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

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.675-683
• /
• 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.

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

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

• Journal of the Chungcheong Mathematical Society
• /
• v.15 no.2
• /
• pp.47-56
• /
• 2003

This note is concerned with some properties of fixed points and periodic points. First, we have constructed a generalized continuous function to give a proof for the fact that, as the reverse of the Sharkovsky theorem[16], for a given positive integer n, there exists a continuous function with a period-n point but no period-m points wherem is a predecessor of n in the Sharkovsky ordering. Also we show that the composition of two transcendental meromorphic functions, one of which has at least three poles, has infinitely many fixed points.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.795-814
• /
• 2021

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: fⁿ + P(f) = R(z)e^α(z) and fⁿ + P_*(f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z) in the complex plane, where P(f) and P_*(f) are differential polynomials in f of degree n - 1 with coefficients being small functions and rational functions respectively, R is a non-vanishing small function of f, α is a nonconstant entire function, p₁, p₂ are non-vanishing rational functions, and α₁, α₂ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when p₁, p₂ are nonzero constants, and deg α₁ = deg α₂ = 1. Our results are improvements and complements of Liao ([9]), and Rong-Xu ([11]), etc., which partially answer a question proposed by Li ([7]).

• Journal of applied mathematics & informatics
• /
• v.41 no.4
• /
• pp.765-780
• /
• 2023

In this paper, we explore the uniqueness property between the transcendental meromorphic functions and differential polynomial. With the notion of weighted sharing, we generalised the many previous results on uniqueness property. Here we discussed the uniqueness of [P(f)(αf^m + β)^s]^(k) - η(z) and [P(g)(αg^m + β)^s]^(k) - η(z). Meanwhile, we generalised the result of Harina P. waghamore and Rajeshwari S[1].

• Proceedings of the IEEK Conference
• /
• 2005.11a
• /
• pp.715-718
• /
• 2005

Mobile devices is getting to include more functions according to the demand of digital convergence. Applications based on 3D graphic calculation such as 3D games and navigation are one of the functions. 3D graphic calculation requires heavy calculation. Therefore, we need dedicated 3D graphic hardware unit with high performance. 3D graphic calculation needs a lot of complicated floating-point arithmetic operation. However, most of current mobile 3D graphics processors do not have efficient architecture for mobile devices because they are based on those for conventional computer systems. In this paper, we propose arithmetic units for special functions of lighting operation of 3D graphics. Transcendental arithmetic units are designed using approximation of logarithm function. Special function units for lighting operation such as reciprocal, square root, reciprocal of square root, and power can be obtained. The proposed arithmetic unit has lower error rate and smaller silicon area than conventional arithmetic architecture.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.573-583
• /
• 2005

For a certain set G in the complex plane, we construct a transcendental entire function f whose translated family ${f(2^{n}z)}$ is normal only at z in G and establish the relation between the normal family and the Julia direction of f(z).

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1523-1534
• /
• 2008

We investigate the uniqueness of transcendental analytic functions that share three values DM in one angular domain instead of the whole complex plane.