• Title/Summary/Keyword: Complex Number

### RADII PROBLEMS OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS WITH FIXED SECOND COEFFICIENTS

• PORWAL, SAURABH;BULUT, SERAP
• Honam Mathematical Journal
• /
• v.37 no.3
• /
• pp.317-323
• /
• 2015
• The purpose of the present paper is to study certain radii problems for the function $$f(z)=${\frac{z^{1-{\gamma}}}{{\gamma}+{\beta}}}$z^{\gamma}[D^nF(z)]^{\beta}$^{\prime}$^{1/{\beta}}$$, where ${\beta}$ is a positive real number, ${\gamma}$ is a complex number such that ${\gamma}+{\beta}{\neq}0$ and the function F(z) varies various subclasses of analytic functions with fixed second coefficients. Relevant connections of the results presented herewith various well-known results are briefly indicated.

### A CHARACTERIZATION OF LOCAL RESOLVENT SETS

• Han Hyuk;Yoo Jong-Kwang
• Communications of the Korean Mathematical Society
• /
• v.21 no.2
• /
• pp.253-259
• /
• 2006
• Let T be a bounded linear operator on a Banach space X. And let ${{\rho}T}(X)$ be the local resolvent set of T at $x\;{\in}\;X$. Then we prove that a complex number ${\lambda}$ belongs to ${{\rho}T}(X)$ if and only if there is a sequence $\{x_{n}\}$ in X such that $x_n\;=\;(T - {\lambda})x_{n+1}$ for n = 0, 1, 2,..., $x_0$ = x and $\{{\parallel}x_n{\parallel}^{\frac{1}{n}}\}$ is bounded.

### Effects of Hydrocortisone on Cardiac Endothelial Cells in Vitro (배양중 심장내피세포에 미치는 Hydrocortisone 의 영향)

• 정태은
• Journal of Chest Surgery
• /
• v.22 no.1
• /
• pp.16-24
• /
• 1989
• To investigate the effects of hydrocortisone on new-born rat cardiac endothelial cells in culture, the endothelial cells were isolated by means of enzyme-cocktail method. The cells were cultivated in Lees modified Dulbeco\ulcorner medium and 10[M or 10[M of hydrocortisone was added to the medium. The cells were harvested or coverglass and processed for thiamin pyrophosphatase reaction and Feulgen reaction. The enzymatic activities of Golgi complex, number of cells and number of large nucleated[more than tetraploid] cells were counted and discussed for their significance. The results were summarized as follows; 1. Hydrocortisone seemed to accelerate the rate of recovery of cardiac endothelial cells from isolation damage. 2. Endothelial cells treated with hydrocortisone revealed strong positive reaction to thiamine pyrophosphatase in early culture and 10 M group had stronger reaction than that of 10 AM group 3. Hydrocortisone had inhibiting effects on endothelial proliferation and the higher the concentration of the reagent was the stronger effects. 4. Hydrocortisone inhibited the appearance of large nucleate cells in endothelial cell population. 5. Hydrocortisone seemed to suppress the nuclear DNA synthesis.

### BLASCHKE PRODUCTS AND RATIONAL FUNCTIONS WITH SIEGEL DISKS

• Katagata, Koh
• Journal of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.151-170
• /
• 2009
• Let m be a positive integer. We show that for any given real number ${\alpha}\;{\in}\;[0,\;1]$ and complex number $\mu$ with $|\mu|{\leq}1$ which satisfy $e^{2{\pi}i{\alpha}}{\mu}^m\;{\neq}\;1$, there exists a Blaschke product B of degree 2m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity such that the restriction of the Blaschke product B on the unit circle is a critical circle map with rotation number $\alpha$. Moreover if the given real number $\alpha$ is irrational of bounded type, then a modified Blaschke product of B is quasiconformally conjugate to some rational function of degree m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity and a Siegel disk whose boundary is a quasicircle containing its critical point.

### CERTAIN DIFFERENCE POLYNOMIALS AND SHARED VALUES

• Li, Xiao-Min;Yu, Hui
• Bulletin of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1529-1561
• /
• 2018
• Let f and g be nonconstant meromorphic (entire, respectively) functions in the complex plane such that f and g are of finite order, let a and b be nonzero complex numbers and let n be a positive integer satisfying $n{\geq}21$ ($n{\geq}12$, respectively). We show that if the difference polynomials $f^n(z)+af(z+{\eta})$ and $g^n(z)+ag(z+{\eta})$ share b CM, and if f and g share 0 and ${\infty}$ CM, where ${\eta}{\neq}0$ is a complex number, then f and g are either equal or at least closely related. The results in this paper are difference analogues of the corresponding results from.

### The Role of Principle of Continuity in the Development of Mathematical Knowledge (수학적 지식의 발달에서 연속성 원리의 역할)

• Lee, Dong Hwan
• Journal for History of Mathematics
• /
• v.27 no.1
• /
• pp.67-79
• /
• 2014
• When imaginary numbers were first encountered in the 16th century, mathematicians were able to calculate the imaginary numbers the same as they are today. However, it required 200 years to mathematically acknowledge the existence of imaginary numbers. The new mathematical situation that arose with a development in mathematics required a harmony of real numbers and imaginary numbers. As a result, the concept of complex number became clear. A history behind the development of complex numbers involved a process of determining a comprehensive perspective that ties real numbers and imaginary numbers in a single category, complex numbers. This came after a resolution of conflict between real numbers and imaginary numbers. This study identified the new perspective and way of mathematical thinking emerging from resolving the conflicts. Also educational implications of the analysis were discussed.

### THE FLAT EXTENSION OF NONSINGULAR EMBRY MOMENT MATRICES E(3)

• Li, Chunji;Liang, Hongkai
• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.137-149
• /
• 2020
• Let γ(n) ≡ {γij} (0 ≤ i+j ≤ 2n, |i-j| ≤ n) be a sequence in the complex number set ℂ and let E (n) be the Embry truncated moment matrices corresponding from γ(n). For an odd number n, it is known that γ(n) has a rank E (n)-atomic representing measure if and only if E(n) ≥ 0 and E(n) admits a flat extension E(n + 1). In this paper we suggest a related problem: if E(n) is positive and nonsingular, does E(n) have a flat extension E(n + 1)? and give a negative answer in the case of E(3). And we obtain some necessary conditions for positive and nonsingular matrix E (3), and also its sufficient conditions.

### MEROMORPHIC FUNCTIONS SHARING A NONZERO POLYNOMIAL CM

• Li, Xiao-Min;Gao, Ling
• Bulletin of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.319-339
• /
• 2010
• In this paper, we prove that if $f^nf'\;-\;P$ and $g^ng'\;-\;P$ share 0 CM, where f and g are two distinct transcendental meromorphic functions, $n\;{\geq}\;11$ is a positive integer, and P is a nonzero polynomial such that its degree ${\gamma}p\;{\leq}\;11$, then either $f\;=\;c_1e^{cQ}$ and $g\;=\;c_2e^{-cQ}$, where $c_1$, $c_2$ and c are three nonzero complex numbers satisfying $(c_1c_2)^{n+1}c^2\;=\;-1$, Q is a polynomial such that $Q\;=\;\int_o^z\;P(\eta)d{\eta}$, or f = tg for a complex number t such that $t^{n+1}\;=\;1$. The results in this paper improve those given by M. L. Fang and H. L. Qiu, C. C. Yang and X. H. Hua, and other authors.

### Parameterized Soft IP Design of Complex-number Multiplier Core (복소수 승산기 코어의 파라미터화된 소프트 IP 설계)

• 양대성;이승기;신경욱
• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.26 no.10B
• /
• pp.1482-1490
• /
• 2001
• 디지털 통신 시스템 및 신호처리 회로의 핵심 연산블록으로 사용될 수 있는 복소수 승산기 코어의 파라미터화된 소프트 IP (Intellectual Property)를 설계하였다. 승산기는 응용분야에 따라 요구되는 비트 수가 매우 다양하므로, 승산기 코어 IP는 비트 수를 파라미터화하여 설계하는 것이 필요하다. 본 논문에서는 복소수 승산기의 비트 수를 파라미터화 함으로써 사용자의 필요에 따라 승수와 피승수를 8-b∼24-b 범위에서 2-b 단위로 선택하여 사용할 수 있도록 하였으며, GUI 환경의 코어 생성기 PCMUL_GEN는 지정된 비트 크기를 갖는 복소수 승산기의 VHDL 모델을 생성한다. 복소수 승산기 코어 IP는 redundant binary (RB) 수치계와 본 논문에서 제안하는 새로운 radix-4 Booth 인코딩/디코딩 회로를 적용하여 설계되었으며, 이를 통해 기존의 방식보다 단순화된 내부 구조와 고속/저전력 특성을 갖는다. 설계된 IP는 Xilinx FPGA로 구현하여 기능을 검증하였다.

### First Order Differential Subordinations and Starlikeness of Analytic Maps in the Unit Disc

• Singh, Sukhjit;Gupta, Sushma
• Kyungpook Mathematical Journal
• /
• v.45 no.3
• /
• pp.395-404
• /
• 2005
• Let α be a complex number with 𝕽α > 0. Let the functions f and g be analytic in the unit disc E = {z : |z| < 1} and normalized by the conditions f(0) = g(0) = 0, f'(0) = g'(0) = 1. In the present article, we study the differential subordinations of the forms $${\alpha}{\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}+{\frac{zf^{\prime}(z)}{f(z)}}{\prec}{\alpha}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}}+{\frac{zg^{\prime}(z)}{g(z)}},\;z{\in}E,$$ and $${\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}{\prec}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}},\;z{\in}E.$$ As consequences, we obtain a number of sufficient conditions for star likeness of analytic maps in the unit disc. Here, the symbol ' ${\prec}$ ' stands for subordination