• 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.

• 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.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제7권3호
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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.

• 영어영문학
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• 제58권6호
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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.

• 대한수학회보
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• 제50권1호
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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 $k{\rightarrow}{\infty}$.

• 충청수학회지
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• 제23권4호
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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.

• 대한수학회보
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• 제57권4호
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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.

• 대한수학회보
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• 제48권4호
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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.

• 대한수학회보
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• 제38권2호
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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.

• 혜화의학회지
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• 제13권1호
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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.