [4], we give algebraic integers of certain values of quotients of Weierstrass $\delta'(\tau),\delta'(\tau)$-functions. We also show that special values of elliptic functions are transcendental numbers.

• 한국수학사학회지
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• 제23권3호
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• pp.57-73
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• 2010

초월수의 연구는 2000년 이상 수학자들을 괴롭혀 왔던 고대 그리스의 기하학 문제의 하나인 원적문제가 불가능하다는 것을 보여줌으로써 수학사의 중요한 분야임을 입증하였다. Liouville은 1844년에 처음으로 구체적인 초월수의 예를 제시하였고, 칸토어는 1874년에 초월수의 존재성을 증명하였다. Louville 정리는 많은 초월수를 만들어 낼 뿐 아니라 초월수의 존재성을 증명하는데 이용할 수 있다. 1873년에 Hermite가 자연로그의 밑수 e가 초월수임을 보이고, 1882년에 Lindemann이 원주율 $\pi$가 초월수임 증명하였다. 1934년에 Gelfond와 Schneider는 각각 힐버트의 7번째 문제에 대한 서로 다른 완전한 해를 찾았다. 1966년에 Baker는 Gelfond-Schneider 정리의 일반화된 결과를 증명하였다. 이 연구의 목적은 초월수의 개념과 발달과정을 살피고, 미해결 문제를 제시하여 초월수의 연구가 촉진되도록 후학들에게 연구 동기를 부여하고자 한다.

• 대한수학회지
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• 제44권1호
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• pp.55-107
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k,\;q=e^{{\pi}i\tau}$. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, $\frac{q^{1/8}}{1}+\frac{-q}{1+q}+\frac{-q^2}{1+q^2}+\cdots$ ([1]) is transcendental.

• 대한수학회지
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• 제40권6호
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• pp.977-998
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• 2003

Let k be an imaginary quadratic field, η the complex upper half plane, and let $\tau$ $\in$ η $textsc{k}$, p = $e^{{\pi}i{\tau}}$. In this article, using the infinite product formulas for g2 and g3, we prove that values of certain infinite products are transcendental whenever $\tau$ are imaginary quadratic. And we derive analogous results of Berndt-Chan-Zhang ([4]). Also we find the values of (equation omitted) when we know j($\tau$). And we construct an elliptic curve E : $y^2$ = $x^3$ ＋ 3 $x^2$ ＋ {3-(j/256)}x ＋ 1 with j = j($\tau$) $\neq$ 0 and P = (equation omitted) $\in$ E.

• 한국수학교육학회지시리즈A:수학교육
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• 제14권2호
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• pp.17-22
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• 1976

• 대한수학회보
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• 제54권1호
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• pp.225-242
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• 2017

A family of $Ap{\acute{e}}ry$-like series involving reciprocals of central binomial coefficients is studied and it is shown that they represent transcendental numbers. The structure of such series is further examined in terms of finite combinations of logarithms and arctangents with arguments and coefficients belonging to a suitable algebraic extension of rationals. Monotonicity of certain quotients of weighted binomial sums which arise in the study of competitive cheap talk models is established with the help of a continuous extension of the discrete model at hand. The monotonic behavior of such quotients turns out to have important applications in game theory.

• 대한수학회논문집
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• 제22권3호
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• pp.331-351
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k$, $q=e^{{\pi}i\tau}$. We find a lot of algebraic properties derived from theta functions, and by using this we explore some new algebraic numbers from Rogers-Ramanujan continued fractions.

• 인지과학
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• 제29권2호
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• pp.105-120
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• 2018

현대 신경과학은 인간의 마음이 신체기관인 뇌 활동의 산물이며, 뇌의 활동이 멈추면 마음의 작용도 함께 정지한다는 심신 일원론을 지지한다. 그러나 상당수의 일반인은 여전히 일원론적 입장으로 설명하기 어려운 마음영속성과 사후세계에 대한 믿음을 갖고 있다. 본 연구에서는 죽은 사람의 마음이 단순히 작동정지하거나 약화된 마음이 아니라, 살아있는 사람의 마음과 구별되는, 시공간의 물리적 제약을 초월하는 마음으로 간주되는지 살펴보았다. 참가자들은 주인공이 교통사고 후 사망하거나, 생존하거나, 또는 뇌사상태가 되는 가상의 시나리오를 읽은 뒤, 각 상태의 주인공이 보유한 '일반적 정신능력'과 '초월적 정보수집 능력' 수준을 평정하였다. 연구 결과, 주인공이 사망한 조건에서는 주인공의 일반적 정신능력이 높다고 평가할수록 초월적 정보수집 능력도 높다고 응답하는 상관관계가 관찰되었으나, 생존 조건에서는 이러한 경향성이 관찰되지 않았다. 이는 죽은 사람과 산 사람에게 기대되는 정신능력의 속성이 서로 달라서, 죽은 사람이 소유한 높은 일반 정신능력은 초월적인 능력을 함축함을 시사한다. 추가적으로, 참가자의 종교적 믿음 또한 사망한 사람의 초월적 정보수집 능력에 대한 태도에 영향을 주는 변인임을 확인하였다.

• Wind and Structures
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• 제8권2호
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• pp.89-106
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• 2005

For estimating the vortex excited vibrations of overhead transmission lines, the Energy Balance Principle (EBP) is well established for spans damped near the ends. Although it involves radical simplifications, the method is known to give useful estimates of the maximum vibration levels. For very long spans, there often is the need for a large number of in-span fittings, such as in-span Stockbridge dampers, aircraft warning spheres etc. This adds complexity to the problem and makes the energy balance principle in its original form unsuitable. In this paper, a modified version of EBP is described taking into account in-span damping and in particular also aircraft warning spheres. In the first step the complex transcendental eigenvalue problem is solved for the conductor with in-span fittings. With the thus determined complex eigenvalues and eigenfunctions a modified energy balance principle is then used for scaling the amplitudes of vibrations at each resonance frequency. Bending strains are then estimated at the critical points of the conductor. The approach has been used by the authors for studying the influence of in-span Stockbridge dampers and aircraft warning spheres; and for optimizing their positions in the span. The modeling of the aircraft warning sphere is also described in some detail.

• 건축역사연구
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• 제22권3호
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• pp.15-26
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• 2013

This research takes as its object a body of historical researches by a new generation of French architects in the 1970s, who tried to confront the deep crisis in architecture since the years 1960. The research begins by noting that the ideology of the architect as an autonomous and transcendental subject, an ideology held by the architects of the previous generation, was a main target that young architects wanted to criticize and overcome. From this observation, the research focuses on a antihumanistic project which gave basis for a significant number of historical researches on modern architecture and was the result of a reappropriation of the French structuralism intensively developed in the human and social sciences of that time in France. After a series of textual analyzes, we argue that a new perspective on the city and the relationship of the latter with the architecture on the one hand, and the proposal for an "modest" architect as an alternative figure after rejection of the autonomous and transcendental one on the other hand, have been derived as the outcome of anti-humanist historiographic works. Finally, we assume that these historical adventure gave conceptual basis for postmodern architecture in France, freed from the modern myth of unity of author and that of work of art, but tinted by a moralism requesting modesty to architects.