• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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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.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.57-73
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• 2010

Transcendental numbers are important in the history of mathematics because their study provided that circle squaring, one of the geometric problems of antiquity that had baffled mathematicians for more than 2000 years was insoluble. Liouville established in 1844 that transcendental numbers exist. In 1874, Cantor published his first proof of the existence of transcendentals in article [10]. Louville's theorem basically can be used to prove the existence of Transcendental number as well as produce a class of transcendental numbers. The number e was proved to be transcendental by Hermite in 1873, and $\pi$ by Lindemann in 1882. In 1934, Gelfond published a complete solution to the entire seventh problem of Hilbert. Within six weeks, Schneider found another independent solution. In 1966, A. Baker established the generalization of the Gelfond-Schneider theorem. He proved that any non-vanishing linear combination of logarithms of algebraic numbers with algebraic coefficients is transcendental. This study aims to examine the concept and development of transcendental numbers and to present students with its open problems promoting a research on it any further.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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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.

• The Mathematical Education
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• v.14 no.2
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• pp.17-22
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• 1976

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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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.

• Korean Journal of Cognitive Science
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• v.29 no.2
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• pp.105-120
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• 2018

Current neuroscience views the mind-body problem from the monistic perspective which claims that the human mind is the result of brain activity and that the mind shuts down when the brain does. However, a considerable number of lay people still believe in the existence of the soul and the afterlife, concepts that are hard to explain from the monistic perspective. This study examines whether lay people think that the mind of the dead is capable of exceeding the physical constraints if they believe that such mind exists. After reading one of three vignettes which describes the state of the protagonist as alive, dead, or brain dead, the participants evaluated the protagonist's general mental capacity and transcendental ability to obtain new information. The participants rated that the dead protagonist had more 'transcendental ability to obtain new information' than the alive one if they evaluated high general mental capacity to the protagonist. In addition, unlike the alive condition, in the dead and the brain dead condition, there was a correlation between the general mind capacity rating and the transcendental ability rating. The results suggest that lay people expect the mind of the alive and the dead to be different, as they believe the latter's general mind capacity connotes transcendental ability. We also found that the participants' religiosity affected their beliefs about the transcendental ability of dead person.

• Wind and Structures
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• v.8 no.2
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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.

• Journal of architectural history
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• v.22 no.3
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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.