• 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.

• 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.

• Research in Mathematical Education
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• v.7 no.3
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• pp.191-209
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• 2003

In this paper, we present a new environment of learning and teaching of trigonometric, exponential and logarithmic functions, the most difficult parts for students to learn among functions, through sound and music, students like the most. First, by using sound and music, we try to arouse student's interest. Second, we let students see and hear properties of transcendental functions so that students can understand and remember them easily. Finally we encourage students to compose their favorite song using transcendental functions so that they can experience the practicality of transcendental functions.

• Journal of English Language & Literature
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• v.58 no.6
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• pp.1193-1213
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• 2012

This essay "Twain's Contestation of Emersonian Transcendental Manhood in Huckleberry Finn" explores how Mark Twain's Adventures of Huckleberry Finn (1884) manifests his postwar contestation of Ralph Waldo Emerson's transcendental manhood that endorses the dogmatic, egocentric, and decorporealized position of the Cartesian subject, who believes his being's unity, elevation, and centrality through his fantasy of possessing direct access to divine truth. The connection between Emerson and Twain is based not on Emerson's influence on Twain but on their common interest in American landscape as a site for the redefinition of manhood and masculinity. I examine different types of manhood in their association with nature in Huckleberry Finn by comparing them with the two fundamental concepts of Emerson's philosophy: "a true man" in "Self-Reliance" (1841) and transparent eyeball vision in Nature (1836). Twain's use of Huck's ambivalent position-his centrality as a protagonist in the novel in spite of his marginality in society-renegotiates Emerson's valorization of nonconformity, wholeness, and nonchalance as the characteristics of both boyhood and "a true man," Emerson's term for the ideal individual in "Self-Reliance." I also read Twain's satire of two different types of masculine characters-Bob and the Child of Calamity, boatmen of the Southern frontier, and Colonel Grangerford, patriarch of a Southern aristocratic family-as Twain's denouncement of the antebellum desire for transcendental vision, which Emerson crystalizes into his notion of transparent eyeball in Nature.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.343-351
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• 2013

In this paper, the dynamics on a transcendental entire semigroup G is investigated. We show the possible values of any limit function of G in strictly wandering domains and Fatou components, respectively. Moreover, if G is of class $\mathfrak{B}$, for any $z$ in a Fatou domain, there does not exist a sequence $\{g_k\}$ of G such that $g_k(z){\rightarrow}{\infty}$ as $k{\rightarrow}{\infty}$.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.773-784
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• 2010

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.991-1002
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• 2020

We show that when n > m, the following delay differential equation fⁿ(z)f'(z) + p(z)(f(z + c) - f(z))^m = r(z)e^q(z) of rational coefficients p, r doesn't admit any transcendental entire solutions f(z) of finite order. Furthermore, we study the conditions of α₁, α₂ that ensure existence of transcendental meromorphic solutions of the equation fⁿ(z) + f^n-2(z)f'(z) + P_d(z, f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z). These results have improved some known theorems obtained most recently by other authors.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.713-724
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• 2011

We study the dynamics of transcendental entire functions with Siegel disks whose singular values are just two points. One of the two singular values is not only a superattracting fixed point with multiplicity more than two but also an asymptotic value. Another one is a critical value with free dynamics under iterations. We prove that if the multiplicity of the superattracting fixed point is large enough, then the restriction of the transcendental entire function near the Siegel point is a quadratic-like map. Therefore the Siegel disk and its boundary correspond to those of some quadratic polynomial at the level of quasiconformality. As its applications, the logarithmic lift of the above transcendental entire function has a wandering domain whose shape looks like a Siegel disk of a quadratic polynomial.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.369-378
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• 2001

In this paper, we obtain the following results: Let f be a transcendental entire function with log M(r,f)=$O(log r)^\beta (e^{log r}^\alpha)\; (0\leq\alpha<1,\beta>1$). Then every component of N(f) is bounded. This result generalizes the result of Baker.

• Journal of Haehwa Medicine
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• v.13 no.1
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• pp.97-105
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• 2004

In the Oriental medicine, it was recognized that mind and body have a inseparable relationship. The goal of this study was to examine the body(肉體) and self-be1ief(自己信念) and methods of self-therapy(自己治癒) in transcendental meditation(冥想療法). We will furnish the information of the basic concepts and methods in transcendental meditation. The findings are as follows: 1. The thing that you have in mind does not stay in abstract idea but materializes and operates the body. 2. When you have disease implies that you have negative belief, thought and mind. 3. When you can observe the things happening in your body and mind- just like meditation- you can have positive changes. 4. When you change the negative beliefs into positive ones on body, you feel gratitude and the disease will be cured.